Direct 3D-Rotation Estimation from Spherical Images via a Generalized Shift Theorem

Omnidirectional images arising from 3D-motion of a camera contain persistent structures over a large variation of motions because of their large field of view. This persistence made appearance-based methods attractive for robot localization given reference views. Assuming that central omnidirectional images can be mapped to the sphere, the question is what are the underlying mappings of the sphere that can reflect a rotational camera motion. Given such a mapping, we propose a systematic way for finding invariance and the mapping parameters themselves based on the generalization of the Fourier transform. Using results from representation theory, we can generalize the Fourier transform to any homogeneous space with a transitively acting group. Such a case is the sphere with rotation as the acting group. The spherical harmonics of an image pair are related to each other through a shift theorem involving the irreducible representation of the rotation group. We show how to extract Euler an...

• Type: Conference
• Year: 2003
• Where: CVPR
• Authors: Ameesh Makadia, Kostas Daniilidis
• Keywords: Central Omnidirectional Images, Computer Vision, CVPR 2003, Fourier Transform, Localization Given Reference, Rotational Camera Motion, Spherical Harmonic Coefficients