NDLI: Direct 3D-rotation estimation from spherical images via a generalized shift theorem

Content Provider	IEEE Xplore Digital Library
Author	Makadia, A. Daniilidis, K.
Copyright Year	2003
Description	Author affiliation: GRASP Lab., Pennsylvania Univ., USA (Makadia, A.; Daniilidis, K.)
Abstract	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 angles using this theorem. We study the effect of the number of spherical harmonic coefficients as well as the effect of violation of appearance persistence in real imagery.
Sponsorship	IEEE Comput. Soc Tech. Committee on Pattern Anal. & Machine Intelligence (TCPAMI)
File Size	618081
File Format	PDF
ISBN	0769519008
ISSN	10636919
DOI	10.1109/CVPR.2003.1211473
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2003-06-18
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Cameras Fourier transforms Motion estimation Robot vision systems Optical sensors Layout Laboratories Robot localization Image motion analysis Spatiotemporal phenomena
Content Type	Text
Resource Type	Article
Subject	Computer Vision and Pattern Recognition Software

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