PPT-Laplacian

Matrices of Graphs Algorithms and Applications ICML June 21 2016 Daniel A Spielman Laplacians Interpolation on graphs Spring networks Clustering Isotonic regression Sparsification. 1 Introduction Spectral graph theory has a long history In the early days matrix theory and linear algebra were used to analyze adjacency matrices of graphs Algebraic meth ods have proven to be especially e64256ective in treating graphs which are reg Computational Photography. Connelly Barnes. Many slides from . James Hays, Alexei . Efros. Blending + Compositing. Previously:. Color perception in humans, cameras. Bayer mosaic. Color spaces (L*a*b*, RGB, HSV). Classification Outline. Introduction, Overview. Classification using Graphs. Graph classification – Direct Product Kernel. Predictive Toxicology example dataset. Vertex classification – . Laplacian. Computer Vision, winter 2012-13. CS Department, . Technion. Topics. The Gaussian Pyramid. The . Laplacian. Pyramid. Applications:. Pattern Matching. Coding (Compression). Enhancement. Blending. Gaussian Pyramid. n. 1/2. n. 1/3. 2D. 3D. Space (fill):. O(n log n). O(n . 4/3 . ). Time (flops):. O(n . 3/2 . ). O(n . 2 . ). Time and space to solve any problem on any well-shaped finite element mesh. Complexity of linear solvers. c. t. r. a. l. methods. © Alexander & Michael Bronstein, 2006-2009. © Michael Bronstein, 2010. tosca.cs.technion.ac.il/book. 048921 Advanced topics in vision. Processing and Analysis of Geometric Shapes. and Semi-Supervised Learning. Longin Jan Latecki. Based on :. Xiaojin. Zhu. Semi-Supervised Learning with Graphs. PhD thesis. CMU-LTI-05-192, May 2005. Page, Lawrence and . Brin. , Sergey and . Motwani. Edges = jumps in brightness/color. Brightness jumps marked in white. Edges. Edges = jumps in brightness/color. Important!. Give object outlines and . shapes. Brightness jumps marked in white. Edges. Edges = jumps in brightness/color. Matrices of Graphs:. Algorithms and Applications. ICML, June 21, 2016. Daniel A. Spielman. Laplacians. . Interpolation on graphs. Spring networks. . Clustering. . Isotonic regression. Sparsification. mailing . list:. http. ://www.wisdom.weizmann.ac.il/~. vision/courses/2017_1/intro_to_vision/index.html. (or just google . “Weizmann Vision”).. 2D Image. Fourier Spectrum. Convolution. Good for:. Motion Editing. Manmyung. Kim, . Kyunglyul. Hyun, . Jongmin. Kim, . Jehee. Lee. Seoul National University. Multi-character Interaction. : synchronization in space and time . Cumbersome to Maintain Synchronization. David S. Bindel. Cornell University. ABSTRACT. Most spectral graph theory: . extremal. eigenvalues . and associated eigenvectors.. Spectral geometry, material science: also eigenvalue . distributions. Kazhdan. [. Taubin. , 1995] . A Signal Processing Approach to Fair Surface . Design. [. Desbrun. , . et al.. , 1999] Implicit Fairing of Arbitrary Meshes…. [. Vallet. and Levy, 2008] . Spectral Geometry Processing with Manifold . Fall 2016. Review. Alignment. Registering source to target by rotation and translation. Rigid-body transformations. Methods. Aligning principle directions (PCA). Aligning corresponding points (SVD). Iterative improvement (ICP) .