Relevant bibliographies by topics / Laplacian of Gaussian

Contents

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

Academic literature on the topic 'Laplacian of Gaussian'

Author: Grafiati
Published: 4 June 2021
Last updated: 10 February 2022

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Journal articles on the topic "Laplacian of Gaussian"

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Gazor, S., and Wei Zhang. "Speech enhancement employing Laplacian-Gaussian mixture." IEEE Transactions on Speech and Audio Processing 13, no. 5 (September 2005): 896–904. http://dx.doi.org/10.1109/tsa.2005.851943.

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Resdiana Hutagalung. "Mendeteksi Tepi Citra Penyakit Hemokromatosis Dengan Menggunakan Metode Log (Laplacian Of Gaussian)." JUKI : Jurnal Komputer dan Informatika 2, no. 1 (May 27, 2020): 49–58. http://dx.doi.org/10.53842/juki.v2i1.28.

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Hemochromatosis is a genetic or hereditary disease. Abnormalities of iron metabolism characterized by excessive deposition of iron in the tissues. Derivative conditions that cause the body to absorb too much iron from the food eaten. Excess iron is stored in organs such as the liver, heart and pancreas. Excess iron can cause toxicity to these organs, and is life threatening because it can cause diseases such as cancer, cardiac arrhythmias, and cirrhosis. LOG method (Laplacian of Gaussian) is a second-order edge detection operator or has a derivative filter whose function can detect areas that have rapid changes (rapit change) such as edges (edges) in the image. But this laplacian is very sensitive or low to the presence of noise. For that, the image will be smoothed first by using Gaussian. Thus a new derivative function is known, namely LoG or Laplacian of Gaussian. Many methods are used in solving edge detection problems, including Prewitt Operators, Sobel Operators, Canny Operators, but among all these methods, the Laplacian of Gaussian method is the method most often used in detecting edges. For this reason, it is hoped that the LoG (Laplacian of Gaussian) method can help to detect hemochromatosis. Can help how severe the disease has developed, and what symptoms can later be caused, so that it can help in the healing process.
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Gibson, Jerry, and Hoontaek Oh. "Mutual Information Loss in Pyramidal Image Processing." Information 11, no. 6 (June 15, 2020): 322. http://dx.doi.org/10.3390/info11060322.

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Gaussian and Laplacian pyramids have long been important for image analysis and compression. More recently, multiresolution pyramids have become an important component of machine learning and deep learning for image analysis and image recognition. Constructing Gaussian and Laplacian pyramids consists of a series of filtering, decimation, and differencing operations, and the quality indicator is usually mean squared reconstruction error in comparison to the original image. We present a new characterization of the information loss in a Gaussian pyramid in terms of the change in mutual information. More specifically, we show that one half the log ratio of entropy powers between two stages in a Gaussian pyramid is equal to the difference in mutual information between these two stages. We show that this relationship holds for a wide variety of probability distributions and present several examples of analyzing Gaussian and Laplacian pyramids for different images.
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Chen, J. S., A. Huertas, and G. Medioni. "Fast Convolution with Laplacian-of-Gaussian Masks." IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI-9, no. 4 (July 1987): 584–90. http://dx.doi.org/10.1109/tpami.1987.4767946.

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Tabbone, S. A., L. Alonso, and D. Ziou. "Behavior of the Laplacian of Gaussian Extrema." Journal of Mathematical Imaging and Vision 23, no. 1 (July 2005): 107–28. http://dx.doi.org/10.1007/s10851-005-4970-7.

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Singh, Meghna, Mrinal K. Mandal, and Anup Basu. "Gaussian and Laplacian of Gaussian weighting functions for robust feature based tracking." Pattern Recognition Letters 26, no. 13 (October 2005): 1995–2005. http://dx.doi.org/10.1016/j.patrec.2005.03.015.

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Sumaiya, M. N., and R. Shantha Selva Kumari. "Satellite Image Change Detection Using Laplacian–Gaussian Distributions." Wireless Personal Communications 97, no. 3 (August 4, 2017): 4621–30. http://dx.doi.org/10.1007/s11277-017-4741-y.

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Pei, Soo-Chang, and Ji-Hwei Horng. "Design of FIR bilevel Laplacian-of-Gaussian filter." Signal Processing 82, no. 4 (April 2002): 677–91. http://dx.doi.org/10.1016/s0165-1684(02)00136-6.

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Cho, Yongju, Dojin Kim, Saleh Saeed, Muhammad Umer Kakli, Soon-Heung Jung, Jeongil Seo, and Unsang Park. "Keypoint Detection Using Higher Order Laplacian of Gaussian." IEEE Access 8 (2020): 10416–25. http://dx.doi.org/10.1109/access.2020.2965169.

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He, Xiaofei, Deng Cai, Yuanlong Shao, Hujun Bao, and Jiawei Han. "Laplacian Regularized Gaussian Mixture Model for Data Clustering." IEEE Transactions on Knowledge and Data Engineering 23, no. 9 (September 2011): 1406–18. http://dx.doi.org/10.1109/tkde.2010.259.

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Dissertations / Theses on the topic "Laplacian of Gaussian"

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Jakkula, Vinayak Reddy. "Efficient feature detection using OBAloG : optimized box approximation of Laplacian of Gaussian." Thesis, Manhattan, Kan. : Kansas State University, 2010. http://hdl.handle.net/2097/3651.

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Chen, Luna. "Fast generation of Gaussian and Laplacian image pyramids using an FPGA-based custom computing platform." Thesis, This resource online, 1994. http://scholar.lib.vt.edu/theses/available/etd-12042009-020239/.

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Mavridou, Evanthia. "Robust image description with laplacian profile and radial Fourier transform." Thesis, Grenoble, 2014. http://www.theses.fr/2014GRENM065/document.

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L'objectif de cette thèse est l'étude d'un descripteur d'images adapté à une grande variété d'applications. Nous cherchons à obtenir un descripteur robuste et discriminant, facile à adapter et peu coûteux en calcul et en mémoire.Nous définissons un nouveau descripteur, composé de valeurs du Laplacien à différentes échelles et de valeurs d'une transformée de Fourier radiale, calculées à partir d'une pyramide Gaussienne. Ce descripteur capture une information de forme multi-échelle autour d'un point de l'image. L'expérimentation a montré que malgré une taille mémoire réduite les performances en robustesse et en pouvoir discriminant de ce descripteur sont à la heuteur de l'état de l'art.Nous avons expérimenté ce descripteur avec trois types de tâches différentes.Le premier type de tâche est la mise en correspondance de points-clés avec des images transformées par rotation, changement d'échelle, floutage, codage JPEG, changement de point de vue, ou changement d'éclairage. Nous montrons que la performance de notre descripteur est au niveau des meilleurs descripteurs connus dans l'état de l'art. Le deuxième type de tâche est la détection de formes. Nous avons utilisé le descripteur pour la création de deux détecteurs de personnes, construits avec Adaboost. Comparé à un détecteur semblable construit avec des histogrammes de gradients (HOG) nos détecteurs sont très compétitifs tout en utilisant des descripteurs sensiblement plus compacts. Le dernier type de tâche est la détection de symétries de réflexion dans des images "du monde réel". Nous proposons une technique de détection d'axes potentiels de symétries en miroir. Avec cette tâche nous montrons que notre descripteur peut être genéralisé à des situations complexes. L'expérimentation montre que cette méthode est robuste et discriminante, tout en conservant un faible coût en calcul et en mémoire
In this thesis we explore a new image description method composed of a multi-scale vector of Laplacians of Gaussians, the Laplacian Profile, and a Radial Fourier Transform. This method captures shape information with different proportions around a point in the image. A Gaussian pyramid of scaled images is used for the extraction of the descriptor vectors. The aim of this new method is to provide image description that can be suitable for diverse applications. Adjustability as well as low computational and memory needs are as important as robustness and discrimination power. We created a method with the ability to capture the image signal efficiently with descriptor vectors of particularly small length compared to the state of the art. Experiments show that despite its small vector length, the new descriptor shows reasonable robustness and discrimination power that are competitive to the state of the art performance.We test our proposed image description method on three different visual tasks. The first task is keypoint matching for images that have undergone image transformations like rotation, scaling, blurring, JPEG compression, changes in viewpoint and changes in light. We show that against other methods from the state of the art, the proposed descriptor performs equivalently with a very small vector length. The second task is on pattern detection. We use the proposed descriptor to create two different Adaboost based detectors for people detection in images. Compared to a similar detector using Histograms of Oriented Gradients (HOG), the detectors with the proposed method show competitive performance using significantly smaller descriptor vectors. The last task is on reflection symmetry detection in real world images. We introduce a technique that exploits the proposed descriptor for detecting possible symmetry axes for the two reflecting parts of a mirror symmetric pattern. This technique introduces constraints and ideas of how to collect more efficiently the information that is important to identify reflection symmetry in images. With this task we show that the proposed descriptor can be generalized for rather complicated applications. The set of the experiments confirms the qualities of the proposed method of being easily adjustable and requires relatively low computational and storage requirements while remaining robust and discriminative
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Brand, Howard James Jarrell. "Towards Autonomous Cotton Yield Monitoring." Thesis, Virginia Tech, 2016. http://hdl.handle.net/10919/72908.

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One important parameter of interest in remote sensing to date is yield variability. Proper understanding of yield variability provides insight on the geo-positional dependences of field yields and insight on zone management strategies. Estimating cotton yield and observing cotton yield variability has proven to be a challenging problem due to the complex fruiting behavior of cotton from reactions to environmental conditions. Current methods require expensive sensory equipment on large manned aircrafts and satellites. Other systems, such as cotton yield monitors, are often subject to error due to the collection of dust/trash on photo sensors. This study was aimed towards the development of a miniature unmanned aerial system that utilized a first-person view (FPV) color camera for measuring cotton yield variability. Outcomes of the study led to the development of a method for estimating cotton yield variability from images of experimental cotton plot field taken at harvest time in 2014. These plots were treated with nitrogen fertilizer at five different rates to insure variations in cotton yield across the field. The cotton yield estimates were based on the cotton unit coverage (CUC) observed as the cotton boll image signal density. The cotton boll signals were extracted via their diffusion potential in the image intensity space. This was robust to gradients in illumination caused by cloud coverage as well as fruiting positions in the field. These estimates were provided at a much higher spatial resolution (9.0 cm2) at comparable correlations (R2=0.74) with current expensive systems. This method could prove useful for the development of low cost automated systems for cotton yield estimation as well as yield estimation systems for other crops.
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Jiménez, Tauste Albert, and Niklas Rydberg. "Area of Interest Identification Using Circle Hough Transform and Outlier Removal for ELISpot and FluoroSpot Images." Thesis, KTH, Skolan för elektroteknik och datavetenskap (EECS), 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-254256.

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The aim of this project is to design an algorithm that identifies the Area of Interest (AOI) in ELISpot and FluoroSpot images. ELISpot and FluoroSpot are two varieties of a biochemical test used to analyze immune responses by quantifying the amount of cytokine secreted by cells. ELISpot and FluoroSpot images show a well that contains the cytokinesecreting cells which appear as scattered spots. Prior to counting the number of spots, it is required to detect the area in which to count the spots, i.e. the area delimited by the contour of the well. We propose to use the Circle Hough Transform together with filtering and the Laplacian of Gaussian edge detector in order to accurately detect such area. Furthermore we develop an outlier removal method that contributes to increase the robustness of the proposed detection method. Finally we compare our algorithm with another algorithm already in use. A Swedish biotech company called Mabtech has implemented an AOI identifier in the same field. Our proposed algorithm proves to be more robust and provides consistent results for all the images in the dataset.
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Bednařík, Jan. "Nalezení známého objektu v sérii digitálních snímků." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2011. http://www.nusl.cz/ntk/nusl-218973.

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The aim of the thesis is detection of a known object in series of pictures. Detection is divided into two methods. First method is based on edge and color detection and comparison. Edge detection is based on detection using both Gradient and Laplacian, so on the first-order and the second-order derivative. Sobel operators were used as well as Laplacian of gaussian method. Thresholding is also used as well as autothreshold calculation. There are two variants of color detection considered in the thesis, direct color comparison and detection based on interest color search. The second part of the thesis is based on interested point detection using a modified SURF method to detect a known object in series of pictures.
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Sharpnack, James. "Graph Structured Normal Means Inference." Research Showcase @ CMU, 2013. http://repository.cmu.edu/dissertations/246.

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This thesis addresses statistical estimation and testing of signals over a graph when measurements are noisy and high-dimensional. Graph structured patterns appear in applications as diverse as sensor networks, virology in human networks, congestion in internet routers, and advertising in social networks. We will develop asymptotic guarantees of the performance of statistical estimators and tests, by stating conditions for consistency by properties of the graph (e.g. graph spectra). The goal of this thesis is to demonstrate theoretically that by exploiting the graph structure one can achieve statistical consistency in extremely noisy conditions. We begin with the study of a projection estimator called Laplacian eigenmaps, and find that eigenvalue concentration plays a central role in the ability to estimate graph structured patterns. We continue with the study of the edge lasso, a least squares procedure with total variation penalty, and determine combinatorial conditions under which changepoints (edges across which the underlying signal changes) on the graph are recovered. We will shift focus to testing for anomalous activations in the graph, using the scan statistic relaxations, the spectral scan statistic and the graph ellipsoid scan statistic. We will also show how one can form a decomposition of the graph from a spanning tree which will lead to a test for activity in the graph. This will lead to the construction of a spanning tree wavelet basis, which can be used to localize activations on the graph.
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Simpson, Daniel Peter. "Krylov subspace methods for approximating functions of symmetric positive definite matrices with applications to applied statistics and anomalous diffusion." Queensland University of Technology, 2008. http://eprints.qut.edu.au/29751/.

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Matrix function approximation is a current focus of worldwide interest and finds application in a variety of areas of applied mathematics and statistics. In this thesis we focus on the approximation of A..=2b, where A 2 Rnn is a large, sparse symmetric positive definite matrix and b 2 Rn is a vector. In particular, we will focus on matrix function techniques for sampling from Gaussian Markov random fields in applied statistics and the solution of fractional-in-space partial differential equations. Gaussian Markov random fields (GMRFs) are multivariate normal random variables characterised by a sparse precision (inverse covariance) matrix. GMRFs are popular models in computational spatial statistics as the sparse structure can be exploited, typically through the use of the sparse Cholesky decomposition, to construct fast sampling methods. It is well known, however, that for sufficiently large problems, iterative methods for solving linear systems outperform direct methods. Fractional-in-space partial differential equations arise in models of processes undergoing anomalous diffusion. Unfortunately, as the fractional Laplacian is a non-local operator, numerical methods based on the direct discretisation of these equations typically requires the solution of dense linear systems, which is impractical for fine discretisations. In this thesis, novel applications of Krylov subspace approximations to matrix functions for both of these problems are investigated. Matrix functions arise when sampling from a GMRF by noting that the Cholesky decomposition A = LLT is, essentially, a `square root' of the precision matrix A. Therefore, we can replace the usual sampling method, which forms x = L..T z, with x = A..1=2z, where z is a vector of independent and identically distributed standard normal random variables. Similarly, the matrix transfer technique can be used to build solutions to the fractional Poisson equation of the form n = A..=2b, where A is the finite difference approximation to the Laplacian. Hence both applications require the approximation of f(A)b, where f(t) = t..=2 and A is sparse. In this thesis we will compare the Lanczos approximation, the shift-and-invert Lanczos approximation, the extended Krylov subspace method, rational approximations and the restarted Lanczos approximation for approximating matrix functions of this form. A number of new and novel results are presented in this thesis. Firstly, we prove the convergence of the matrix transfer technique for the solution of the fractional Poisson equation and we give conditions by which the finite difference discretisation can be replaced by other methods for discretising the Laplacian. We then investigate a number of methods for approximating matrix functions of the form A..=2b and investigate stopping criteria for these methods. In particular, we derive a new method for restarting the Lanczos approximation to f(A)b. We then apply these techniques to the problem of sampling from a GMRF and construct a full suite of methods for sampling conditioned on linear constraints and approximating the likelihood. Finally, we consider the problem of sampling from a generalised Matern random field, which combines our techniques for solving fractional-in-space partial differential equations with our method for sampling from GMRFs.
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Bao, Xin. "Sketch-based intuitive 3D model deformations." Thesis, University of Manchester, 2014. https://www.research.manchester.ac.uk/portal/en/theses/sketchbased-intuitive-3d-model-deformations(2c12a1f9-cf0c-45d1-926e-a5f3db0d5acb).html.

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In 3D modelling software, deformations are used to add, to remove, or to modify geometric features of existing 3D models to create new models with similar but slightly different details. Traditional techniques for deforming virtual 3D models require users to explicitly define control points and regions of interest (ROIs), and to define precisely how to deform ROIs using control points. The awkwardness of defining these factors in traditional 3D modelling software makes it difficult for people with limited experience of 3D modelling to deform existing 3D models as they expect. As applications which require virtual 3D model processing become more and more widespread, it becomes increasingly desirable to lower the "difficulty of use" threshold of 3D model deformations for users. This thesis argues that the user experience, in terms of intuitiveness and ease of use, of a user interface for deforming virtual 3D models, can be greatly enhanced by employing sketch-based 3D model deformation techniques, which require the minimal quantities of interactions, while keeping the plausibility of the results of deformations as well as the responsiveness of the algorithms, based on modern home grade computing devices. A prototype system for sketch-based 3D model deformations is developed and implemented to support this hypothesis, which allows the user to perform a deformation using a single deforming stroke, eliminating the need to explicitly select control points, the ROI and the deforming operation. GPU based accelerations have been employed to optimise the runtime performance of the system, so that the system is responsive enough for real-time interactions. The studies of the runtime performance and the usability of the prototype system are conducted to provide evidence to support the hypothesis.
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Janda, Miloš. "Detekce hran pomocí neuronové sítě." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2010. http://www.nusl.cz/ntk/nusl-237175.

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Aim of this thesis is description of neural network based edge detection methods that are substitute for classic methods of detection using edge operators. First chapters generally discussed the issues of image processing, edge detection and neural networks. The objective of the main part is to show process of generating synthetic images, extracting training datasets and discussing variants of suitable topologies of neural networks for purpose of edge detection. The last part of the thesis is dedicated to evaluating and measuring accuracy values of neural network.
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Books on the topic "Laplacian of Gaussian"

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Deruelle, Nathalie, and Jean-Philippe Uzan. Curvilinear coordinates. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0003.

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This chapter presents a discussion on curvilinear coordinates in line with the introduction on Cartesian coordinates in Chapter 1. First, the chapter introduces a new system C of curvilinear coordinates xⁱ = xⁱ(Xj) (also sometimes referred to as Gaussian coordinates), which are nonlinearly related to Cartesian coordinates. It then introduces the components of the covariant derivative, before considering parallel transport in a system of curvilinear coordinates. Next, the chapter shows how connection coefficients of the covariant derivative as well as the Euclidean metric can be related to each other. Finally, this chapter turns to the kinematics of a point particle as well as the divergence and Laplacian of a vector and the Levi-Civita symbol and the volume element.
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Book chapters on the topic "Laplacian of Gaussian"

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Kim, Hyuntae, Jingyu Do, Gyuyeong Kim, Jangsik Park, and Yunsik Yu. "Vehicle Detection Using Running Gaussian Average and Laplacian of Gaussian in the Nighttime." In Communications in Computer and Information Science, 172–77. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-35521-9_25.

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Kozhan, Rostyslav. "On Gaussian random matrices coupled to the discrete Laplacian." In Analysis as a Tool in Mathematical Physics, 434–47. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-31531-3_24.

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Terdik, Gyorgy H. "Covariance Functions for Gaussian Laplacian Fields in Higher Dimension." In Contributions to Statistics, 19–29. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-56219-9_2.

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Karande, Kailash Jagannath, and Sanjay Nilkanth Talbar. "Laplacian of Gaussian Edge Detection for Face Recognition Using ICA." In Independent Component Analysis of Edge Information for Face Recognition, 35–47. India: Springer India, 2013. http://dx.doi.org/10.1007/978-81-322-1512-7_3.

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Ferro, Luis, Pedro Leal, Marco Marques, Joana Maciel, Marta I. Oliveira, Mario A. Barbosa, and Pedro Quelhas. "Multinuclear Cell Analysis Using Laplacian of Gaussian and Delaunay Graphs." In Pattern Recognition and Image Analysis, 441–49. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-38628-2_52.

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Karande, Kailash Jagannath, and Sanjay Nilkanth Talbar. "Oriented Laplacian of Gaussian Edge Detection for Face Recognition Using ICA." In Independent Component Analysis of Edge Information for Face Recognition, 49–61. India: Springer India, 2013. http://dx.doi.org/10.1007/978-81-322-1512-7_4.

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Boyer, K. L., and G. E. Sotak. "Depth Perception for Robots: Structural Stereo from Extended Laplacian-of-Gaussian Features." In Advanced Robotics: 1989, 349–59. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-83957-3_24.

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Xue, Wufeng, Xuanqin Mou, and Lei Zhang. "Decoupled Marginal Distribution of Gradient Magnitude and Laplacian of Gaussian for Texture Classification." In Communications in Computer and Information Science, 418–28. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-48558-3_42.

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Iwanowski, Marcin. "Image Contrast Enhancement Based on Laplacian-of-Gaussian Filter Combined with Morphological Reconstruction." In Advances in Intelligent Systems and Computing, 305–15. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-19738-4_31.

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Mabaso, Matsilele, Daniel Withey, and Bhekisipho Twala. "An Extension of 2D Laplacian of Gaussian (LoG)-Based Spot Detection Method to 3D." In Advances in Intelligent Systems and Computing, 15–26. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-10-7868-2_2.

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Conference papers on the topic "Laplacian of Gaussian"

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Shenoy, Saahil, and Dimitry Gorinevsky. "Gaussian-Laplacian mixture model for electricity market." In 2014 IEEE 53rd Annual Conference on Decision and Control (CDC). IEEE, 2014. http://dx.doi.org/10.1109/cdc.2014.7039647.

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Singh, M., M. Mandal, and A. Basu. "Robust KLT tracking with Gaussian and Laplacian of Gaussian weighting functions." In Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004. IEEE, 2004. http://dx.doi.org/10.1109/icpr.2004.1333859.

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Gao, Yicheng, Jian Yang, Huan Wang, and Hongyang Bai. "Object Tracking via Multi-task Gaussian-Laplacian Regression." In 2013 2nd IAPR Asian Conference on Pattern Recognition (ACPR). IEEE, 2013. http://dx.doi.org/10.1109/acpr.2013.128.

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Nandhini, R., and T. Sivasakthi. "Underwater Image Detection using Laplacian and Gaussian Technique." In 2020 7th International Conference on Smart Structures and Systems (ICSSS). IEEE, 2020. http://dx.doi.org/10.1109/icsss49621.2020.9202077.

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Eberly, David H., Daniel S. Fritsch, and Charles Kurak. "Filtering with a normalized Laplacian of a Gaussian kernel." In San Diego '92, edited by David C. Wilson and Joseph N. Wilson. SPIE, 1992. http://dx.doi.org/10.1117/12.130889.

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Nutter, B., and S. Mitra. "Fast Implementation Of A Laplacian Of Gaussian Edge Detector." In 33rd Annual Techincal Symposium, edited by Andrew G. Tescher. SPIE, 1990. http://dx.doi.org/10.1117/12.962324.

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Chen, Zitai, Chuan Chen, Zong Zhang, Zibin Zheng, and Qingsong Zou. "Variational Graph Embedding and Clustering with Laplacian Eigenmaps." 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.2019/297.

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As a fundamental machine learning problem, graph clustering has facilitated various real-world applications, and tremendous efforts had been devoted to it in the past few decades. However, most of the existing methods like spectral clustering suffer from the sparsity, scalability, robustness and handling high dimensional raw information in clustering. To address this issue, we propose a deep probabilistic model, called Variational Graph Embedding and Clustering with Laplacian Eigenmaps (VGECLE), which learns node embeddings and assigns node clusters simultaneously. It represents each node as a Gaussian distribution to disentangle the true embedding position and the uncertainty from the graph. With a Mixture of Gaussian (MoG) prior, VGECLE is capable of learning an interpretable clustering by the variational inference and generative process. In order to learn the pairwise relationships better, we propose a Teacher-Student mechanism encouraging node to learn a better Gaussian from its instant neighbors in the stochastic gradient descent (SGD) training fashion. By optimizing the graph embedding and the graph clustering problem as a whole, our model can fully take the advantages in their correlation. To our best knowledge, we are the first to tackle graph clustering in a deep probabilistic viewpoint. We perform extensive experiments on both synthetic and real-world networks to corroborate the effectiveness and efficiency of the proposed framework.
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Yuan, Suzhen, Salvador E. Venegas-Andraca, Chaoping Zhu, Yan Wang, Xuefeng Mao, and Yuan Luo. "Fast Laplacian of Gaussian Edge Detection Algorithm for Quantum Images." In 2019 IEEE International Conferences on Ubiquitous Computing & Communications (IUCC) and Data Science and Computational Intelligence (DSCI) and Smart Computing, Networking and Services (SmartCNS). IEEE, 2019. http://dx.doi.org/10.1109/iucc/dsci/smartcns.2019.00162.

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Anand, Ashish, Sanjaya Shankar Tripathy, and R. Sukesh Kumar. "An improved edge detection using morphological Laplacian of Gaussian operator." In 2015 2nd International Conference on Signal Processing and Integrated Networks (SPIN). IEEE, 2015. http://dx.doi.org/10.1109/spin.2015.7095391.

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Mpinda Ataky, Steve Tsham, Jonathan de Matos, Alceu de S. Britto, Luiz E. S. Oliveira, and Alessandro L. Koerich. "Data Augmentation for Histopathological Images Based on Gaussian-Laplacian Pyramid Blending." In 2020 International Joint Conference on Neural Networks (IJCNN). IEEE, 2020. http://dx.doi.org/10.1109/ijcnn48605.2020.9206855.

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