Variational Analysis of Spherical Images

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.

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