Iso-charts: Stretch-Driven Parameterization via Nonlinear Dimension Reduction Kun Zhou, John Snyder, Baining Guo, Harry Shum presented at SGP, June 2004.

Slides:

Advertisements

Similar presentations

Signal-Specialized Parametrization Microsoft Research 1 Harvard University 2 Microsoft Research 1 Harvard University 2 Steven J. Gortler 2 Hugues Hoppe.

Advertisements

Texture-Mapping Progressive Meshes

Multi-chart Geometry Images Pedro Sander Harvard Harvard Hugues Hoppe Microsoft Research Hugues Hoppe Microsoft Research Steven Gortler Harvard Harvard.

Large Mesh Deformation Using the Volumetric Graph Laplacian

Robust spectral 3D-bodypart segmentation along time Fabio Cuzzolin, Diana Mateus, Edmond Boyer, Radu Horaud Perception project meeting 24/4/2007 Submitted.

Computer examples Tenenbaum, de Silva, Langford “A Global Geometric Framework for Nonlinear Dimensionality Reduction”

1 Manifold Alignment for Multitemporal Hyperspectral Image Classification H. Lexie Yang 1, Melba M. Crawford 2 School of Civil Engineering, Purdue University.

Manifold Learning Dimensionality Reduction. Outline Introduction Dim. Reduction Manifold Isomap Overall procedure Approximating geodesic dist. Dijkstra’s.

SGP 2008 A Local/Global Approach to Mesh Parameterization Ligang Liu Lei Zhang Yin Xu Zhejiang University, China Craig Gotsman Technion, Israel Steven.

Presented by: Mingyuan Zhou Duke University, ECE April 3, 2009

Non-linear Dimensionality Reduction CMPUT 466/551 Nilanjan Ray Prepared on materials from the book Non-linear dimensionality reduction By Lee and Verleysen,

11 A Multi-Source Geodesic Distance Field approach for Procedural Texturing of Complex Meshes A Multi-Source Geodesic Distance Field approach for Procedural.

Consistent Spherical Parameterization Arul Asirvatham, Emil Praun (University of Utah) Hugues Hoppe (Microsoft Research)

University of Joensuu Dept. of Computer Science P.O. Box 111 FIN Joensuu Tel fax Isomap Algorithm.

New quadric metric for simplifying meshes with appearance attributes Hugues Hoppe Microsoft Research IEEE Visualization 1999 Hugues Hoppe Microsoft Research.

Signal-Specialized Parametrization Microsoft Research 1 Harvard University 2 Microsoft Research 1 Harvard University 2 Steven J. Gortler 2 Hugues Hoppe.

“Random Projections on Smooth Manifolds” -A short summary

Iso-charts: Stretch-driven Mesh Parameterization using Spectral Analysis Kun Zhou, John Snyder*, Baining Guo, Heung-Yeung Shum Microsoft Research Asia.

Bounded-distortion Piecewise Mesh Parameterization

LLE and ISOMAP Analysis of Robot Images Rong Xu. Background Intuition of Dimensionality Reduction Linear Approach –PCA(Principal Component Analysis) Nonlinear.

Dimensionality Reduction

Algorithmic Classification of Resonant Orbits Using Persistent Homology in Poincaré Sections Thomas Coffee.

Correspondence & Symmetry

1 Numerical geometry of non-rigid shapes Spectral Methods Tutorial. Spectral Methods Tutorial 6 © Maks Ovsjanikov tosca.cs.technion.ac.il/book Numerical.

Manifold Learning: ISOMAP Alan O'Connor April 29, 2008.

1 Dr. Scott Schaefer Surface Parameterization. Parameterization and Texturing 2/30.

Three Algorithms for Nonlinear Dimensionality Reduction Haixuan Yang Group Meeting Jan. 011, 2005.

Mesh Parameterization: Theory and Practice Non-Planar Domains.

Flattening via Multi- Dimensional Scaling Ron Kimmel Computer Science Department Geometric Image Processing Lab Technion-Israel.

Manifold learning and pattern matching with entropic graphs Alfred O. Hero Dept. EECS, Dept Biomed. Eng., Dept. Statistics University of Michigan - Ann.

A Global Geometric Framework for Nonlinear Dimensionality Reduction Joshua B. Tenenbaum, Vin de Silva, John C. Langford Presented by Napat Triroj.

Texture Mapping using Surface Flattening via Multi-Dimensional Scaling G.Zigelman, R.Kimmel, N.Kiryati IEEE Transactions on Visualization and Computer.

Atul Singh Junior Undergraduate CSE, IIT Kanpur.  Dimension reduction is a technique which is used to represent a high dimensional data in a more compact.

Consistent Parameterizations Arul Asirvatham Committee Members Emil Praun Hugues Hoppe Peter Shirley.

NonLinear Dimensionality Reduction or Unfolding Manifolds Tennenbaum|Silva|Langford [Isomap] Roweis|Saul [Locally Linear Embedding] Presented by Vikas.

Lightseminar: Learned Representation in AI An Introduction to Locally Linear Embedding Lawrence K. Saul Sam T. Roweis presented by Chan-Su Lee.

Dimensionality Reduction. Multimedia DBs Many multimedia applications require efficient indexing in high-dimensions (time-series, images and videos, etc)

Random Projections of Signal Manifolds Michael Wakin and Richard Baraniuk Random Projections for Manifold Learning Chinmay Hegde, Michael Wakin and Richard.

Nonlinear Dimensionality Reduction Approaches. Dimensionality Reduction The goal: The meaningful low-dimensional structures hidden in their high-dimensional.

Projective Texture Atlas for 3D Photography Jonas Sossai Júnior Luiz Velho IMPA.

Manifold learning: Locally Linear Embedding Jieping Ye Department of Computer Science and Engineering Arizona State University

Graph Embedding: A General Framework for Dimensionality Reduction Dong XU School of Computer Engineering Nanyang Technological University

Computer Graphics Some slides courtesy of Pierre Alliez and Craig Gotsman Texture mapping and parameterization.

Computer Vision Lab. SNU Young Ki Baik Nonlinear Dimensionality Reduction Approach (ISOMAP, LLE)

Computer examples Tenenbaum, de Silva, Langford “A Global Geometric Framework for Nonlinear Dimensionality Reduction”

Local Fisher Discriminant Analysis for Supervised Dimensionality Reduction Presented by Xianwang Wang Masashi Sugiyama.

ISOMAP TRACKING WITH PARTICLE FILTER Presented by Nikhil Rane.

GRASP Learning a Kernel Matrix for Nonlinear Dimensionality Reduction Kilian Q. Weinberger, Fei Sha and Lawrence K. Saul ICML’04 Department of Computer.

TextureAmendment Reducing Texture Distortion in Constrained Parameterizations Yu-Wing TaiNational University of Singapore Michael S. BrownNational University.

Manifold learning: MDS and Isomap

1 LING 696B: MDS and non-linear methods of dimension reduction.

Nonlinear Dimensionality Reduction Approach (ISOMAP)

H. Lexie Yang1, Dr. Melba M. Crawford2

Non-Linear Dimensionality Reduction

Spectral Sequencing Based on Graph Distance Rong Liu, Hao Zhang, Oliver van Kaick {lrong, haoz, cs.sfu.ca {lrong, haoz, cs.sfu.ca.

David Levin Tel-Aviv University Afrigraph 2009 Shape Preserving Deformation David Levin Tel-Aviv University Afrigraph 2009 Based on joint works with Yaron.

Optimal Dimensionality of Metric Space for kNN Classification Wei Zhang, Xiangyang Xue, Zichen Sun Yuefei Guo, and Hong Lu Dept. of Computer Science &

Math 285 Project Diffusion Maps Xiaoyan Chong Department of Mathematics and Statistics San Jose State University.

Manifold Learning JAMES MCQUEEN – UW DEPARTMENT OF STATISTICS.

Nonlinear Dimensionality Reduction

Unsupervised Riemannian Clustering of Probability Density Functions

Dimensionality Reduction

Spectral Methods Tutorial 6 1 © Maks Ovsjanikov

Machine Learning Dimensionality Reduction

ISOMAP TRACKING WITH PARTICLE FILTERING

Jianping Fan Dept of CS UNC-Charlotte

Outline Nonlinear Dimension Reduction Brief introduction Isomap LLE

Mesh Parameterization: Theory and Practice

Video Analysis via Nonlinear Dimensionality Reduction Technique

NonLinear Dimensionality Reduction or Unfolding Manifolds

Presentation transcript:

Iso-charts: Stretch-Driven Parameterization via Nonlinear Dimension Reduction Kun Zhou, John Snyder, Baining Guo, Harry Shum presented at SGP, June 2004

Goals of Mesh Parameterization Large Charts Low Distortion

Stretch-Driven Parameterization l Advantages n measures distortion properly for texturing apps l Disadvantages n requires nonlinear optimization (slow!) n provides no help in forming charts –resort to simple heuristics like planarity or compactness l Solution: apply Isomap (NDR technique) n stretch and Isomap related: both preserve lengths n eigenanalysis rather than nonlinear optimization n provides: –good initial guess for stretch optimization –good chartification heuristic via “spectral clustering” l Advantages n measures distortion properly for texturing apps l Disadvantages n requires nonlinear optimization (slow!) n provides no help in forming charts –resort to simple heuristics like planarity or compactness l Solution: apply Isomap (NDR technique) n stretch and Isomap related: both preserve lengths n eigenanalysis rather than nonlinear optimization n provides: –good initial guess for stretch optimization –good chartification heuristic via “spectral clustering”

IsoMapIsoMap Data points in high dimensional space [Tenenbaum et al, 2000] Data points in low dimensional space Neighborhood graph

Surface Spectral Analysis Geodesic Distance Distortion (GDD)

Surface Spectral Analysis 1. Construct matrix of squared geodesic distances D N

Surface Spectral Analysis 2. Perform eigenanalysis on D N to get embedding coords y i

Isomap → low stretch (take first two coords) IsoMap, L 2 = 1.04, 2s IsoMap+Optimization, L 2 = 1.03, 6s [stretch, Sander01], L 2 = 1.04, 222s [stretch, Sander02], L 2 = 1.03, 39s

Isomap → good charts (spectral clustering) Analysis Clustering

ResultsResults 19 charts, L 2 =1.03, running time 98s, 97k faces

ResultsResults 38 charts, L 2 =1.07, running time 287s, 150k faces

ResultsResults 23 charts, L 2 =1.06, running time 162s, 112k faces

ResultsResults 11 charts, L 2 =1.01, running time 4s, 10k faces

Remeshing Comparison Original model [Sander03], 79.5dBIso-chart, 82.9dB

Texture Synthesis Results