Subpixel estimation of shifts directly in the Fourier domain

In this paper, 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 two-dimensional sawtooth signal. Subpixel registration can, thus, be performed directly in the Fourier domain by counting the number of cycles of the phase difference matrix along each frequency axis. The subpixel portion is given by the noninteger fraction of the last cycle along each axis. The problem is formulated as an overdetermined homogeneous quadratic cost function under rank constraint for the phase difference, and the shape constraint for the filter that computes the group delay. The optimal tradeoff for imposing the constraints is determined using the method of generalized cross validation. Also, in order to robustify the solution, we assume a mixture model of inlying and outlying estimated shifts and truncate our quadratic cost function using expectation maximization.

[1]  Roger Y. Tsai,et al.  Multiframe image restoration and registration , 1984 .

[2]  G. Golub,et al.  Generalized cross-validation for large scale problems , 1997 .

[3]  Josiane Zerubia,et al.  Subpixel image registration by estimating the polyphase decomposition of cross power spectrum , 1996, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[4]  M. Viergever,et al.  Medical image matching-a review with classification , 1993, IEEE Engineering in Medicine and Biology Magazine.

[5]  J. Hajnal,et al.  A Registration and Interpolation Procedure for Subvoxel Matching of Serially Acquired MR Images , 1995, Journal of computer assisted tomography.

[6]  Michael T. Orchard,et al.  A fast direct Fourier-based algorithm for subpixel registration of images , 2001, IEEE Trans. Geosci. Remote. Sens..

[7]  C. D. Kuglin,et al.  Video-Rate Image Correlation Processor , 1977, Optics & Photonics.

[8]  G. McLachlan,et al.  The EM algorithm and extensions , 1996 .

[9]  J. Hogg.  Magnetic resonance imaging. , 1994, Journal of the Royal Naval Medical Service.

[10]  Shmuel Peleg,et al.  Improving image resolution using subpixel motion , 1987, Pattern Recognit. Lett..

[11]  Berthold K. P. Horn,et al.  Determining Optical Flow , 1981, Other Conferences.

[12]  Thomas S. Huang,et al.  Image Sequence Analysis: Motion Estimation , 1981 .

[13]  Alan V. Oppenheim,et al.  Discrete-Time Signal Pro-cessing , 1989 .

[14]  Michael Unser,et al.  A pyramid approach to subpixel registration based on intensity , 1998, IEEE Trans. Image Process..

[15]  Hans-Hellmut Nagel,et al.  On the Estimation of Optical Flow: Relations between Different Approaches and Some New Results , 1987, Artif. Intell..

[16]  Yu-Chung N. Cheng,et al.  Magnetic Resonance Imaging: Physical Principles and Sequence Design , 1999 .

[17]  A. N. Tikhonov,et al.  Solutions of ill-posed problems , 1977 .

[18]  Michael I. Jordan,et al.  On Convergence Properties of the EM Algorithm for Gaussian Mixtures , 1996, Neural Computation.

[19]  Michal Irani,et al.  Improving resolution by image registration , 1991, CVGIP Graph. Model. Image Process..

[20]  Ardeshir Goshtasby,et al.  A Region-Based Approach to Digital Image Registration with Subpixel Accuracy , 1986, IEEE Transactions on Geoscience and Remote Sensing.

[21]  Jan Flusser,et al.  Image registration methods: a survey , 2003, Image Vis. Comput..

[22]  Gene H. Golub,et al.  Generalized cross-validation as a method for choosing a good ridge parameter , 1979, Milestones in Matrix Computation.

[23]  William Scott Hoge,et al.  A subspace identification extension to the phase correlation method [MRI application] , 2003, IEEE Transactions on Medical Imaging.

[24]  C. D. Kuglin,et al.  The phase correlation image alignment method , 1975 .

[25]  Hassan Foroosh,et al.  Extension of phase correlation to subpixel registration , 2002, IEEE Trans. Image Process..

[26]  Max A. Viergever,et al.  A survey of medical image registration , 1998, Medical Image Anal..

[27]  A. Verri,et al.  Differential techniques for optical flow , 1990 .

[28]  K. J. Ray Liu,et al.  Interpolation-free subpixel motion estimation techniques in DCT domain , 1998, IEEE Trans. Circuits Syst. Video Technol..

[29]  Alon Efrat,et al.  Subpixel image registration using circular fiducials , 1993, [1993] The 2nd Israel Symposium on Theory and Computing Systems.

[30]  Qi Tian,et al.  Algorithms for subpixel registration , 1986 .

[31]  Eric C. Olson,et al.  A geometric approach to subpixel registration accuracy , 1987, Computer Vision Graphics and Image Processing.

[32]  Michael Werman,et al.  Sub-pixel Bayesian estimation of albedo and height , 1996, International Journal of Computer Vision.

[33]  Lisa M. Brown,et al.  A survey of image registration techniques , 1992, CSUR.

[34]  Michael J. Black,et al.  The outlier process: unifying line processes and robust statistics , 1994, 1994 Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[35]  V. N. Dvornychenko,et al.  Bounds on (Deterministic) Correlation Functions with Application to Registration , 1983, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[36]  R. J. Althof,et al.  A rapid and automatic image registration algorithm with subpixel accuracy , 1997, IEEE Transactions on Medical Imaging.

[37]  Rama Chellappa,et al.  Data-driven multichannel superresolution with application to video sequences , 1999 .

[38]  D. Robinson,et al.  Fundamental performance limits in image registration , 2004, Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429).

[39]  Hassan Foroosh,et al.  Sub-pixel registration and estimation of local shifts directly in the Fourier domain , 2004, 2004 International Conference on Image Processing, 2004. ICIP '04..

[40]  S. P. Kim,et al.  Subpixel accuracy image registration by spectrum cancellation , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.