Volume registration using the 3-D pseudopolar Fourier transform

Yosi Keller*, Yoel Shkolnisky, Amir Averbuch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)4323-4331
Number of pages9
JournalIEEE Transactions on Signal Processing
Issue number11
StatePublished - Nov 2006


FundersFunder number
Ministry of Science, Israel


    • Non-Carlesian FFT
    • Pseudopolar FFT
    • Volume registration


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