Variational analysis of spherical images

Authors:
Atsushi Imiya;Hironobu Sugaya;Akihiko Torii;Yoshihiko Mochizuki
Affiliations:
Institute of Media and Information Technology, Chiba University;School of Science and Technology, Chiba University, Chiba, Japan;School of Science and Technology, Chiba University, Chiba, Japan;School of Science and Technology, Chiba University, Chiba, Japan
Venue:
CAIP'05 Proceedings of the 11th international conference on Computer Analysis of Images and Patterns
Year:
2005

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Abstract

This paper focuses on variational image analysis on a sphere. Since a sphere is a closed Riemannian manifold with the positive constant curvature and no holes, a sphere has similar geometrical properties with a plane, whose curvature is zero. Images observed through a catadioptric system with a conic-mirror and a dioptric system with fish-eye lens are transformed to images on the sphere. Therefore, in robot vision, image analysis on the sphere is an essential requirement to the application of the omni-directional imaging system with conic-mirror and fish-eye lens for navigation and control. We introduce algorithms for optical flow computation for images on a sphere.