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

Yosi Keller; Amir Averbuch; Yoel Shkolnisky

doi:10.1109/CVPR.2005.66

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

Yosi Keller^*, Amir Averbuch, Yoel Shkolnisky

^*Corresponding author for this work

Yale University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

12 Scopus citations

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 language	English
Title of host publication	Proceedings - 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005
Publisher	IEEE Computer Society
Pages	795-800
Number of pages	6
ISBN (Print)	0769523722, 9780769523729
DOIs	https://doi.org/10.1109/CVPR.2005.66
State	Published - 2005
Event	2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005 - San Diego, CA, United States Duration: 20 Jun 2005 → 25 Jun 2005

Publication series

Name	Proceedings - 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005
Volume	II

Conference

Conference	2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005
Country/Territory	United States
City	San Diego, CA
Period	20/06/05 → 25/06/05

Access to Document

10.1109/CVPR.2005.66

Cite this

Keller, Y., Averbuch, A., & Shkolnisky, Y. (2005). Algebraically accurate volume registration using Euler's theorem and the 3-D pseudo-polar FFT. In Proceedings - 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005 (pp. 795-800). Article 1467524 (Proceedings - 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005; Vol. II). IEEE Computer Society. https://doi.org/10.1109/CVPR.2005.66

Keller, Yosi ; Averbuch, Amir ; Shkolnisky, Yoel. / Algebraically accurate volume registration using Euler's theorem and the 3-D pseudo-polar FFT. Proceedings - 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005. IEEE Computer Society, 2005. pp. 795-800 (Proceedings - 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005).

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

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.",

author = "Yosi Keller and Amir Averbuch and Yoel Shkolnisky",

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Keller, Y, Averbuch, A & Shkolnisky, Y 2005, Algebraically accurate volume registration using Euler's theorem and the 3-D pseudo-polar FFT. in Proceedings - 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005., 1467524, Proceedings - 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005, vol. II, IEEE Computer Society, pp. 795-800, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005, San Diego, CA, United States, 20/06/05. https://doi.org/10.1109/CVPR.2005.66

Algebraically accurate volume registration using Euler's theorem and the 3-D pseudo-polar FFT. / Keller, Yosi; Averbuch, Amir ; Shkolnisky, Yoel.
Proceedings - 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005. IEEE Computer Society, 2005. p. 795-800 1467524 (Proceedings - 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005; Vol. II).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Keller Y, Averbuch A , Shkolnisky Y. Algebraically accurate volume registration using Euler's theorem and the 3-D pseudo-polar FFT. In Proceedings - 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005. IEEE Computer Society. 2005. p. 795-800. 1467524. (Proceedings - 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005). doi: 10.1109/CVPR.2005.66

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

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