Manifold statistics for essential matrices

Authors:
Gijs Dubbelman;Leo Dorst;Henk Pijls
Affiliations:
The Robotics Institute, Carnegie Mellon University, Pittsburgh;Faculty of Science, University of Amsterdam, Amsterdam, The Netherlands;Faculty of Science, University of Amsterdam, Amsterdam, The Netherlands
Venue:
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part II
Year:
2012

Citing 16
Cited 0

Uniform Distribution, Distance and Expectation Problems for Geometric Features Processing

Journal of Mathematical Imaging and Vision
Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography

Communications of the ACM
Geometrical Methods in Robotics

Geometrical Methods in Robotics
Optimization Criteria and Geometric Algorithms for Motion and Structure Estimation

International Journal of Computer Vision
Optimization Criteria, Sensitivity and Robustness of Motion and Structure Estimation

ICCV '99 Proceedings of the International Workshop on Vision Algorithms: Theory and Practice
Feature-Based Registration of Medical Images: Estimation and Validation of the Pose Accuracy

MICCAI '98 Proceedings of the First International Conference on Medical Image Computing and Computer-Assisted Intervention
Multiple View Geometry in Computer Vision

Multiple View Geometry in Computer Vision
Simultaneous Multiple 3D Motion Estimation via Mode Finding on Lie Groups

ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
Nonlinear Mean Shift for Clustering over Analytic Manifolds

CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Affine Invariance Revisited

CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 2
Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements

Journal of Mathematical Imaging and Vision
Riemannian geometry for the statistical analysis of diffusion tensor data

Signal Processing
Nonlinear Mean Shift for Robust Pose Estimation

WACV '07 Proceedings of the Eighth IEEE Workshop on Applications of Computer Vision
Essential Matrix Estimation Using Gauss-Newton Iterations on a Manifold

International Journal of Computer Vision
Pedestrian Detection via Classification on Riemannian Manifolds

IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonlinear Mean Shift over Riemannian Manifolds

International Journal of Computer Vision

Quantified Score

Hi-index	0.00

Visualization

Abstract

Riemannian geometry allows for the generalization of statistics designed for Euclidean vector spaces to Riemannian manifolds. It has recently gained popularity within computer vision as many relevant parameter spaces have such a Riemannian manifold structure. Approaches which exploit this have been shown to exhibit improved efficiency and accuracy. The Riemannian logarithmic and exponential mappings are at the core of these approaches. In this contribution we review recently proposed Riemannian mappings for essential matrices and prove that they lead to sub-optimal manifold statistics. We introduce correct Riemannian mappings by utilizing a multiple-geodesic approach and show experimentally that they provide optimal statistics.