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. Feature detection with . s. cale selection. We want to extract features with characteristic scale that is . covariant. with the image transformation. Blob detection: Basic idea. To detect blobs, convolve the image with a “blob filter” at multiple scales and look for . Computer Vision and Image Processing (CVIP). Ifeoma. Nwogu. inwogu@buffalo.edu. Lecture 11 – Local Features. 1. Schedule. Last class . We started local features. Today. More on local features. Readings for today: . Jacob Beal. Social Concepts in Self-Adaptive and Self-Organising Systems. IEEE SASO. September, 2013. Asymmetry trades robustness for speed. Spanning Tree. Consensus. Laplacian. Consensus. O(diameter). Computer Vision, winter 2012-13. CS Department, . Technion. Topics. The Gaussian Pyramid. The . Laplacian. Pyramid. Applications:. Pattern Matching. Coding (Compression). Enhancement. Blending. Gaussian Pyramid. Jacob Beal. 2013 Spatial Computing Workshop @ AAMAS. May, 2013. PLD-Consensus:. With asymmetry from a self-organizing overlay…. … we can cheaply trade precision for speed.. Motivation: approximate consensus. Achieving scale covariance. Goal: independently detect corresponding regions in scaled versions of the same image. Need . scale selection. mechanism for finding characteristic region size that is . covariant. 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. Begue. ). The Heat Equation on Fractals and other Discrete Domains. Outline. Introduction to . Fractals. Contractions maps and the self-similar identity. The Graph Laplacian. The Heat Equation. The Cycle . keypoint. detection. D. Lowe, . Distinctive . image features from scale-invariant . keypoints. ,. . IJCV. 60 (2), pp. 91-110, 2004. . Keypoint. detection with . s. cale selection. We want to extract . 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:. Matrices of Graphs:. Algorithms and Applications. ICML, June 21, 2016. Daniel A. Spielman. Laplacians. . Interpolation on graphs. Spring networks. . Clustering. . Isotonic regression. Sparsification. Jacob Beal. Social Concepts in Self-Adaptive and Self-Organising Systems. IEEE SASO. September, 2013. Asymmetry trades robustness for speed. Spanning Tree. Consensus. Laplacian. Consensus. O(diameter). 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) .