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Satkin, Scott. "Data-Driven Geometric Scene Understanding." Research Showcase @ CMU, 2013. http://repository.cmu.edu/dissertations/280.
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In this thesis, we describe a data-driven approach to leverage repositories of 3D models for scene understanding. Our ability to relate what we see in an image to a large collection of 3D models allows us to transfer information from these models, creating a rich understanding of the scene. We develop a framework for auto-calibrating a camera, rendering 3D models from the viewpoint an image was taken, and computing a similarity measure between each 3D model and an input image. We demonstrate this data-driven approach in the context of geometry estimation and show the ability to find the identities, poses and styles of objects in a scene.
We begin by presenting a proof-of-concept algorithm for matching 3D models with input images. Next, we present a series of extensions to this baseline approach. Our goals here are three-fold. First, we aim to produce more accurate reconstructions of a scene by determining both the exact style and size of objects as well as precisely localizing their positions. In addition, we aim to increase the robustness of our scene-matching approach by incorporating new features and expanding our search space to include many viewpoint hypotheses. Lastly, we address the computational challenges of our approach by presenting algorithms for more efficiently exploring the space of 3D scene hypotheses, without sacrificing the quality of results.
We conclude by presenting various applications of our geometric scene understanding approach. We start by demonstrating the effectiveness of our algorithm for traditional applications such as object detection and segmentation. In addition, we present two novel applications incorporating our geometry estimates: affordance estimation and geometryaware object insertion for photorealistic rendering.
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Diaz, Garcia Raul. "Strong geometric context for scene understanding." Thesis, University of California, Irvine, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10195873.
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Humans are able to recognize objects in a scene almost effortlessly. Our visual system can easily handle ambiguous settings, like partial occlusions or large variations in viewpoint. One hypothesis that explains this ability is that we process the scene as a global instance. Using global contextual reasoning (e.g., a car sits on a road, but not on a building facade) can constrain interpretations of objects to plausible, coherent precepts. This type of reasoning has been explored in Computer Vision using weak 2D context, mostly extracted from monocular cues. In this thesis, we explore the benefits of strong 3D context extracted from multiple-view geometry. We demonstrate strong ties between geometric reasoning and object recognition, effectively bridging the gap between them to improve scene understanding.
In the first part of this thesis, we describe the basic principles of structure from motion, which provide strong and reliable geometric models that can be used for contextual scene understanding. We present a novel algorithm for camera localization that leverages search space partitioning to allow a more aggressive filtering of potential correspondences. We exploit image covisibility using a coarse-to-fine, prioritized search approach that can recognize scene landmarks rapidly. This system achieves state of the art results in large-scale camera localization, especially in difficult scenes with frequently repeated structures.
In the second part of this thesis, we study how to exploit these strong geometric models and localized cameras to improve recognition. We introduce an unsupervised training pipeline to generate scene-specific object detectors. These classifiers outperform state of the art and can be used when the rough camera location is known. When precise camera pose is available, we can inject additional geometric cues into novel re-scoring framework to further improve detection. We demonstrate the utility of background scene models for false positive pruning, akin to video-surveillance background subtraction strategies. Finally, we observe that the increasing availability of mapping data stored in Geographic Information Systems (GIS) provides strong geo-semantic information that can be used when cameras are located in world coordinates. We propose a novel contextual reasoning pipeline that uses lifted 2D GIS models to quickly retrieve precise geo-semantic priors. We use these cues to to improve object detection and image semantic segmentation, providing a successful trade-off of false positives that boosts average precision over baseline detection models.
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Ranjan, Anurag [Verfasser]. "Towards Geometric Understanding of Motion / Anurag Ranjan." Tübingen : Universitätsbibliothek Tübingen, 2020. http://d-nb.info/1214639763/34.
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Pan, Jiyan. "Coherent Scene Understanding With 3D Geometric Reasoning." Research Showcase @ CMU, 2011. http://repository.cmu.edu/dissertations/375.
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When looking at a single 2D image of a scene, humans could effortlessly understand the 3D world behind the scene even though stereo and motion cues are not available. Due to this remarkable human capability, one of the ultimate goals of computer vision is to enable machines to automatically infer the 3D structure of a scene given a single 2D image. This dissertation proposes methods that produce a geometrically and semantically coherent 3D interpretation of urban scenes from a single image, and shows the benefits of reasoning in 3D when analyzing 2D images. In this dissertation, we model an urban scene using three types of elements. The first type is global geometries such as ground plane and gravity direction. The second type is objects such as cars and pedestrians that have definitive shapes and extents. The third type is vertical surfaces such as building facades that do not have definitive shapes and extents. Such a modeling allows for a richer characterization of an urban scene than existing works. To tackle the inherent ambiguity involved in recovering the 3D structure from a single 2D image, we systematically identify geometric constraints among the three types of elements in our model, and encode such constraints in a Conditional Random Field (CRF). For objects, we consider both their global geometric compatibility with ground plane and gravity direction, and their local geometric compatibility between adjacent objects. For building facades, we decompose them into a set of continuously-oriented planes mutually related by 3D geometric relationships, and constrained by nearby objects in 3D. We also propose a generalized RANSAC algorithm to make the inference of the model tractable. We show that performing 3D geometric reasoning using our model benefits individual tasks such as object detection, viewpoint estimation, and facade layout recovery. In addition, it yields a more informative interpretation of the 3D scene behind the image.
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Kacem, Anis. "Novel geometric tools for human behavior understanding." Thesis, Lille 1, 2018. http://www.theses.fr/2018LIL1I076/document.
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Récemment, le développement de systèmes intelligents dédiés pour la compréhension du comportement humain est devenu un axe de recherche très important. En effet, il est très important de comprendre le comportement humain pour rendre les machines capables d'aider et interagir avec les humains. Pour cela, plusieurs approches de l'état de l'art commencent par détecter automatiquement un ensemble de points 2D ou 3D, appelés marqueurs, sur le corps et/ou le visage humain à partir de données visuelles. L’analyse des séquences temporelles de ces marqueurs pose plusieurs défis dus aux erreurs de suivi et aux variabilités temporelles et de pose. Dans cette thèse, nous proposons deux nouvelles représentations spatio-temporelles avec des outils de calcul appropriés pour la compréhension du comportement humain. La première consiste à représenter une séquence temporelle de marqueurs par une trajectoire de matrices de Gram. Les matrices de Gram sont des matrices semi-définies positives de rang fixe et vivent dans un espace non-linéaire dans lequel les outils d’apprentissage automatique conventionnels ne peuvent pas être appliqués directement. Nous évaluons l’efficacité de notre approche dans plusieurs applications, impliquant des marqueurs 2D et 3D de visages et de corps humain, tels que la reconnaissance des émotions à partir des expressions faciales la reconnaissance d’actions et des émotions à partir des données de profondeur 3D. La deuxième représentation proposée dans cette thèse est basée sur les coordonnées barycentriques des marqueurs de visages 2D. Cette représentation permet d’utiliser les outils de calcul et d’apprentissage automatique tels que les techniques d’apprentissage de métrique. Les résultats obtenus en reconnaissance des expressions faciales et en mesure automatique de la sévérité de la dépression à partir du visage montrent tout l’intérêt de la représentation barycentrique combinée à des techniques d’apprentissage automatique. Les résultats obtenus avec les deux méthodes proposées sur des bases de données réelles montrent la compétitivité de nos approches avec les méthodes récentes de l’état de l’artDeveloping intelligent systems dedicated to human behavior understanding has been a very hot research topic in the few recent decades. Indeed, it is crucial to understand the human behavior in order to make machines able to interact with, assist, and help humans in their daily life.. Recent breakthroughs in computer vision and machine learning have made this possible. For instance, human-related computer vision problems can be approached by first detecting and tracking 2D or 3D landmark points from visual data. Two relevant examples of this are given by the facial landmarks detected on the human face and the skeletons tracked along videos of human bodies. These techniques generate temporal sequences of landmark configurations, which exhibit several distortions in their analysis, especially in uncontrolled environments, due to view variations, inaccurate detection and tracking, missing data, etc. In this thesis, we propose two novel space-time representations of human landmark sequences along with suitable computational tools for human behavior understanding. Firstly, we propose a representation based on trajectories of Gram matrices of human landmarks. Gram matrices are positive semi-definite matrices of fixed rank and lie on a nonlinear manifold where standard computational and machine learning techniques could not be applied in a straightforward way. To overcome this issue, we make use of some notions of the Riemannian geometry and derive suitable computational tools for analyzing Gram trajectories. We evaluate the proposed approach in several human related applications involving 2D and 3D landmarks of human faces and bodies such us emotion recognition from facial expression and body movements and also action recognition from skeletons. Secondly, we propose another representation based on the barycentric coordinates of 2D facial landmarks. While being related to the Gram trajectory representation and robust to view variations, the barycentric representation allows to directly work with standard computational tools. The evaluation of this second approach is conducted on two face analysis tasks namely, facial expression recognition and depression severity level assessment. The obtained results with the two proposed approaches on real benchmarks are competitive with respect to recent state-of-the-art methods
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Flint, Alexander John. "Geometric context from single and multiple views." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:f6c11e50-c059-4254-9dfc-5cbd2ee8147f.
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In order for computers to interact with and understand the visual world, they must be equipped with reasoning systems that include high–level quantities such as objects, actions, and scenes. This thesis is concerned with extracting such representations of the world from visual input. The first part of this thesis describes an approach to scene understanding in which texture characteristics of the visual world are used to infer scene categories. We show that in the context of a moving camera, it is common to observe images containing very few individually salient image regions, yet overall texture structure often allows our system to derive powerful contextual cues about the environment. Our approach builds on ideas from texture recognition, and we show that our algorithm out–performs the well–known Gist descriptor on several classification tasks. In the second part of this thesis we we are interested in scene understanding in the context of multiple calibrated views of a scene, as might be obtained from a Structure–from–Motion or Simultaneous Localization and Mapping (SLAM) system. Though such systems are capable of localizing the camera robustly and efficiently, the maps produced are typically sparse point-clouds that are difficult to interpret and of little use for higher–level reasoning tasks such as scene understanding or human-machine interaction. In this thesis we begin to address this deficiency, presenting progress towards modeling scenes using semantically meaningful primitives such as floor, wall, and ceiling planes. To this end we adopt the indoor Manhattan representation, which was recently proposed for single–view reconstruction. This thesis presents the first in–depth description and analysis of this model in the literature. We describe a probabilistic model relating photometric features, stereo photo–consistencies, and 3D point clouds to Manhattan scene structure in a Bayesian framework. We then present a fast dynamic programming algorithm that solves exact MAP inference in this model in time linear in image size. We show detailed comparisons with the state–of–the art in both the single– and multiple–view contexts. Finally, we present a framework for learning within the indoor Manhattan hypothesis class. Our system is capable of extrapolating from labelled training examples to predict scene structure for unseen images. We cast learning as a structured prediction problem and show how to optimize with respect to two realistic loss functions. We present experiments in which we learn to recover scene structure from both single and multiple views — from the perspective of our learning algorithm these problems differ only by a change of feature space. This work constitutes one of the most complicated output spaces (in terms of internal constraints) yet considered within a structure prediction framework.
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Osta, Iman M. "From Physical Model To Proof For Understanding Via DGS: Interplay Among Environments." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-80806.
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The widespread use of Dynamic Geometry Software (DGS) is raising many interesting questions and discussions as to the necessity, usefulness and meaning of proof in school mathematics. With these questions in mind, a didactical sequence on the topic “Conics” was developed in a teacher education course tailored for pre-service secondary math methods course. The idea of the didactical sequence is to introduce “Conics” using a concrete manipulative approach (paper folding) then an explorative DGS-based construction activity embedding the need for a proof. For that purpose, the DGS software serves as an intermediary tool, used to bridge the gap between the
physical model and the formal symbolic system of proof. The paper will present an analysis of participants’ geometric thinking strategies, featuring proof as an embedded process in geometric construction situations.
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Osta, Iman M. "From Physical Model To Proof For Understanding Via DGS:Interplay Among Environments." Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 464 - 468, 2012. https://slub.qucosa.de/id/qucosa%3A1798.
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The widespread use of Dynamic Geometry Software (DGS) is raising many interesting questions and discussions as to the necessity, usefulness and meaning of proof in school mathematics. With these questions in mind, a didactical sequence on the topic “Conics” was developed in a teacher education course tailored for pre-service secondary math methods course. The idea of the didactical sequence is to introduce “Conics” using a concrete manipulative approach (paper folding) then an explorative DGS-based construction activity embedding the need for a proof. For that purpose, the DGS software serves as an intermediary tool, used to bridge the gap between the
physical model and the formal symbolic system of proof. The paper will present an analysis of participants’ geometric thinking strategies, featuring proof as an embedded process in geometric construction situations.
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Andrews, Brock Taylor. "Student understanding of sight distance in geometric design a beginning line of inquiry to characterize student understanding of transportation engineering /." Pullman, Wash. : Washington State University, 2009. http://www.dissertations.wsu.edu/Thesis/Fall2009/B_ANDREWS_111909.pdf.
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Thesis (M.S. in civil engineering)--Washington State University, December 2009.Title from PDF title page (viewed on Jan. 15, 2010). "Department of Civil and Environmental Engineering." Includes bibliographical references (p. 30-31).
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Jacobus, Enoch S. A. "A NEW GEOMETRIC MODEL AND METHODOLOGY FOR UNDERSTANDING PARSIMONIOUS SEVENTH-SONORITY PITCH-CLASS SPACE." UKnowledge, 2012. http://uknowledge.uky.edu/music_etds/10.
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Parsimonious voice leading is a term, first used by Richard Cohn, to describe non-diatonic motion among triads that will preserve as many common tones as possible, while limiting the distance traveled by the voice that does move to a tone or, better yet, a semitone. Some scholars have applied these principles to seventh chords, laying the groundwork for this study, which strives toward a reasonably comprehensive, usable model for musical analysis.
Rather than emphasizing mathematical proofs, as a number of approaches have done, this study relies on two- and three-dimensional geometric visualizations and spatial analogies to describe pitch-class and harmonic relationships. These geometric realizations are based on the organization of the neo-Riemannian Tonnetz, but they expand and apply the organizational principles of the Tonnetz to seventh sonorities. It allows for the descriptive “mapping” or prescriptive “navigation” of harmonic paths through a defined space.
The viability of the theoretical model is examined in analyses of passages from the repertoire of Frédéric Chopin. These passages exhibit a harmonic syntax that is often difficult to analyze as anything other than “tonally unstable” or “transitional.” This study seeks to analyze these passages in terms of what they are, rather than what they are not.
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Genz, Rebekah Loraine. "Determining High School Geometry Students' Geometric Understanding Using van Hiele Levels: Is There a Difference Between Standards-based Curriculum Students and NonStandards-based Curriculum Students?" Diss., CLICK HERE for online access, 2006. http://contentdm.lib.byu.edu/ETD/image/etd1373.pdf.
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Arthur, Christopher. "Understanding Ancient Math Through Kepler: A Few Geometric Ideas from The Harmony of the World." Thesis, University of North Texas, 2002. https://digital.library.unt.edu/ark:/67531/metadc3269/.
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Euclid's geometry is well-known for its theorems concerning triangles and circles. Less popular are the contents of the tenth book, in which geometry is a means to study quantity in general. Commensurability and rational quantities are first principles, and from them are derived at least eight species of irrationals. A recently republished work by Johannes Kepler contains examples using polygons to illustrate these species. In addition, figures having these quantities in their construction form solid shapes (polyhedra) having origins though Platonic philosophy and Archimedean works. Kepler gives two additional polyhedra, and a simple means for constructing the “divine” proportion is given.
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Beck, Joseph A. "Fundamental Understanding of Blisk Analytical Response." Wright State University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=wright1367848915.
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Vorpe, Katherine. "Understanding a Population Model for Mussel-Algae Interaction." Wittenberg University Honors Theses / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=wuhonors1617970789779916.
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Petrov, Aleksandar. "Understanding the relationships between aesthetic properties of shapes and geometric quantities of free-form curves and surfaces using Machine Learning Techniques." Thesis, Paris, ENSAM, 2016. http://www.theses.fr/2016ENAM0007/document.
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Aujourd’hui, sur le marché, on peut trouver une vaste gamme de produits différents ou des formes variées d’un même produit et ce grand assortiment fatigue les clients. Il est clair que la décision des clients d’acheter un produit dépend de l'aspect esthétique de la forme du produit et de l’affection émotionnelle. Par conséquent, il est très important de comprendre les propriétés esthétiques et de les adopter dans la conception du produit, dès le début. L'objectif de cette thèse est de proposer un cadre générique pour la cartographie des propriétés esthétiques des formes gauches en 3D en façon d'être en mesure d’extraire des règles de classification esthétiques et des propriétés géométriques associées. L'élément clé du cadre proposé est l'application des méthodologies de l’Exploration des données (Data Mining) et des Techniques d’apprentissage automatiques (Machine Learning Techniques) dans la cartographie des propriétés esthétiques des formes. L'application du cadre est d'étudier s’il y a une opinion commune pour la planéité perçu de la part des concepteurs non-professionnels. Le but de ce cadre n'est pas seulement d’établir une structure pour repérer des propriétés esthétiques des formes gauches, mais aussi pour être utilisé comme un chemin guidé pour l’identification d’une cartographie entre les sémantiques et les formes gauches différentes. L'objectif à long terme de ce travail est de définir une méthodologie pour intégrer efficacement le concept de l’Ingénierie affective (c.à.d. Affective Engineering) dans le design industrielToday on the market we can find a large variety of different products and differentshapes of the same product and this great choice overwhelms the customers. It is evident that the aesthetic appearance of the product shape and its emotional affection will lead the customers to the decision for buying the product. Therefore, it is very important to understand the aesthetic proper-ties and to adopt them in the early product design phases. The objective of this thesis is to propose a generic framework for mapping aesthetic properties to 3D freeform shapes, so as to be able to extract aesthetic classification rules and associated geometric properties. The key element of the proposed framework is the application of the Data Mining (DM) methodology and Machine Learning Techniques (MLTs) in the mapping of aesthetic properties to the shapes. The application of the framework is to investigate whether there is a common judgment for the flatness perceived from non-professional designers. The aim of the framework is not only to establish a structure for mapping aesthetic properties to free-form shapes, but also to be used as a guided path for identifying a mapping between different semantics and free-form shapes. The long-term objective of this work is to define a methodology to efficiently integrate the concept of Affective Engineering in the Industrial Designing
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Afifi, Ahmed J. M. [Verfasser], Olaf [Akademischer Betreuer] Hellwich, Olaf [Gutachter] Hellwich, Hamid [Gutachter] Laga, and Klaus [Gutachter] Obermayer. "Geometric and semantic understanding of objects from a single image using deep learning / Ahmed J. M. Afifi ; Gutachter: Olaf Hellwich, Hamid Laga, Klaus Obermayer ; Betreuer: Olaf Hellwich." Berlin : Technische Universität Berlin, 2021. http://d-nb.info/1241183503/34.
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Mwiikeni, Eramus. "An analysis of how geogebra can be used as a visualisation tool by selected teachers to develop conceptual understanding of the properties of geometric shapes in grade 9 learners: a case study in Namibia." Thesis, Rhodes University, 2017. http://hdl.handle.net/10962/6989.
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According to Rosken & Rolka (2006), learning mathematics through visualisations can be a powerful tool to explore mathematical problems and give meaning to mathematical concepts and relationships between them. “Visualisation can reduce the complexity of mathematical problems when dealing with a multitude of information” (p.458). This case study focused on using GeoGebra as a visualisation tool to teach angle properties in Grade 9 geometry. This study set out to analyse how GeoGebra visualisations can be used by selected teachers to teach for conceptual understanding. The research is based on a constructivist view of learning and is oriented within an interpretive paradigm. The methodology used is a qualitative case study. The study was conducted in one school and involved 3 mathematics teachers who were purposefully selected because they showed willingness to use technology in their teaching. I used classroom observations and interviews to collect the data. The study identified a number of factors from the participants that related to using GeoGebra in teaching for conceptual understanding. These include the effective use of dynamic visuals to build on prior knowledge, using multiple representations through image generation and image transformation to make connections and using visuals to justify mathematics ideas. The results from this study indicated that GeoGebra can indeed be used effectively as a teaching tool to teach for conceptual understanding in mathematics.
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Nili, Hamed. "Understanding brain representational geometries." Thesis, University of Cambridge, 2015. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.708933.
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Chi, Wenjun. "MRI image analysis for abdominal and pelvic endometriosis." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:27efaa89-85cd-4f8b-ab67-b786986c42e3.
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Endometriosis is an oestrogen-dependent gynaecological condition defined as the presence of endometrial tissue outside the uterus cavity. The condition is predominantly found in women in their reproductive years, and associated with significant pelvic and abdominal chronic pain and infertility. The disease is believed to affect approximately 33% of women by a recent study. Currently, surgical intervention, often laparoscopic surgery, is the gold standard for diagnosing the disease and it remains an effective and common treatment method for all stages of endometriosis. Magnetic resonance imaging (MRI) of the patient is performed before surgery in order to locate any endometriosis lesions and to determine whether a multidisciplinary surgical team meeting is required. In this dissertation, our goal is to use image processing techniques to aid surgical planning. Specifically, we aim to improve quality of the existing images, and to automatically detect bladder endometriosis lesion in MR images as a form of bladder wall thickening. One of the main problems posed by abdominal MRI is the sparse anisotropic frequency sampling process. As a consequence, the resulting images consist of thick slices and have gaps between those slices. We have devised a method to fuse multi-view MRI consisting of axial/transverse, sagittal and coronal scans, in an attempt to restore an isotropic densely sampled frequency plane of the fused image. In addition, the proposed fusion method is steerable and is able to fuse component images in any orientation. To achieve this, we apply the Riesz transform for image decomposition and reconstruction in the frequency domain, and we propose an adaptive fusion rule to fuse multiple Riesz-components of images in different orientations. The adaptive fusion is parameterised and switches between combining frequency components via the mean and maximum rule, which is effectively a trade-off between smoothing the intrinsically noisy images while retaining the sharp delineation of features. We first validate the method using simulated images, and compare it with another fusion scheme using the discrete wavelet transform. The results show that the proposed method is better in both accuracy and computational time. Improvements of fused clinical images against unfused raw images are also illustrated. For the segmentation of the bladder wall, we investigate the level set approach. While the traditional gradient based feature detection is prone to intensity non-uniformity, we present a novel way to compute phase congruency as a reliable feature representation. In order to avoid the phase wrapping problem with inverse trigonometric functions, we devise a mathematically elegant and efficient way to combine multi-scale image features via geometric algebra. As opposed to the original phase congruency, the proposed method is more robust against noise and hence more suitable for clinical data. To address the practical issues in segmenting the bladder wall, we suggest two coupled level set frameworks to utilise information in two different MRI sequences of the same patients - the T2- and T1-weighted image. The results demonstrate a dramatic decrease in the number of failed segmentations done using a single kind of image. The resulting automated segmentations are finally validated by comparing to manual segmentations done in 2D.
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Clayton, Emanuel. "Pre-Service Teachers’ Understandings of Isometries." The Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1597915853566819.
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Burgess, Steven. "Nietzsche and Heidegger on the Cartesian Atomism of Thought." Scholar Commons, 2013. http://scholarcommons.usf.edu/etd/4448.
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My dissertation has two main parts. In the first half, I draw out an underlying presupposition of Descartes' philosophy: what I term "atomism of thought." Descartes employs a radical procedure of doubt in order to show that the first principle of his philosophy, the cogito, is an unshakeable foundation of knowledge. In the dialogue that follows his dissemination of the Meditations, Descartes reveals that a whole set of concepts and rational principles innate in our minds are never doubted. These fundamental units of thought are indivisible, distinct, and isolated, and enable the possibility of any rational demonstration. Atoms of thought are perfectly individuated because God has created them as such. Likewise, our minds have been fashioned such that we necessarily have a clear and distinct perception every time we alight upon these simple notions.
In the second part of the dissertation, I take up critiques of Descartes' view given by Nietzsche and Heidegger. In the chapter on Nietzsche, I attempt to fill a lacuna in scholarship about Nietzsche's commentary on Descartes. More specifically, I argue that once the foundation of God is displaced, the basis for accepting atomism of thought dissolves. In the final chapter, I analyze Heidegger's critique of Cartesian atomism. I first look at Heidegger's critique of classical truth as correspondence from Being and Time, and show how it is relevant to a critique of atomism. Then I show how the early Heidegger's holistic philosophical framework can provide an alternative that avoids the pitfalls of atomism.
While I limit the scope of my analysis to Descartes' particular formulation, atomism of thought was an influential doctrine throughout modern philosophy. This aspect of Cartesianism has persisted and continues to be a significant theoretical underpinning of many contemporary views. It is my contention that Nietzsche and Heidegger have important contributions to make to this area of thought, and the relative neglect of their work in recent scholarship is a detrimental oversight.
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Cai, Li-Dong. "Scale-based surface understanding using diffusion smoothing." Thesis, University of Edinburgh, 1991. http://hdl.handle.net/1842/6587.
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The research discussed in this thesis is concerned with surface understanding from the viewpoint of recognition-oriented, scale-related processing based on surface curvatures and diffusion smoothing. Four problems below high level visual processing are investigated: 1) 3-dimensional data smoothing using a diffusion process; 2) Behaviour of shape features across multiple scales, 3) Surface segmentation over multiple scales; and 4) Symbolic description of surface features at multiple scales. In this thesis, the noisy data smoothing problem is treated mathematically as a boundary value problem of the diffusion equation instead of the well-known Gaussian convolution, In such a way, it provides a theoretical basis to uniformly interpret the interrelationships amongst diffusion smoothing, Gaussian smoothing, repeated averaging and spline smoothing. It also leads to solving the problem with a numerical scheme of unconditional stability, which efficiently reduces the computational complexity and preserves the signs of curvatures along the surface boundaries. Surface shapes are classified into eight types using the combinations of the signs of the Gaussian curvature K and mean curvature H, both of which change at different scale levels. Behaviour of surface shape features over multiple scale levels is discussed in terms of the stability of large shape features, the creation, remaining and fading of small shape features, the interaction between large and small features and the structure of behaviour of the nested shape features in the KH sign image. It provides a guidance for tracking the movement of shape features from fine to large scales and for setting up a surface shape description accordingly. A smoothed surface is partitioned into a set of regions based on curvature sign homogeneity. Surface segmentation is posed as a problem of approximating a surface up to the degree of Gaussian and mean curvature signs using the depth data alone How to obtain feasible solutions of this under-determined problem is discussed, which includes the surface curvature sign preservation, the reason that a sculptured surface can be segmented with the KH sign image alone and the selection of basis functions of surface fitting for obtaining the KH sign image or for region growing. A symbolic description of the segmented surface is set up at each scale level. It is composed of a dual graph and a geometrical property list for the segmented surface. The graph describes the adjacency and connectivity among different patches as the topological-invariant properties that allow some object's flexibility, whilst the geometrical property list is added to the graph as constraints that reduce uncertainty. With this organisation, a tower-like surface representation is obtained by tracking the movement of significant features of the segmented surface through different scale levels, from which a stable description can be extracted for inexact matching during object recognition.
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Plaza, Floran. "Measuring, modelling and understanding the mechanical behaviour of bagasse." University of Southern Queensland, Faculty of Engineering and Surveying, 2002. http://eprints.usq.edu.au/archive/00001485/.
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In the Australian sugar industry, sugar cane is smashed into a straw like material by hammers before being squeezed between large rollers to extract the sugar juice. The straw like material is initially called prepared cane and then bagasse as it passes through successive roller milling units. The sugar cane materials are highly compressible, have high moisture content, are fibrous, and they resemble some peat soils in both appearance and mechanical behaviour. A promising avenue to improve the performance of milling units for increased throughput and juice extraction, and to reduce costs is by modelling of the crushing process. To achieve this, it is believed necessary that milling models should be able to reproduce measured bagasse behaviour. This investigation sought to measure the mechanical (compression, shear, and volume) behaviour of prepared cane and bagasse, to identify limitations in currently used material models, and to progress towards a material model that can predict bagasse behaviour adequately. Tests were carried out using a modified direct shear test equipment and procedure at most of the large range of pressures occurring in the crushing process. The investigation included an assessment of the performance of the direct shear test for measuring bagasse behaviour. The assessment was carried out using finite element modelling. It was shown that prepared cane and bagasse exhibited critical state behaviour similar to that of soils and the magnitudes of material parameters were determined. The measurements were used to identify desirable features for a bagasse material model. It was shown that currently used material models had major limitations for reproducing bagasse behaviour. A model from the soil mechanics literature was modified and shown to achieve improved reproduction while using magnitudes of material parameters that better reflected the measured values. Finally, a typical three roller mill pressure feeder configuration was modelled. The predictions and limitations were assessed by comparison to measured data from a sugar factory.
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Knight, Kathleen Chesley. "An Investigation into the Change in the Van Hiele Levels of Understanding Geometry of Pre-service Elementary and Secondary Mathematics Teachers." Fogler Library, University of Maine, 2006. http://www.library.umaine.edu/theses/pdf/KnightKC2006.pdf.
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Harvey, William John. "Understanding High-Dimensional Data Using Reeb Graphs." The Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1342614959.
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Saez, Mario Carlos Cortes. "Towards understanding a tower : the design of the Staten Island Ferry Terminal /." Thesis, This resource online, 1995. http://scholar.lib.vt.edu/theses/available/etd-02132009-172714/.
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Kynigos, Polychronis. "From intrinsic to non-intrinsic geometry : a study of children's understandings in Logo-based microworlds." Thesis, University College London (University of London), 1988. http://discovery.ucl.ac.uk/10020179/.
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The aim of the present study was to investigate the potential for children to use the turtle methaphor to develop understandings of intrinsic, euclidean and cartesian geometrical ideas. Four aspects of the problem were investigated. a) the nature of the schema children form when they identify with the turtle in order to change its state on the screen; b) whether it is possible for them to use the schema to gain insights into certain basic geometrical principles of the cartesian geometrical system; c) how they might use the schema to form understandings of euclidean geometry developed inductively from specific experiences; d) the criteria they develop for choosing between intrinsic and euclidean ideas. Ten 11 to 12 year - old children participated in the research, previously having had 40 to 50 hours of experience with Turtle geometry. The research involved three case - studies of pairs of children engaging in cooperative activities, each case - study within a geometrical Logo microworld. The data included hard copies of everything that was said, typed and written. Issues a) and b) were investigated by means of the first case - study which involved three pairs of children and a microworld embedding intrinsic and coordinate ideas. A model of the children's intrinsic schema and a model of the coordinate schema which they formed during the study were devised. The analysis shows that the two schemas remained separate in the children's minds with the exception of a limited number of occasions of context specific links between the two. Issue c) was investigated in the second case - study involving one pair of children and a microworld where the turtle was equipped with distance and turn measuring instruments and a facility to mark positions. The analysis illustrates how a turtle geometric environment of a dynamic mathematical nature was generated by the children, who used their intrinsic schema and predominantly engaged in inductive thinking. The geometrical content available to the children within this environment was extended from intrinsic to both intrinsic and euclidean geometry. Issue d) was investigated by means of the third case - study involving a pair of children and a microworld where the children could choose among circle procedures embedding intrinsic and/or euclidean notions in order to construct figures of circle compositions. The analysis shows that the children employed their turtle schema in using both kinds of notions and did not seem to perceive qualitative differences between them. Their decisions on which type of notion to use were influenced by certain broader aspects of the mathematical situations generated in the study.
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Ustun, Isil. "Developing The Understanding Of Geometry Through A Computer-based Learning Environment." Master's thesis, METU, 2003. http://etd.lib.metu.edu.tr/upload/4/1206523/index.pdf.
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The main purpose of the study was to investigate the effects of
a dynamic instructional environment (based on use of Geometer&rsquos Sketchpad) on 7th grade students&rsquo
understandings of lines, angles, and polygons and their retention. Besides that, the students&rsquo
attitudes towards computer instruction and its relation with students&rsquo
performance on geometry and retention were investigated. The study was carried out with 63 7th grade students from two classes taught by the same teacher in a state elementary school. One class was assigned as the experimental group (EG), the other as the control group (CG). Students in CG received the instruction on lines, angles, and polygons by the regular traditional method used at the school. In the EG, students worked on the computer activities named as &ldquo
Sketchsheets&rdquo
, prepared by the researcher, with computers provided at the computer-lab. The usage of GSP with Sketchsheets enabled students to create the shapes first and after they explored and discovered the properties of shapes and make generalisations for the development of conjectures. Geometry Performance Test (GPT) and Computer Attitude Scale (CAS) were used in this study. The GPT was administered to both groups of students as a pre-test, post-test, and a delayed post-test. CAS was administered only to the EG students as a post-test. Furthermore, interviews were carried out with three students from EG in order to get their feelings about the dynamic instructional environment. Besides that, both of these classroom and computer sessions were observed and recorded with camera. The results of t-test suggest that GPT mean scores in EG and CG did not significantly differ in pre-test, but EG achieved significantly better than the CG in post and delay-post tests. CAS mean scores and interviews showed that students had positive feelings and decisions towards computer instruction and they preferred computer instruction to traditional instruction. Furthermore, Pearson product-moment correlation coefficient was performed in order to investigate the relationship between GPT scores and CAS scores. From this analysis, a significant correlation was observed between the GPT scores and CAS scores. This means that the students who had positive attitudes towards computer instruction, achieved significantly better at GPT. The results of this study revealed that Geometer&rsquo
s Sketchpad for learning and teaching geometry in elementary school level is an effective tool.
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Wosilait, Karen. "Research as a guide for the development of tutorials to improve student understanding of geometrical and physical optics /." Thesis, Connect to this title online; UW restricted, 1996. http://hdl.handle.net/1773/9652.
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Pires, Junior Wanderlei José. "A educação matemática e a elaboração de livros didáticos: a coleção Matemática de Imenes e Lellis." Universidade Federal de Juiz de Fora (UFJF), 2016. https://repositorio.ufjf.br/jspui/handle/ufjf/3802.
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O presente trabalho tem por objetivo analisar uma coleção didática de matemática, sob a perspectiva da história da educação matemática. Para isto, tomamos como fontes de pesquisa os quatro livros do professor, que compõem a coleção Matemática de Imenes e Lellis para o ensino fundamental II, obras escritas em 1999, primeira edição, sétima impressão. Além disso, duas entrevistas fornecidas por um dos autores da coleção, Luiz Marcio Imenes. Esse trabalho foi norteado pelas seguintes questões: Que apropriações de propostas para o ensino de Matemática a partir do campo da Educação Matemática podem ser identificadas na Coleção Matemática, de Imenes e Lellis? Mais especificamente, como se situa o ensino de Geometria nessa Coleção? Para seu desenvolvimento, amparou-se nas concepções de produção histórica de Marc Bloch, nos aportes da história das disciplinas escolares de André Chervel, na importância dos estudos sobre manuais didáticos como fontes de pesquisas de Alain Choppin, além da pesquisa em história da educação matemática no Brasil baseada principalmente em Wagner Valente. Tendo a Geometria como fio condutor, percebemos na Coleção de Imenes e Lellis a alternância entre os ramos da matemática ao longo dos capítulos em todos os livros, além do número bem expressivo de páginas destinadas à Geometria. Pontos que se diferem de outros livros da época. Apropriando-se das ideias da Educação Matemática, os autores também relacionam a Geometria, a Álgebra e a Aritmética, na busca pela construção do conhecimento que leve ao aluno a um aprendizado com compreensão.
The present work aims to analyze one Maths didactic collection from the perspective of the Mathematical Education’s history. To do this, we have used as sources four teacher’s books from Imenes and Lellis’ Mathematical collection for Elementary Education II, all written in 1999, first edition, seventh impression. In addition, we have conducted two interviews with one of the authors of the collection, Luiz Marcio Imenes. This work was based on some questions: What appropriations of proposals for teaching Maths in the field of Mathematics Education can be identified in the Mathematical Collection of Imenes and Lellis? More specifically, how is Geometry taught in this Collection? What are the differentials of this collection when compared with other didactic collections? This work was based on Marc Bloch's conceptions of historical production, on the contributions of André Chervel on the history of school subjects, under the importance of didactic manuals studies as sources of research by Alain Choppin, in additionto the research on the mathematical education history in Brazil, especially by Wagner Valente. Using the Geometry as the guiding thread, we notice that the Collection of Imenes and Lelis works with an alternation between the branches of Maths throughout the chapters in all the books, besides expressing a significantly number of pages talking about Geometry. These are differential points from other contemporary books. The authors use Mathematics Education in order to relate geometry, algebra and arithmetic in search for the construction of knowledge which leads students to learning along with understanding to contruct student’s knowledgment.
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Thórhallsson, Torfi. "Symmetric objects in multiple affine views." Thesis, University of Oxford, 2000. http://ora.ox.ac.uk/objects/uuid:49ec4596-7086-4645-81f8-8dacf48b694a.
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This thesis is concerned with the utilization of object symmety as a cue for segmentation and object recognition. In particular it investigates the problem of detecting 3D bilaterally symmetric objects from affine views. The first part of the thesis investigates the problem of detecting 3D bilateral symmetry within a scene from known point correspondences across two or more affine views. We begin by extending the notion of skewed symmetry to three dimensions, and give a definition in terms of degenerate structure that applies equally to an affine 3D structure or to point correspondences across two or more affine views. We then consider the effects of measurement errors on symmetry detection, and derive an optimal statistical test of degenerate structure, and thereby of 3D-skewed symmetry. We then move on to the problem of searching for 3D skewed symmetric sets within a larger scene. We discuss two approaches to the problem, both of which we have implemented, and we demonstrate fully automatic detection of 3D skewed symmetry on images of uncluttered scenes. We conclude the first part by investing means of verifying the presence of bilateral rather than skewed symmetry in the Euclidean space, by enforcing mutual consistency between multiple skewed symmetric sets, and by drawing on partial knowledge about the camera calibration. The second part of the thesis is concerned with the problem of obtaining feature correspondences across multiple affine views, as required for the detection of symmetry. In particular we investigate the geometric matching constraints that exist between affine views. We start by specilizing the four projective multifocal tensors to the affine case, and use these to carry the bulk of all known projective multi-view matching relations to affine views, unearthing some new relations in the process. Having done that, we address the problem of estimating the affine tensors. We provide a minimal set of constraints on the affine trifocal tensor, and search for ways of estimating the affine tensors from point and line correspondences.
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Saito, Ken. "Theoretical Studies on Electronic Excited States of Transition Metal Complexes: Explanation and Understanding Based on Molecular Geometries and Electronic Structures." 京都大学 (Kyoto University), 2012. http://hdl.handle.net/2433/161018.
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Simó, Serra Edgar. "Understanding human-centric images : from geometry to fashion." Doctoral thesis, Universitat Politècnica de Catalunya, 2015. http://hdl.handle.net/10803/327030.
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Understanding humans from photographs has always been a fundamental goal of computer vision. Early works focused on simple tasks such as detecting the location of individuals by means of bounding boxes. As the field progressed, harder and more higher level tasks have been undertaken. For example, from human detection came the 2D and 3D human pose estimation in which the task consisted of identifying the location in the image or space of all different body parts, e.g., head, torso, knees, arms, etc. Human attributes also became a great source of interest as they allow recognizing individuals and other properties such as gender or age. Later, the attention turned to the recognition of the action being performed. This, in general, relies on the previous works on pose estimation and attribute classification. Currently, even higher level tasks are being conducted such as predicting the motivations of human behavior or identifying the fashionability of an individual from a photograph.
In this thesis we have developed a hierarchy of tools that cover all these range of problems, from low level feature point descriptors to high level fashion-aware conditional random fields models, all with the objective of understanding humans from monocular, RGB images. In order to build these high level models it is paramount to have a battery of robust and reliable low and mid level cues. Along these lines, we have proposed two low-level keypoint descriptors: one based on the theory of the heat diffusion on images, and the other that uses a convolutional neural network to learn discriminative image patch representations. We also introduce distinct low-level generative models for representing human pose: in particular we present a discrete model based on a directed acyclic graph and a continuous model that consists of poses clustered on a Riemannian manifold. As mid level cues we propose two 3D human pose estimation algorithms: one that estimates the 3D pose given a noisy 2D estimation, and an approach that simultaneously estimates both the 2D and 3D pose. Finally, we formulate higher level models built upon low and mid level cues for human understanding. Concretely, we focus on two different tasks in the context of fashion: semantic segmentation of clothing, and predicting the fashionability from images with metadata to ultimately provide fashion advice to the user.
In summary, to robustly extract knowledge from images with the presence of humans it is necessary to build high level models that integrate low and mid level cues. In general, using and understanding strong features is critical for obtaining reliable performance. The main contribution of this thesis is in proposing a variety of low, mid and high level algorithms for human-centric images that can be integrated into higher level models for comprehending humans from photographs, as well as tackling novel fashion-oriented problems.Siempre ha sido una meta fundamental de la visión por computador la comprensión de los seres humanos. Los primeros trabajos se fijaron en objetivos sencillos tales como la detección en imágenes de la posición de los individuos. A medida que la investigación progresó se emprendieron tareas mucho más complejas. Por ejemplo, a partir de la detección de los humanos se pasó a la estimación en dos y tres dimensiones de su postura por lo que la tarea consistía en identificar la localización en la imagen o el espacio de las diferentes partes del cuerpo, por ejemplo cabeza, torso, rodillas, brazos, etc...También los atributos humanos se convirtieron en una gran fuente de interés ya que permiten el reconocimiento de los individuos y de sus propiedades como el género o la edad. Más tarde, la atención se centró en el reconocimiento de la acción realizada. Todos estos trabajos reposan en las investigaciones previas sobre la estimación de las posturas y la clasificación de los atributos. En la actualidad, se llevan a cabo investigaciones de un nivel aún superior sobre cuestiones tales como la predicción de las motivaciones del comportamiento humano o la identificación del tallaje de un individuo a partir de una fotografía. En esta tesis desarrollamos una jerarquía de herramientas que cubre toda esta gama de problemas, desde descriptores de rasgos de bajo nivel a modelos probabilísticos de campos condicionales de alto nivel reconocedores de la moda, todos ellos con el objetivo de mejorar la comprensión de los humanos a partir de imágenes RGB monoculares. Para construir estos modelos de alto nivel es decisivo disponer de una batería de datos robustos y fiables de nivel bajo y medio. En este sentido, proponemos dos descriptores novedosos de bajo nivel: uno se basa en la teoría de la difusión de calor en las imágenes y otro utiliza una red neural convolucional para aprender representaciones discriminativas de trozos de imagen. También introducimos diferentes modelos de bajo nivel generativos para representar la postura humana: en particular presentamos un modelo discreto basado en un gráfico acíclico dirigido y un modelo continuo que consiste en agrupaciones de posturas en una variedad de Riemann. Como señales de nivel medio proponemos dos algoritmos estimadores de la postura humana: uno que estima la postura en tres dimensiones a partir de una estimación imprecisa en el plano de la imagen y otro que estima simultáneamente la postura en dos y tres dimensiones. Finalmente construimos modelos de alto nivel a partir de señales de nivel bajo y medio para la comprensión de la persona a partir de imágenes. En concreto, nos centramos en dos diferentes tareas en el ámbito de la moda: la segmentación semántica del vestido y la predicción del buen ajuste de la prenda a partir de imágenes con meta-datos con la finalidad de aconsejar al usuario sobre moda. En resumen, para extraer conocimiento a partir de imágenes con presencia de seres humanos es preciso construir modelos de alto nivel que integren señales de nivel medio y bajo. En general, el punto crítico para obtener resultados fiables es el empleo y la comprensión de rasgos fuertes. La aportación fundamental de esta tesis es la propuesta de una variedad de algoritmos de nivel bajo, medio y alto para el tratamiento de imágenes centradas en seres humanos que pueden integrarse en modelos de alto nivel, para mejor comprensión de los seres humanos a partir de fotografías, así como abordar problemas planteados por el buen ajuste de las prendas.
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Svensson, Frida. "Can you describe your home? : A study about students understanding about concepts within construction." Thesis, Linnéuniversitetet, Institutionen för matematikdidaktik (MD), 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-36357.
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The purpose with this research paper is to examine the students’ shown knowledge in geometry, with a focus on construction and its concepts, and the educational value and teaching the students got in this area. The students’ homes are used as a starting-point. The students shall, from a self-made drawing of their home and a photograph of it, describe what their home looks like. In this paper, the mathematical concepts the students used will be analyzed and compared with the education they received. The analytical framework is based on Van Hieles levels of knowledge and Blooms Taxonomy. The study was done at a Secondary School in Kenya. Four students were selected and interviewed. The lesson observations were made with the purpose to get an understanding for how the education for these students look like and to get examples on how the teaching is conducted for these students. Finally, interviews with the teachers were carried out. The students show a good knowledge in the national exams. However, the study shows that when the students are supposed to use this particular knowledge outside of the classroom, the students experience difficulties. Mostly, the students encounter problems when they are supposed to estimate measurements. Furthermore, they lack the ability to compare scales. The research also shows that the education for these students is monotone and much time during the lessons is spend either with a teacher lecturing in front of the board or students working with examples in the textbook. According to the Variation Theory, the knowledge of the students should deepen if the objects of learning are varying. This variation is not something the students receive in the present situation.Syftet är att undersöka några gymnasieelevers visade kunskaper i geometri med fokus på konstruktion och begreppsanvändning samt den undervisning som erbjuds eleverna inom området. Elevernas hem används som utgångspunkt. Eleverna ska utifrån en teckning, som de själva ritat, och ett fotografi beskriva hemmet. De matematiska begrepp som eleverna använder analyseras. Analysverktyget bygger på van Hieles kvalitativa kunskapsnivåer och Blooms Taxonomi. Undersökningen genomfördes på en gymnasieskola i Kenya. Fyra utvalda elever intervjuades. Lektionsobservationer genomfördes i syfte att få förståelse för hur elevernas undervisningssituation ser ut och få exempel på hur undervisningen bedrivs. Slutligen intervjuades två av elevernas lärare. Eleverna har goda kunskaper på nationella prov men undersökningen visar att när dessa kunskaper skall överföras till något utanför lektionssalen stöter eleverna på problem. De har svårt att uppskatta längdenheter och svårt att jämföra skala. Det kommer också fram att deras undervisning är ganska monoton. Mycket tid läggs till att läraren undervisar eleverna framme vid tavlan eller att eleverna jobbar med uppgifter i sin övningsbok. Enligt variationsteorin, som beskrivs i arbetet, skulle elevernas kunskaper ges möjlighet att fördjupas om de geometriska objekt som skall förstås varieras. Denna variation erbjuds inte eleverna i nuläget.
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Taylor, Carol H. "Promoting Mathematical Understanding through Open-Ended Tasks; Experiences of an Eighth-Grade Gifted Geometry Class." Digital Archive @ GSU, 2008. http://digitalarchive.gsu.edu/msit_diss/36.
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Promoting Mathematical Understanding Through Open-Ended Tasks; Experiences of an Eighth-Grade Gifted Geometry Class by Carol H. Taylor Gifted students of mathematics served through acceleration often lack the opportunities to engage in challenging, complex investigations involving higher-level thinking. This purpose of this study was to examine the ways mathematically gifted students think about and do mathematics creatively as indicators of deep understanding through collaborative work on four open-ended tasks with high-level cognitive demand. The study focused on the mathematical thinking involved in students’ construction of mathematical understanding through the social interaction of group problem solving. This case study used ethnographic methodology within a social constructivist frame with gifted education and sociocultural contextual influences. Participants were 15 gifted students in an 8th-grade gifted geometry class. Data collection included field notes, student artifacts, student journal entries, audio recordings, and reflections. Transcribed audio recordings were segmented (Tesch, 1990) into phases of interaction, coded by function, then coded by levels of exhibited mathematical thinking from observable cognitive actions (Dreyfus, Hershkowitz, & Schwarz, 2001; Williams, 2000; Wood, Williams, & McNeal, 2006), and analyzed for maintenance or decline of high-level cognitive demand (Stein, Smith, Henningsen, & Silver, 2000). Interpretive data analysis was connected to data analysis of transcribed recordings. Results indicated social interaction among students enabled them to talk through the mathematics to understand mathematical concepts and relationships, to construct more complex meaning, and exhibit mathematical creativity, inventiveness, flexibility, and originality. Students consistently exhibited these characteristics indicating mathematical thinking at the levels of building-with analyzing, building-with synthetic-analyzing, building-with evaluative-analyzing, constructing synthesizing, and occasionally constructing evaluating (Dreyfus et al., 2001; Williams, 2000; Wood et al., 2006). The results of the study support the claim of a relationship between mathematical giftedness and the ability to abstract and generalize (Sriraman, 2003), provide evidence that given the opportunity, students can construct deep mathematical understanding, and indicate the importance of social interaction in the construction of knowledge. This study adds to the body of knowledge needed in research on gifted education, problem solving, small-group interaction, mathematical thinking, and mathematical understanding, through empirically assessed classroom practice (Friedman-Nima et al., 2005; Good, Mulryan, & McCaslin, 1992; Hiebert & Carpenter, 1992; Lester & Kehle, 2003; Phillipson, 2007; Wood, Williams, & McNeal, 2006).
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Muhembo, Gottfried Mbundu. "An analysis of how visualisation processes can be used by teachers participating in an intervention programme to teach for conceptual understanding of geometry." Thesis, Rhodes University, 2018. http://hdl.handle.net/10962/62439.
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Visualisation in general and visualisation processes in particular have received much attention in the mathematics education research literature. Literature suggests that the appropriate use of visualisation helps learners to develop their conceptual understanding and skills of geometry as it allows them to visually interpret and understand fundamental mathematical and geometrical concepts. It is claimed that visual tools play an important role in communicating mathematical ideas through diagrams, gestures, images, sketches or drawings. Learning mathematics through visualisation can be a powerful tool to explore mathematical problems and give meaning to mathematical concepts and relationships between them. This interpretive case study focused on how selected teachers taught concepts in geometry through visualisation processes for conceptual understanding as a result of an intervention programme. The study was conducted at four high schools by four mathematics teachers in the Kavango East Region in Northern Namibia. The participants were involved in a three-week intervention programme and afterwards taught three lessons each on the topic of geometry. The data collection method of this research was: focus group and stimulus recall interviews, classroom observations and recorded videos. This research is located in constructivism. I used vertical and horizontal analysis strategies to analyse the data. My analytical instrument consisted of an observation schedule which I used in each lesson to identify how each of the visualisation processes was evident in each of the observed lessons. This study revealed that the participant teachers used visualisation processes in most of their lessons and these processes were used accurately in line with the requirements of the grade 8 mathematics syllabi. The visualisation processes were used through designed visual materials, posters and through the use of geometrical objects such as chalkboard ruler, protractor and compass. The results from this study also confirmed that visualisation processes can be a powerful instructional tool for enhancing learners’ conceptual understanding of geometry.
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Oesau, Sven. "Modélisation géométrique de scènes intérieures à partir de nuage de points." Thesis, Nice, 2015. http://www.theses.fr/2015NICE4034/document.
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La modélisation géométrique et la sémantisation de scènes intérieures à partir d'échantillon de points et un sujet de recherche qui prend de plus en plus d'importance. Cependant, le traitement d'un ensemble volumineux de données est rendu difficile d'une part par le nombre élevé d'objets parasitant la scène et d'autre part par divers défauts d'acquisitions comme par exemple des données manquantes ou un échantillonnage de la scène non isotrope. Cette thèse s'intéresse de près à de nouvelles méthodes permettant de modéliser géométriquement un nuage de point non structuré et d’y donner de la sémantique. Dans le chapitre 2, nous présentons deux méthodes permettant de transformer le nuage de points en un ensemble de formes. Nous proposons en premier lieu une méthode d'extraction de lignes qui détecte des segments à partir d'une coupe horizontale du nuage de point initiale. Puis nous introduisons une méthode par croissance de régions qui détecte et renforce progressivement des régularités parmi les formes planaires. Dans la première partie du chapitre 3, nous proposons une méthode basée sur de l'analyse statistique afin de séparer de la structure de la scène les objets la parasitant. Dans la seconde partie, nous présentons une méthode d'apprentissage supervisé permettant de classifier des objets en fonction d'un ensemble de formes planaires. Nous introduisons dans le chapitre 4 une méthode permettant de modéliser géométriquement le volume d'une pièce (sans meubles). Une formulation énergétique est utilisée afin de labelliser les régions d’une partition générée à partir de formes élémentaires comme étant intérieur ou extérieur de manière robuste au bruit et aux donnéesGeometric modeling and semantization of indoor scenes from sampled point data is an emerging research topic. Recent advances in acquisition technologies provide highly accurate laser scanners and low-cost handheld RGB-D cameras for real-time acquisition. However, the processing of large data sets is hampered by high amounts of clutter and various defects such as missing data, outliers and anisotropic sampling. This thesis investigates three novel methods for efficient geometric modeling and semantization from unstructured point data: Shape detection, classification and geometric modeling. Chapter 2 introduces two methods for abstracting the input point data with primitive shapes. First, we propose a line extraction method to detect wall segments from a horizontal cross-section of the input point cloud. Second, we introduce a region growing method that progressively detects and reinforces regularities of planar shapes. This method utilizes regularities common to man-made architecture, i.e. coplanarity, parallelism and orthogonality, to reduce complexity and improve data fitting in defect-laden data. Chapter 3 introduces a method based on statistical analysis for separating clutter from structure. We also contribute a supervised machine learning method for object classification based on sets of planar shapes. Chapter 4 introduces a method for 3D geometric modeling of indoor scenes. We first partition the space using primitive shapes detected from permanent structures. An energy formulation is then used to solve an inside/outside labeling of a space partitioning, the latter providing robustness to missing data and outliers
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Donevska-Todorova, Ana. "Utilizing Technology to Facilitate the Transition from Secondary- to Tertiary Level Linear Algebra." Doctoral thesis, Humboldt-Universität zu Berlin, 2017. http://dx.doi.org/10.18452/18561.
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Es ist eine weit verbreitete Wahrnehmung, dass der Übergang zwischen der Mathematik der gymnasialen Oberstufe und der Mathematik an der Universität für Studierende problematisch sein kann. Besondere Verständnisschwierigkeiten in Bereich der lineare Algebra (lA) bereiten den Studierenden die verschiedenen Herangehensweisen auf diesen beiden Ebenen. Dies lässt sich auf die strukturell-axiomatischer Herangehensweisen an die lA an der Universität, im Gegensatz zu ihrer arithmetisch-geometrischen Darstellung in der Schule, zurückführen. Dies bedingt ebenfalls Unterschiede im prozeduralen und konzeptuellen Verständnis. Ziel dieser Arbeit ist es, zu untersuchen, wie Schüler konzeptuelles Verständnis, Bezug nehmend auf die Theorien von concept definition/image in Verbindung mit multiplen Modi der Beschreibung und des Denkens von Konzepten wie Bilinearität z.B. Skalarprodukt und Multilinearität z.B. Determinanten gewinnen können. Um dies zu erreichen wurde eine substanzielle Lehr-Lernumgebung unter Verwendung einer dynamischen Geometriesoftware (DGS) entwickelt. Die Lerneinheit wurde an einem Berliner Gymnasium eingesetzt und dabei ein vollständiger design-based research Zyklus durchlaufen und eine multiple-level Datenanalyse durchgeführt. Die Ergebnisse der Untersuchung zeigen nicht nur, dass eine Erweiterung der Vorstellungen der Schüler, eine Entwicklung multipler Denkmodi und ein Gewinn tieferen konzeptuellen Verständnisses in der lA erfolgreich vermittelt werden können, sondern geben auch Einblicke in ein mögliches theoretisches Modell, mit dessen Hilfe sich diese Prozesse weiter untersuchen lassen. Weiterhin werden die interaktiven Lehr-Lernmaterialien für die weitere Verwendung im Rahmen von Lehre und Forschung zur Verfügung gestellt. Es öffnen sich neue Forschungsfragen hinsichtlich lokalen Axiomatisierens in der lA der gymnasialen Oberstufe, welches auf einer Integration geometrischer, algebraischer und axiomatischer Denkmodi, unterstützt durch DGS, basieren könnte.A common perception among researchers in mathematics education is that the transition between secondary- and tertiary level of mathematics may be problematic for the students. In particular, the exact and abstract nature of the theory of Linear algebra versus its arithmetic-geometric presentation in school appears to be difficult for the novice students. The application of properties for defining concepts at university in contrast to their usage for describing concepts in school points out a possible occurrence of obstacles for learning and discrepancies in procedural and conceptual understanding. The aim of this study is to examine how could upper-high school students develop a conceptual understanding based on concept definition and concept image in connection to multiple modes of description and thinking about concepts such as bi-linearity exemplified by the dot product of vectors and multi-linearity exemplified by determinants. In order to achieve this, I have created a specific teaching/ learning sequence in a dynamic geometry environment (DGE), then implemented it and evaluated it in a high school in Berlin, following a complete cycle of design-based research and conducting a multiple-level data analysis. The findings of the study show not only that widening students' concept images, developing multiple modes of thinking and gaining deeper conceptual understanding can successfully be mediated by dynamic geometries, but also give insights into an eventual theoretical model of how can they be further examined. Moreover, the study promotes authorized open-source interactive teaching/ learning materials for further sustainable practice and research. It opens new research questions about revisiting axiomatic approaches on local levels in upper high-school Linear algebra which may base on the integration of all three modes of description and thinking geometric, algebraic and abstract possibly facilitated by DGE.
Честа перцепција кај многумина истражувачи во областа на математичкото образование е дека транзицијата помеѓу средното и високото образование по математика може да биде проблематична за студентите. Егзакноста и апстрактноста на теоријата по Линеарна алгебра наспроти нејзината аритметичко-геометриска презентација во средното гимназиско образование се покажува како особено тешка за студентите. Примена на својствата на математичките поими за нивно дефинирање на универзитетско ниво наспроти нивното употреба за опишување на претходно дефинирани поими на училишно ниво, укажува на можна појава на тешкотии при нивното изучување и несовпаѓање на процедуралното и концептуалното разбирање на истите. Целта на оваа студија е да истражи како средношколците би можеле да развијат концептуално разбирање на поимите врз основа на концепт дефиниција и концепт слика во врска со мулти-моди на мислење, конкретно за поими како билинеарност, пр. скаларен производ на вектори, и мултилинеарност, пр. детерминанти. За да ја постигнам оваа цел, креирав наставна содржина поддржана од еден динамичен геометриски систем (ДГС) и следејќи целосен циклус на т.н. design-based research и спрoведувајќи мулти-анализа на податоци, истата ја имплементирав и евалуирав во едно средно училиште во Берлин. Резултатите од студијата укажуваат не само на фактот дека проширувањето на концепт сликите на учениците, развојот на мулти-моди на мислење и стекнувањето на длабоко концептуално разбирање на поимите можат да бидат успешно посредувани од ДГС туку овозможија и увид во еден теоретски модел за тоа коко тие можат понатаму да се истражуваат. Уште повеќе, студијата промовира авторизирани open-source интерактивни материјали за предавање и учење на содржините кои може да служат за понатамошни одржливи истражувања и развој. Студијата отвора нови истражувачки прашања за средношколската Линеарна алгебра која може да се базира на интеграција на сите три моди на мислење, геометриски, алгебарски и апстрактен, поддржан од ДГС.
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Verdie, Yannick. "Modélisation de scènes urbaines à partir de données aériennes." Thesis, Nice, 2013. http://www.theses.fr/2013NICE4078.
Full textAbstract:
L'analyse et la reconstruction automatique de scène urbaine 3D est un problème fondamental dans le domaine de la vision par ordinateur et du traitement numérique de la géométrie. Cette thèse présente des méthodologies pour résoudre le problème complexe de la reconstruction d'éléments urbains en 3D à partir de données aériennes Lidar ou bien de maillages générés par imagerie Multi-View Stereo (MVS). Nos approches génèrent une représentation précise et compacte sous la forme d'un maillage 3D comportant une sémantique de l'espace urbain. Deux étapes sont nécessaires ; une identification des différents éléments de la scène urbaine, et une modélisation des éléments sous la forme d'un maillage 3D. Le Chapitre 2 présente deux méthodes de classifications des éléments urbains en classes d'intérêts permettant d'obtenir une compréhension approfondie de la scène urbaine, et d'élaborer différentes stratégies de reconstruction suivant le type d'éléments urbains. Cette idée, consistant à insérer à la fois une information sémantique et géométrique dans les scènes urbaines, est présentée en détails et validée à travers des expériences. Le Chapitre 3 présente une approche pour détecter la 'Végétation' incluses dans des données Lidar reposant sur les processus ponctuels marqués, combinée avec une nouvelle méthode d'optimisation. Le Chapitre 4 décrit à la fois une approche de maillage 3D pour les 'Bâtiments' à partir de données Lidar et de données MVS. Des expériences sur des structures urbaines larges et complexes montrent les bonnes performances de nos systèmesAnalysis and 3D reconstruction of urban scenes from physical measurements is a fundamental problem in computer vision and geometry processing. Within the last decades, an important demand arises for automatic methods generating urban scenes representations. This thesis investigates the design of pipelines for solving the complex problem of reconstructing 3D urban elements from either aerial Lidar data or Multi-View Stereo (MVS) meshes. Our approaches generate accurate and compact mesh representations enriched with urban-related semantic labeling.In urban scene reconstruction, two important steps are necessary: an identification of the different elements of the scenes, and a representation of these elements with 3D meshes. Chapter 2 presents two classification methods which yield to a segmentation of the scene into semantic classes of interests. The beneath is twofold. First, this brings awareness of the scene for better understanding. Second, deferent reconstruction strategies are adopted for each type of urban elements. Our idea of inserting both semantical and structural information within urban scenes is discussed and validated through experiments. In Chapter 3, a top-down approach to detect 'Vegetation' elements from Lidar data is proposed using Marked Point Processes and a novel optimization method. In Chapter 4, bottom-up approaches are presented reconstructing 'Building' elements from Lidar data and from MVS meshes. Experiments on complex urban structures illustrate the robustness and scalability of our systems
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Casero, Cañas Ramón. "Left ventricle functional analysis in 2D+t contrast echocardiography within an atlas-based deformable template model framework." Thesis, University of Oxford, 2008. http://ora.ox.ac.uk/objects/uuid:b17b3670-551d-4549-8f10-d977295c1857.
Full textAbstract:
This biomedical engineering thesis explores the opportunities and challenges of 2D+t contrast echocardiography for left ventricle functional analysis, both clinically and within a computer vision atlas-based deformable template model framework. A database was created for the experiments in this thesis, with 21 studies of contrast Dobutamine Stress Echo, in all 4 principal planes. The database includes clinical variables, human expert hand-traced myocardial contours and visual scoring. First the problem is studied from a clinical perspective. Quantification of endocardial global and local function using standard measures shows expected values and agreement with human expert visual scoring, but the results are less reliable for myocardial thickening. Next, the problem of segmenting the endocardium with a computer is posed in a standard landmark and atlas-based deformable template model framework. The underlying assumption is that these models can emulate human experts in terms of integrating previous knowledge about the anatomy and physiology with three sources of information from the image: texture, geometry and kinetics. Probabilistic atlases of contrast echocardiography are computed, while noting from histograms at selected anatomical locations that modelling texture with just mean intensity values may be too naive. Intensity analysis together with the clinical results above suggest that lack of external boundary definition may preclude this imaging technique for appropriate measuring of myocardial thickening, while endocardial boundary definition is appropriate for evaluation of wall motion. Geometry is presented in a Principal Component Analysis (PCA) context, highlighting issues about Gaussianity, the correlation and covariance matrices with respect to physiology, and analysing different measures of dimensionality. A popular extension of deformable models ---Active Appearance Models (AAMs)--- is then studied in depth. Contrary to common wisdom, it is contended that using a PCA texture space instead of a fixed atlas is detrimental to segmentation, and that PCA models are not convenient for texture modelling. To integrate kinetics, a novel spatio-temporal model of cardiac contours is proposed. The new explicit model does not require frame interpolation, and it is compared to previous implicit models in terms of approximation error when the shape vector changes from frame to frame or remains constant throughout the cardiac cycle. Finally, the 2D+t atlas-based deformable model segmentation problem is formulated and solved with a gradient descent approach. Experiments using the similarity transformation suggest that segmentation of the whole cardiac volume outperforms segmentation of individual frames. A relatively new approach ---the inverse compositional algorithm--- is shown to decrease running times of the classic Lucas-Kanade algorithm by a factor of 20 to 25, to values that are within real-time processing reach.
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Jung, Inchul. "Student representation and understanding of geometric transformations with technology experience." 2002. http://purl.galileo.usg.edu/uga%5Fetd/jung%5Finchul%5F200205%5Fphd.
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Cassim, Ishaak. "An exploratory study into grade 12 learners’ understanding of Euclidean Geometry with special emphasis on cyclic quadrilateral and tangent theorems." Thesis, 2007. http://hdl.handle.net/10539/2037.
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Student Number : 8800092K -
MSc research report -
School of Education -
Faculty of ScienceThis research report explored the strategies which grade 12 learners employ to solve geometric problems. The purpose of this research was to gain an understanding of how grade 12 learners begin to solve geometric problems involving cyclic quadrilateral and tangent theorems. A case study method was used as the main research method. The study employed the van Hiele level’s of geometric thought as a method for categorising learners levels of understanding. Data about the strategies which learners recruit to solve geometric problems were gathered using learner-based tasks, semi-structured interviews and document analysis. From the data gathered, the following patterns emerged: learners incorrect use of theorems to solve geometrical problems; learners base their responses on the visual appearance of the diagram; learners “force “ a solution when one is not available; learners’ views of proof. Each of these aspects is discussed. The report concludes that learners strategies to solving geometric problems are based largely on the manner in which educators approach the solving of geometrical problems.
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San, Luis Weng. "First-year university students' algebraic thinking and its relationship to geometric conceptual understanding." Thesis, 2011. http://hdl.handle.net/10539/9251.
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This study investigated how first-year university students at Universidade Pedagógica (Pedagogical University) in Maputo-Mozambique brought their knowledge and thinking of algebra in understanding and working with geometry. The study explored how these students connected and used algebraic and geometric concepts and investigated whether this connection promoted students’ conceptual understanding and problem solving performance in geometry.
The main body of the research was done in three phases, which were analysed separately. The three phases were the Pilot Study, the Main Study – Euclidean Geometry Course, and the Main Study – Analytic Geometry Course. Transcripts from the interviews with the target students, and the artefacts collected from the students (Pilot test, Diagnostic test, and written responses to the Elaboration and Concept Mapping Task) constituted the bulk of the data for this study. The data collection was carried out during two successive semesters.
The constant comparative method and the grounded theory were used in the analysis of the data. A model was adapted from the literature (Charbonneau, 1996; Stillwell, 1998; and Duval, 1998) to explore how algebraic thinking might be an aid to geometrical understanding . It shows that the cognitive processes (symbolization, relations, and abstraction), which underlie algebraic thinking, are interconnected. These cognitive processes might jointly be used to aid any of the cognitive processes which constitute geometrical understanding (visualization processes, construction processes, and reasoning), either separately or jointly. Prawat’s (1989) framework on transfer and learning appeared to be relevant to analyse the data collected in the study: (Knowledge connectedness and communication, general and specific strategy, and mastery and performance disposition).
The results showed that in Analytic Geometry the students needed intuition (synthetic strategies) to inform their reasoning (analytic strategies). In the contrary, in Euclidean Geometry they needed reasoning (analytic strategies) to inform their intuition (synthetic strategies). However, I observed that this balance still needed to take place in my target students’ mind. In other words, in Analytic Geometry, my students needed geometric thinking to aid their algebraic thinking and in Euclidean Geometry, they needed algebraic thinking to aid their geometric thinking. This mutuality in geometry seems to underpin what Schoenfeld (1986) found that the interaction of deductive (as a means of discovery) and empirical (as a means of development of intuition) approaches to geometry leads students to reap the benefits of their knowledge.
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Bibi, Adel. "Understanding a Block of Layers in Deep Neural Networks: Optimization, Probabilistic and Tropical Geometric Perspectives." Diss., 2020. http://hdl.handle.net/10754/662589.
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This dissertation aims at theoretically studying a block of layers that is common in al- most all deep learning models. The block of layers of interest is the composition of an affine layer followed by a nonlinear activation that is followed by another affine layer. We study this block from three perspectives. (i) An Optimization Perspective. Is it possible that the output of the forward pass through this block is an optimal solution to a certain convex optimization problem? We show an equivalency between the forward pass through this block and a single iteration of deterministic and stochastic algorithms solving a ten- sor formulated convex optimization problem. As consequence, we derive for the first time a formula for computing the singular values of convolutional layers surpassing the need for the prohibitive construction of the underlying linear operator. Thereafter, we show that several deep networks can have this block replaced with the corresponding optimiza- tion algorithm predicted by our theory resulting in networks with improved generalization performance. (ii) A Probabilistic Perspective. Is it possible to analytically analyze the output of a deep network upon subjecting the input to Gaussian noise? To that regard, we derive analytical formulas for the first and second moments of this block under Gaussian input noise. We demonstrate that the derived expressions can be used to efficiently analyze the output of an arbitrary deep network in addition to constructing Gaussian adversarial attacks surpassing any need for prohibitive data augmentation procedures. (iii) A Tropi- cal Geometry Perspective. Is it possible to characterize the decision boundaries of this block as a geometric structure representing a solution set to a certain class of polynomials
(tropical polynomials)? If so, then, is it possible to utilize this geometric representation of the decision boundaries for novel reformulations to classical computer vision and machine learning tasks on arbitrary deep networks? We show that the decision boundaries of this block are a subset of a tropical hypersurface, which is intimately related to a the polytope that is the convex hull of two zonotopes. We utilize this geometric characterization to shed lights on new perspectives of network pruning.
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Khembo, Elspeth. "An investigation into grade 6 teachers' understanding of geometry according to the Van Hiele level of geometric thought." Thesis, 2012. http://hdl.handle.net/10539/11430.
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A qualitative three phase research study was undertaken to explore the geometric thinking of Grade 6
teachers in the context of low performance of the Gauteng learners in the International Competitions
and Assessments for Schools (ICAS) tests in 2006. The van Hiele theory of geometric thinking was
used as a theoretical framework. Data was collected by means of document analysis, teachers
responding in writing to ICAS items and task based interviews. This research shows that the ICAS
items map very well with the National Curriculum Statement (NCS) Assessment Standards and the
van Hiele levels. The mapping of the 82 geometry ICAS items to the (NCS) Assessments Standards
and the van Hiele levels revealed that 59% of the ICAS items were at van Hiele level 2 across all
grades and therefore accessible to the majority of the learners. The written responses conducted with
40 ACE teachers and the task based interviews conducted with six teachers indicate that the majority
of teachers are not at the required level of geometric thinking as expected by the NCS Assessment
Standards and the van Hiele levels. This finding has serious implications for classroom practice in the
learning and teaching of geometry in primary schools. The challenge for teacher education is to take
into consideration the relationship between language and the van Hiele levels; the use of van Hiele
levels in the development of teachers’ geometric thinking and the possible use of the van Hiele levels
in identifying, explaining and rectifying geometric misconceptions.
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Ndlovu, Mdutshekelwa. "An analysis of teacher competencies in a problem-centred approach to dynamic Geometry teaching." Diss., 2004. http://hdl.handle.net/10500/2036.
Full textAbstract:
The subject of teacher competencies or knowledge has been a key issue in mathematics
education reform. This study attempts to identify and analyze teacher competencies
necessary in the orchestration of a problem-centred approach to dynamic geometry
teaching and learning. The advent of dynamic geometry environments into classrooms
has placed new demands and expectations on mathematics teachers.
In this study the Teacher Development Experiment was used as the main method of
investigation. Twenty third-year mathematics major teachers participated in workshop
and microteaching sessions involving the use of the Geometer's Sketchpad dynamic
geometry software in the teaching and learning of the geometry of triangles and
quadrilaterals. Five intersecting categories of teacher competencies were identified:
mathematical/geometrical competencies. pedagogical competencies. computer and
software competences, language and assessment competencies.Mathematical Sciences
M. Ed. (Mathematical Education)
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Mabotja, Koena Samuel. "An exploration of folding back in improving grade 10 students’ reasoning in geometry." Thesis, 2017. http://hdl.handle.net/10386/1805.
Full textAbstract:
Thesis (M. Ed. (Mathematics Education)) -- University of Limpopo, 2017The purpose of this study was to explore the role of folding back in enriching grade 10 students’ reasoning in geometry. Although various attempts are made in teaching and learning geometry, evidence from several research studies shows that most learners struggle with geometric reasoning. Hence, this study came as a result of such learners’ struggles as shown in the literature as well as personal experiences. The study was a constructivist teaching experiment methodology that sought to answer the following research questions: How does folding back support learners’ interaction with geometric reasoning tasks during the lessons? How does a Grade 10 mathematics teacher use folding back to enrich student reasoning in geometry? The teaching experiment as a research design in this study was found useful in studying learners’ geometric reasoning as a result of mathematical interactions in their learning of geometry. Therefore, it should be noted that the teaching experiments were not conducted as an attempt to implement a particular way of teaching, but rather to understand the role of folding back in enriching learners’ reasoning in geometry. As a referent to the teaching experiment methodology, the participants in this study were 7 grade 10 mathematics learners’ sampled from a classroom of 54 learners. These seven learners did not necessarily represent the whole class in accordance with the purpose of the study. This requirement was not necessary in determining rigour in teaching experiments. Instead interest was on “organising and guiding [teacher-researchers] experience of learners doing mathematics” (Steffe & Thompson, 2000, p. 300). Furthermore, the participants were divided into two groups while working on the learning activities. Participants were further encouraged to share ideas with each other as they solved the learning activities. Data was collected through video recording while learners were working on mathematical learning activities. The focus was on the researcher-teacher – learners and learners-learners interactions while working on geometric reasoning learning activities. Learning activities and observations served as subsets of the video data. Learners were encouraged to share ideas with each other as they v solved the learning activities as recommended by Steffe and Thompson (2000). Likewise, in order to learn the learners’ mathematics, the researcher could teach and interact with learners in a way that encourage them to improve their current thinking (Steffe & Thompson, 2000). In analysing data, the study adopted narrative analysis. The researcher performed verbatim transcription of the video recordings. Subsequently, information-rich interaction for each mathematical learning activity, where folding back was observed was selected. The selections of such information-rich interactions were guided by Martin’s (2008) framework for describing folding back. The main findings of the study revealed that in a learning environment where folding back takes place, learners’ reasoning in geometry is enriched. The researcher-teacher’s instructional decisions such as discouraging, questioning, modelling and guiding were found to be effective sources through which learners fold back. The findings also revealed that learners operating at different layers of mathematical understanding are able to share their geometry knowledge with their peers. Moreover, the findings indicated that in a learning environment where folding back takes place, learners questioning ability is enriched. Based on the findings of the study, the recommendations were that Mathematics teachers should create a learning environment where learners are afforded the opportunity to interact with each other during geometry problem solving; such is a powerful quest for folding back to take place.
Research Chair Developmental Grant at the University of Limpopo
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Ndlovu, Mdutshekelwa. "An analysis of teacher competences in a problem-centred approach to dynamic geometry teaching." Diss., 2004. http://hdl.handle.net/10500/23786.
Full textAbstract:
The subject of teacher competences or knowledge has been a key issue in mathematics education reform. This study attempts to identify and analyze teacher competences necessary in the orchestration of a problem-centred approach to dynamic geometry teaching and learning. The advent of dynamic geometry environments into classrooms has placed new demands and expectations on mathematics teachers.
In this study the Teacher Development Experiment was used as the main method of investigation. Twenty third-year mathematics major teachers participated in workshop and microteaching sessions involving the use of the Geometer’s Sketchpad dynamic geometry software in the teaching and learning of the geometry of triangles and quadrilaterals. Five intersecting categories of teacher competences were identified: mathematical/geometrical competences, pedagogical competences, computer and software competences, language and assessment competencies.Mathematics Education
M. Ed. (Mathematics Education)
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Kovář, Vojtěch. "O původu geometrie ve fundamentální ontologii." Master's thesis, 2013. http://www.nusl.cz/ntk/nusl-321148.
Full textAbstract:
The following text attempts to rethink the challenge of Edmund Husserl in his text On the Origin of Geometry. Interpretation of fundamental ontology developed by Martin Heidegger in Being and Time provides field on which it is possible to try to answer the question of the origin of geometry. It is conceived as a completely unique ontological possibility that nature is able to vouch for an explanation of the geometry.
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Kovář, Vojtěch. "O původu geometrie ve fundamentální ontologii." Master's thesis, 2014. http://www.nusl.cz/ntk/nusl-340004.
Full textAbstract:
The following text attempts to rethink the challenge of Edmund Husserl in his text On the Origin of Geometry. Interpretation of fundamental ontology developed by Martin Heidegger in Being and Time provides field on which it is possible to try to answer the question of the origin of geometry. It is conceived as a completely unique ontological possibility that nature is able to vouch for an explanation of the geometry.