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Subpixel Registration Directly from the Phase Difference

Abstract

This paper proposes a new approach to subpixel registration, under local/global shifts or rotation, using the phase-difference matrix. We establish the exact relationship between the continuous and the discrete phase difference of two shifted images and show that their discrete phase difference is a 2-dimensional sawtooth signal. As a result, the exact shifts or rotations can be determined to subpixel or subangle accuracy by counting the number of cycles of the phase-difference matrix along the frequency axes. The subpixel portion is represented by a fraction of a cycle corresponding to the noninteger part of the shift or rotation. The rotation angle is estimated by applying our method using a polar coordinate system. The problem is formulated as an overdetermined system of equations and is solved by imposing a regularity constraint. The tradeoff for imposing the constraint is determined by exploiting the rank constraint leading to a closed-form expression for the optimal regularization parameter.

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Correspondence to Murat Balci.

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Balci, M., Foroosh, H. Subpixel Registration Directly from the Phase Difference. EURASIP J. Adv. Signal Process. 2006, 060796 (2006). https://doi.org/10.1155/ASP/2006/60796

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Keywords

  • Coordinate System
  • Information Technology
  • Rotation Angle
  • Phase Difference
  • Quantum Information