Algebraically accurate volume registration using Euler's theorem and the 3-D pseudo-polar FFT

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Abstract

We present an algorithm for the registration of rotated and translated volumes, which operates in the frequency domain. The Fourier domain allows to compute the rotation and translation parameters separately, thus reducing a problem with six degrees of freedom to two problems of three degrees of freedom each. We propose a three-step procedure. The first step estimates the rotation axis. The second computes the planar rotation relative to the rotation axis, and the third recovers the translational displacement by using the phase correlation technique. The rotation estimation is based on Euler's theorem, which allows to represent a rotation using only three parameters. Two parameters represent the rotation axis and one parameter represents the planar rotation perpendicular to the axis. By using the 3-D pseudo-polar FFT, the estimation of the rotation axis is shown to be algebraically accurate. A variant of the angular difference function registration algorithm is derived for the estimation of the planar rotation around the axis. The experimental results show that the algorithm is accurate and robust to noise.

Original languageEnglish
Title of host publicationProceedings - 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005
PublisherIEEE Computer Society
Pages795-800
Number of pages6
ISBN (Print)0769523722, 9780769523729
DOIs
StatePublished - 2005
Event2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005 - San Diego, CA, United States
Duration: 20 Jun 200525 Jun 2005

Publication series

NameProceedings - 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005
VolumeII

Conference

Conference2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005
Country/TerritoryUnited States
CitySan Diego, CA
Period20/06/0525/06/05

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