Volume registration using the 3-D pseudopolar Fourier transform

Yosi Keller; Yoel Shkolnisky; Amir Averbuch

doi:10.1109/tsp.2006.881217

Volume registration using the 3-D pseudopolar Fourier transform

Yosi Keller, Yoel Shkolnisky, Amir Averbuch

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

Abstract

This paper introduces an algorithm for the registration of rotated and translated volumes using the three-dimensional (3-D) pseudopolar Fourier transform, which accurately computes the Fourier transform of the registered volumes on a near-spherical 3-D domain without using interpolation. We propose a three-step procedure. The first step estimates the rotation axis. The second step computes the planar rotation relative to the rotation axis. The third step recovers the translational displacement. The rotation estimation is based on Euler's theorem, which allows one to represent a 3-D rotation as a planar rotation around a 3-D rotation axis. This axis is accurately recovered by the 3-D pseudopolar Fourier transform using radial integrations. The residual planar rotation is computed by an extension of the angular difference function to cylindrical motion. Experimental results show that the algorithm is accurate and robust to noise.

Original language	English
Pages (from-to)	4323-4331
Number of pages	9
Journal	IEEE Transactions on Signal Processing
Volume	54
Issue number	11
DOIs	https://doi.org/10.1109/tsp.2006.881217
State	Published - Nov 2006
Externally published	Yes

Bibliographical note

Funding Information:
Manuscript received March 13, 2005; accepted February 1, 2006. The work of Y. Shkolnisky was supported by the Ministry of Science, Israel, under a grant. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Hilde M. Huizenga. Y. Keller is with the Mathematics Department, Yale University, New Haven, CT 06511 USA (e-mail: [email protected]). Y. Shkolnisky and Amir Averbuch are with the School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel (e-mail: [email protected]; [email protected]). Color versions of Figs. 1, 2, and 5 are available online at http://ieeexplore. ieee.org. Digital Object Identifier 10.1109/TSP.2006.881217

Funding

Manuscript received March 13, 2005; accepted February 1, 2006. The work of Y. Shkolnisky was supported by the Ministry of Science, Israel, under a grant. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Hilde M. Huizenga. Y. Keller is with the Mathematics Department, Yale University, New Haven, CT 06511 USA (e-mail: [email protected]). Y. Shkolnisky and Amir Averbuch are with the School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel (e-mail: [email protected]; [email protected]). Color versions of Figs. 1, 2, and 5 are available online at http://ieeexplore. ieee.org. Digital Object Identifier 10.1109/TSP.2006.881217

Funders	Funder number
Ministry of Science, Israel

Keywords

Non-Carlesian FFT
Pseudopolar FFT
Volume registration

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10.1109/tsp.2006.881217

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abstract = "This paper introduces an algorithm for the registration of rotated and translated volumes using the three-dimensional (3-D) pseudopolar Fourier transform, which accurately computes the Fourier transform of the registered volumes on a near-spherical 3-D domain without using interpolation. We propose a three-step procedure. The first step estimates the rotation axis. The second step computes the planar rotation relative to the rotation axis. The third step recovers the translational displacement. The rotation estimation is based on Euler's theorem, which allows one to represent a 3-D rotation as a planar rotation around a 3-D rotation axis. This axis is accurately recovered by the 3-D pseudopolar Fourier transform using radial integrations. The residual planar rotation is computed by an extension of the angular difference function to cylindrical motion. Experimental results show that the algorithm is accurate and robust to noise.",

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AB - This paper introduces an algorithm for the registration of rotated and translated volumes using the three-dimensional (3-D) pseudopolar Fourier transform, which accurately computes the Fourier transform of the registered volumes on a near-spherical 3-D domain without using interpolation. We propose a three-step procedure. The first step estimates the rotation axis. The second step computes the planar rotation relative to the rotation axis. The third step recovers the translational displacement. The rotation estimation is based on Euler's theorem, which allows one to represent a 3-D rotation as a planar rotation around a 3-D rotation axis. This axis is accurately recovered by the 3-D pseudopolar Fourier transform using radial integrations. The residual planar rotation is computed by an extension of the angular difference function to cylindrical motion. Experimental results show that the algorithm is accurate and robust to noise.

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Volume registration using the 3-D pseudopolar Fourier transform

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