Riemannian Computing in Computer Vision

1. Front Matter

   Pages i-vi

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2. Welcome to Riemannian Computing in Computer Vision

   • Anuj Srivastava, Pavan K. Turaga

   Pages 1-18

3. Statistical Computing on Manifolds

   1. Front Matter

      Pages 19-19

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   2. Recursive Computation of the Fréchet Mean on Non-positively Curved Riemannian Manifolds with Applications

      • Guang Cheng, Jeffrey Ho, Hesamoddin Salehian, Baba C. Vemuri

      Pages 21-43

   3. Kernels on Riemannian Manifolds

      • Sadeep Jayasumana, Richard Hartley, Mathieu Salzmann

      Pages 45-67

   4. Canonical Correlation Analysis on SPD(n) Manifolds

      • Hyunwoo J. Kim, Nagesh Adluru, Barbara B. Bendlin, Sterling C. Johnson, Baba C. Vemuri, Vikas Singh

      Pages 69-100

   5. Probabilistic Geodesic Models for Regression and Dimensionality Reduction on Riemannian Manifolds

      • P. Thomas Fletcher, Miaomiao Zhang

      Pages 101-121

4. Color, Motion, and Stereo

   1. Front Matter

      Pages 123-123

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   2. Robust Estimation for Computer Vision Using Grassmann Manifolds

      • Saket Anand, Sushil Mittal, Peter Meer

      Pages 125-144

   3. Motion Averaging in 3D Reconstruction Problems

      • Venu Madhav Govindu

      Pages 145-164

   4. Lie-Theoretic Multi-Robot Localization

      • Xiao Li, Gregory S. Chirikjian

      Pages 165-186

5. Shapes, Surfaces, and Trajectories

   1. Front Matter

      Pages 187-187

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   2. Covariance Weighted Procrustes Analysis

      • Christopher J. Brignell, Ian L. Dryden, William J. Browne

      Pages 189-209

   3. Elastic Shape Analysis of Functions, Curves and Trajectories

      • Shantanu H. Joshi, Jingyong Su, Zhengwu Zhang, Boulbaba Ben Amor

      Pages 211-231

   4. Why Use Sobolev Metrics on the Space of Curves

      • Martin Bauer, Martins Bruveris, Peter W. Michor

      Pages 233-255

   5. Elastic Shape Analysis of Surfaces and Images

      • Sebastian Kurtek, Ian H. Jermyn, Qian Xie, Eric Klassen, Hamid Laga

      Pages 257-277

6. Objects, Humans, and Activity

   1. Front Matter

      Pages 279-279

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   2. Designing a Boosted Classifier on Riemannian Manifolds

      • Fatih Porikli, Oncel Tuzel, Peter Meer

      Pages 281-301

   3. A General Least Squares Regression Framework on Matrix Manifolds for Computer Vision

      • Yui Man Lui

      Pages 303-323

   4. Domain Adaptation Using the Grassmann Manifold

      • David A. Shaw, Rama Chellappa

      Pages 325-343

This book presents a comprehensive treatise on Riemannian geometric computations and related statistical inferences in several computer vision problems. This edited volume includes chapter contributions from leading figures in the field of computer vision who are applying Riemannian geometric approaches in problems such as face recognition, activity recognition, object detection, biomedical image analysis, and structure-from-motion. Some of the mathematical entities that necessitate a geometric analysis include rotation matrices (e.g. in modeling camera motion), stick figures (e.g. for activity recognition), subspace comparisons (e.g. in face recognition), symmetric positive-definite matrices (e.g. in diffusion tensor imaging), and function-spaces (e.g. in studying shapes of closed contours).

• Diffusion Tensor Imaging
• Grassmann Manifold
• Inferences on Nonlinear Manifolds
• Linear Dynamical Models
• Riemannian Computing
• Riemannian Computing in Computer Vision
• Riemannian Geometry
• Tensor Manifold

• Arizona State University, Tempe, USA

  Pavan K. Turaga

• Florida State University, Tallahassee, USA

  Anuj Srivastava

Pavan Turaga is an Assistant Professor at Arizona State University Anuj Srivastava is a Professor at Florida State University

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