Relevant bibliographies by topics / Geometric understanding

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Geometric understanding'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Geometric understanding"

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Fan, Jianqing, Hui-Nien Hung, and Wing-Hung Wong. "Geometric Understanding of Likelihood Ratio Statistics." Journal of the American Statistical Association 95, no. 451 (September 2000): 836–41. http://dx.doi.org/10.1080/01621459.2000.10474275.

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Lei, Na, Dongsheng An, Yang Guo, Kehua Su, Shixia Liu, Zhongxuan Luo, Shing-Tung Yau, and Xianfeng Gu. "A Geometric Understanding of Deep Learning." Engineering 6, no. 3 (March 2020): 361–74. http://dx.doi.org/10.1016/j.eng.2019.09.010.

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Elia, Iliada, and Athanasios Gagatsis. "Young children's understanding of geometric shapes: The role of geometric models." European Early Childhood Education Research Journal 11, no. 2 (January 2003): 43–61. http://dx.doi.org/10.1080/13502930385209161.

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Hannibal, Mary Anne. "Young Children's Developing Understanding of Geometric Shapes." Teaching Children Mathematics 5, no. 6 (February 1999): 353–57. http://dx.doi.org/10.5951/tcm.5.6.0353.

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How can we improve geometry instruction at the preschool and primary levels? To answer that question, I conducted research to analyze young children's understanding of the geometric concepts of triangle and rectangle and to determine patterns in the development of this understanding from ages 3 through 6. The research suggests that early childhood educators need to rethink the way that basic shapes are introduced to young children. Since a basic understanding of shapes is essential to a future study of geometry, teachers need to focus on how best to help children develop that initial understanding of shape categories. After a brief explanation of the research, specific ways to present developmentally appropriate activities designed to enhance children's understanding of basic shapes are discussed.
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Arthur, John W. "Understanding geometric algebra for electromagnetic theory [Advertisement]." IEEE Antennas and Propagation Magazine 56, no. 1 (February 2014): 292. http://dx.doi.org/10.1109/map.2014.6821800.

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Özçakır, Bilal, Ahmet Sami Konca, and Nihat Arıkan. "Children';s Geometric Understanding through Digital Activities: The Case of Basic Geometric Shapes." International Journal of Progressive Education 15, no. 3 (June 3, 2019): 108–22. http://dx.doi.org/10.29329/ijpe.2019.193.8.

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Shaw, Jean M., Conn Thomas, Ann Hoffman, and Janis Bulgren. "Using Concept Diagrams to Promote Understanding in Geometry." Teaching Children Mathematics 2, no. 3 (November 1995): 184–89. http://dx.doi.org/10.5951/tcm.2.3.0184.

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The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) and the van Hiele model for geometric thought (Crowley 1987) advocate increasing students' understanding of geometric properties and relationships as they enter the intermediate anil middle grades.
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KAJIYAMA, Kiichiro. "Understanding of Pictortial Drawing with Incorrect Geometric Concept." Journal of Graphic Science of Japan 34, no. 1 (2000): 9–16. http://dx.doi.org/10.5989/jsgs.34.9.

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Soucy McCrone, Sharon M., and Tami S. Martin. "Assessing high school students’ understanding of geometric proof." Canadian Journal of Science, Mathematics and Technology Education 4, no. 2 (April 2004): 223–42. http://dx.doi.org/10.1080/14926150409556607.

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Andrews, Brock, Shane Brown, Devlin Montfort, and Michael P. Dixon. "Student Understanding of Sight Distance in Geometric Design." Transportation Research Record: Journal of the Transportation Research Board 2199, no. 1 (January 2010): 1–8. http://dx.doi.org/10.3141/2199-01.

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Dissertations / Theses on the topic "Geometric understanding"

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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’art
Developing 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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Books on the topic "Geometric understanding"

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Understanding geometric algebra for electromagnetic theory. Hoboken, N.J: Wiley-IEEE Press, 2011.

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Arthur, John W. Understanding Geometric Algebra for Electromagnetic Theory. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2011. http://dx.doi.org/10.1002/9781118078549.

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Understanding geometric algebra: Hamilton, Grassmann, and Clifford for computer vision and graphics. Boca Raton: CRC Press, 2015.

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Geometry: Seeing, doing, understanding. 3rd ed. New York: W.H. Freeman and Co., 2003.

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Goodman, Arthur. Understanding elementary algebra with geometry. Minneapolis/St. Paul: West Pub. Co., 1994.

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Klüver, Jürgen. Social Understanding: On Hermeneutics, Geometrical Models and Artificial Intelligence. Dordrecht: Springer Science+Business Media B.V., 2011.

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Lewis, Hirsch, and Goodman Arthur, eds. Understanding elementary algebra with geometry: A course for college students. 4th ed. Pacific Grove, CA: Brooks/Cole Pub. Co., 1998.

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Arthur, Goodman, ed. Understanding elementary algebra with geometry: A course for college students. 6th ed. Belmont, CA: Thomson Brooks/Cole, 2006.

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Hirsch, Lewis. Understanding elementary algebra with geometry: A course for college students. 5th ed. Pacific Grove, CA: Brooks/Cole, 2002.

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Stevens, Roger T. Understanding self-similar fractals: A graphical guide to the curves of nature. Lawrence, Kan: R&D Technical Books, 1995.

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Book chapters on the topic "Geometric understanding"

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Hofrichter, Julian, Jürgen Jost, and Tat Dat Tran. "Geometric Structures and Information Geometry." In Understanding Complex Systems, 45–76. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-52045-2_3.

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Alvarez, Isabelle, and Sophie Martin. "Geometric Robustness of Viability Kernels and Resilience Basins." In Understanding Complex Systems, 193–218. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20423-4_8.

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Johnson, Dana T., Marguerite M. Mason, and Jill Adelson. "The van Hiele Levels of Geometric Understanding." In Polygons Galore!, 10–11. New York: Routledge, 2021. http://dx.doi.org/10.4324/9781003237204-6.

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Goodearl, K. R., and B. Huisgen-Zimmermann. "Understanding Finite Dimensional Representations Generically." In Geometric and Topological Aspects of the Representation Theory of Finite Groups, 131–79. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94033-5_6.

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Kuzniak, Alain. "Understanding Geometric Work through Its Development and Its Transformations." In Transformation - A Fundamental Idea of Mathematics Education, 311–25. New York, NY: Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4614-3489-4_15.

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Yasuda, Kenji. "Algebraic and Geometric Understanding of Cells: Epigenetic Inheritance of Phenotypes Between Generations." In High Resolution Microbial Single Cell Analytics, 55–81. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/10_2010_97.

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Kuzniak, Alain. "Understanding the Nature of the Geometric Work Through Its Development and Its Transformations." In Selected Regular Lectures from the 12th International Congress on Mathematical Education, 1–15. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-17187-6_1.

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Gulkilik, Hilal. "The Role of Virtual Manipulatives in High School Students’ Understanding of Geometric Transformations." In International Perspectives on Teaching and Learning Mathematics with Virtual Manipulatives, 213–43. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-32718-1_10.

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Macruz, Andrea, Ernesto Bueno, Gustavo G. Palma, Jaime Vega, Ricardo A. Palmieri, and Tan Chen Wu. "Measuring Human Perception of Biophilically-Driven Design with Facial Micro-expressions Analysis and EEG Biosensor." In Proceedings of the 2021 DigitalFUTURES, 231–41. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-5983-6_22.

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AbstractThis paper investigates the role technology and neuroscience play in aiding the design process and making meaningful connections between people and nature. Using two workshops as a vehicle, the team introduced advanced technologies and Quantified Self practices that allowed people to use neural data and pattern recognition as feedback for the design process. The objective is to find clues to natural elements of human perception that can inform the design to meet goals for well-being. A pattern network of geometric shapes that achieve a higher level of monitored meditation levels and point toward a positive emotional valence is proposed. By referencing biological forms found in nature, the workshops utilized an algorithmic process that explored how nature can influence architecture. To measure the impact, the team used FaceOSC for capture and an Artificial Neural Network for micro-expression recognition, and a MindWave sensor manufactured by NeuroSky, which documented the human response further. The methodology allowed us to establish a boundary logic, ranking geometric shapes that suggested positive emotions and a higher level of monitored meditation levels. The results pointed us to a deeper level of understanding relative to geometric shapes in design. They indicate a new way to predict how well-being factors can clarify and rationalize a more intuitive design process inspired by nature.
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Gussenhoven, Carlos, and Haike Jacobs. "Feature geometry." In Understanding Phonology, 232–58. Fourth Edition. | Milton Park, Abingdon, Oxon ; New York, NY : Routledge, [2017] | Series: Understanding language series: Routledge, 2017. http://dx.doi.org/10.4324/9781315267982-14.

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Conference papers on the topic "Geometric understanding"

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Zhang, Xiaochun, and Chuancai Liu. "Image understanding using geometric context." In Ninth International Conference on Digital Image Processing (ICDIP 2017), edited by Charles M. Falco and Xudong Jiang. SPIE, 2017. http://dx.doi.org/10.1117/12.2281685.

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Ying, Shihui, Lipeng Cai, Changzhou He, and Yaxin Peng. "Geometric Understanding for Unsupervised Subspace Learning." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. California: International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/579.

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In this paper, we address the unsupervised subspace learning from a geometric viewpoint. First, we formulate the subspace learning as an inverse problem on Grassmannian manifold by considering all subspaces as points on it. Then, to make the model computable, we parameterize the Grassmannian manifold by using an orbit of rotation group action on all standard subspaces, which are spanned by the orthonormal basis. Further, to improve the robustness, we introduce a low-rank regularizer which makes the dimension of subspace as low as possible. Thus, the subspace learning problem is transferred to a minimization problem with variables of rotation and dimension. Then, we adopt the alternately iterative strategy to optimize the variables, where a structure-preserving method, based on the geodesic structure of the rotation group, is designed to update the rotation. Finally, we compare the proposed approach with six state-of-the-art methods on three different kinds of real datasets. The experimental results validate that our proposed method outperforms all compared methods.
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Choi, Wongun, Yu-Wei Chao, Caroline Pantofaru, and Silvio Savarese. "Understanding Indoor Scenes Using 3D Geometric Phrases." In 2013 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2013. http://dx.doi.org/10.1109/cvpr.2013.12.

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Haralick. "Document image understanding: geometric and logical layout." In Proceedings of IEEE Conference on Computer Vision and Pattern Recognition. IEEE Comput. Soc. Press, 1994. http://dx.doi.org/10.1109/cvpr.1994.323855.

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Macko, Martin, Zbynek Krist, Teodor Balaz, Frantisek Racek, and Karel Abraham. "UNDERSTANDING OF GEOMETRIC PROBABILITY USING BALLISTICS EXAMPLES." In 14th International Technology, Education and Development Conference. IATED, 2020. http://dx.doi.org/10.21125/inted.2020.1845.

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Andrews, Brock, and Shane Brown. "An investigation in student conceptual understanding of geometric design." In 2009 39th IEEE Frontiers in Education Conference (FIE). IEEE, 2009. http://dx.doi.org/10.1109/fie.2009.5350578.

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Becker, Jean-Marie, and Thierry Fournel. "A contribution to a geometric understanding of p-norms." In 2012 11th Euro-American Workshop on Information Optics (WIO). IEEE, 2012. http://dx.doi.org/10.1109/wio.2012.6488926.

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Jian Liang, Rongjie Lai, Tsz Wai Wong, and Hongkai Zhao. "Geometric understanding of point clouds using Laplace-Beltrami operator." In 2012 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2012. http://dx.doi.org/10.1109/cvpr.2012.6247678.

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Battiato, S., G. M. Farinella, E. Messina, and G. Puglisi. "Understanding geometric manipulations of images through bovw-based hashing." In 2011 IEEE International Conference on Multimedia and Expo (ICME). IEEE, 2011. http://dx.doi.org/10.1109/icme.2011.6012160.

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Detry, Renaud, Jeremie Papon, and Larry Matthies. "Task-oriented grasping with semantic and geometric scene understanding." In 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2017. http://dx.doi.org/10.1109/iros.2017.8206162.

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Reports on the topic "Geometric understanding"

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Howard, Isaac, Thomas Allard, Ashley Carey, Matthew Priddy, Alta Knizley, and Jameson Shannon. Development of CORPS-STIF 1.0 with application to ultra-high performance concrete (UHPC). Engineer Research and Development Center (U.S.), April 2021. http://dx.doi.org/10.21079/11681/40440.

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This report introduces the first release of CORPS-STIF (Concrete Observations Repository and Predictive Software – Structural and Thermodynamical Integrated Framework). CORPS-STIF is envisioned to be used as a tool to optimize material constituents and geometries of mass concrete placements specifically for ultra-high performance concretes (UHPCs). An observations repository (OR) containing results of 649 mechanical property tests and 10 thermodynamical tests were recorded to be used as inputs for current and future releases. A thermodynamical integrated framework (TIF) was developed where the heat transfer coefficient was a function of temperature and determined at each time step. A structural integrated framework (SIF) modeled strength development in cylinders that underwent isothermal curing. CORPS-STIF represents a step toward understanding and predicting strength gain of UHPC for full-scale structures and specifically in mass concrete.
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Riveros, Guillermo, Felipe Acosta, Reena Patel, and Wayne Hodo. Computational mechanics of the paddlefish rostrum. Engineer Research and Development Center (U.S.), September 2021. http://dx.doi.org/10.21079/11681/41860.

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Purpose – The rostrum of a paddlefish provides hydrodynamic stability during feeding process in addition to detect the food using receptors that are randomly distributed in the rostrum. The exterior tissue of the rostrum covers the cartilage that surrounds the bones forming interlocking star shaped bones. Design/methodology/approach – The aim of this work is to assess the mechanical behavior of four finite element models varying the type of formulation as follows: linear-reduced integration, linear-full integration, quadratic-reduced integration and quadratic-full integration. Also presented is the load transfer mechanisms of the bone structure of the rostrum. Findings – Conclusions are based on comparison among the four models. There is no significant difference between integration orders for similar type of elements. Quadratic-reduced integration formulation resulted in lower structural stiffness compared with linear formulation as seen by higher displacements and stresses than using linearly formulated elements. It is concluded that second-order elements with reduced integration and can model accurately stress concentrations and distributions without over stiffening their general response. Originality/value – The use of advanced computational mechanics techniques to analyze the complex geometry and components of the paddlefish rostrum provides a viable avenue to gain fundamental understanding of the proper finite element formulation needed to successfully obtain the system behavior and hot spot locations.
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