Riemannian Computing in Computer Vision

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).

Welcome to Riemannian Computing in Computer Vision.- Recursive Computation of the Fr´echet Mean on Non-Positively Curved Riemannian Manifolds with Applications.- Kernels on Riemannian Manifolds.- Canonical Correlation Analysis on SPD(n) manifolds.- Probabilistic Geodesic Models for Regression and Dimensionality Reduction on Riemannian Manifolds.- Robust Estimation for Computer Vision using Grassmann Manifolds.- Motion Averaging in 3D Reconstruction Problems.- Lie-Theoretic Multi-Robot Localization.- CovarianceWeighted Procrustes Analysis.- Elastic Shape Analysis of Functions, Curves and Trajectories.- Why Use Sobolev Metrics on the Space of Curves.- Elastic Shape Analysis of Surfaces and Images.- Designing a Boosted Classifier on Riemannian Manifolds.- A General Least Squares Regression Framework on Matrix Manifolds for Computer Vision.- Domain Adaptation Using the Grassmann Manifold.- Coordinate Coding on the Riemannian Manifold of Symmetric Positive Definite Matrices for Image Classification.- Summarization and Search over Geometric Spaces.

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