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In-band sub-pixel registration of wavelet-encoded images from sparse coefficients

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Abstract

Sub-pixel registration is a crucial step for applications such as super-resolution in remote sensing, motion compensation in magnetic resonance imaging, and nondestructive testing in manufacturing, to name a few. Recently, these technologies have been trending towards wavelet-encoded imaging and sparse/compressive sensing. The former plays a crucial role in reducing imaging artifacts, while the latter significantly increases the acquisition speed. In view of these new emerging needs for applications of wavelet-encoded imaging, we propose a sub-pixel registration method that can achieve direct wavelet domain registration from a sparse set of coefficients. We make the following contributions: (i) We devise a method of decoupling scale, rotation, and translation parameters in the Haar wavelet domain, (ii) we derive explicit mathematical expressions that define in-band sub-pixel registration in terms of wavelet coefficients, (iii) using the derived expressions, we propose an approach to achieve in-band sub-pixel registration, avoiding back and forth transformations. (iv) Our solution remains highly accurate even when a sparse set of coefficients are used, which is due to localization of signals in a sparse set of wavelet coefficients. We demonstrate the accuracy of our method, and show that it outperforms the state of the art on simulated and real data, even when the data are sparse.

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References

  1. Tian, Q., Huhns, M.N.: Algorithms for sub-pixel registration. Comput. Vis. Graph. Image Process. 35(2), 220233 (1986)

    Article  Google Scholar 

  2. Zitova, B., Flusser, J.: Image registration methods: a survey. Image Vis. Comput. 21(11), 9771000 (2003)

    Article  Google Scholar 

  3. Fouad, M.M., Dansereau, R.M., Whitehead, A.D.: Geometric image registration under arbitrarily-shaped locally variant illuminations. SIViP 6(4), 521–532 (2012)

    Article  Google Scholar 

  4. Viola, P., Wells, W.M.I.I.I.: Alignment by maximization of mutual information. IJCV 24.2, 137–154 (1997)

    Article  Google Scholar 

  5. Horn, B.K.P., Fang, Y., Masaki, I.: Time to contact relative to a planar surface. In: IEEE Intelligent Vehicles Symposium (2007)

  6. Foroosh, H., Zerubia, J.B., Berthod, M.: Extension of phase correlation to sub-pixel registration. IEEE TIP 11(3), 188200 (2002)

    Google Scholar 

  7. Shekarforoush, H., Berthod, M., Zerubia, J.: Subpixel image registration by estimating the polyphase decomposition of cross power spectrum. In: Proceedings IEEE CVPR’96

  8. Foroosh, H., Balci, M.: Sub-pixel registration and estimation of local shifts directly in the Fourier domain. ICIP’04, vol. 3. IEEE (2004)

  9. Balci, M., Foroosh, H.: Estimating sub-pixel shifts directly from the phase difference. ICIP, vol. 1. IEEE (2005)

  10. Balci, M., Foroosh, H.: Inferring motion from the rank constraint of the phase matrix. IEEE ICASSP, vol. 2 (2005)

  11. Balci, M., Foroosh, H.: Subpixel estimation of shifts directly in the Fourier domain. IEEE TIP 15(7), 1965–1972 (2006)

    Google Scholar 

  12. Balci, M., Foroosh, H.: Subpixel registration directly from the phase difference. EURASIP J. Appl. Signal Process. 1110–8657, 231–231 (2006)

    Google Scholar 

  13. Evangelidis, G.D., Psarakis, E.Z.: Parametric image alignment using enhanced correlation coefficient maximization. IEEE PAMI 30(10), 18581865 (2008)

    Article  Google Scholar 

  14. Keren, D., Peleg, S., Brada, R.: Image sequence enhancement using sub-pixel displacements. In: CVPR, pp. 742746. IEEE (1988)

  15. Chen, L., Yap, K.: An effective technique for sub-pixel image registration under noisy conditions. Syst. Man Cybern. Part A Syst. Hum. IEEE Trans. 38(4), 881887 (2008)

    Article  Google Scholar 

  16. Guizar-Sicairos, M., Thurman, S.T., Fienup, J.R.: Efficient sub-pixel image registration algorithms. Opt. Lett. 33(2), 156158 (2008)

    Article  Google Scholar 

  17. Stone, H.S., Orchard, M.T., Chang, E., et al.: A fast direct fourier-based algorithm for sub-pixel registration of images. IEEE Trans. Geosci. Remote Sens. 39(10), 2235 (2001). ISSN 01962892

    Article  Google Scholar 

  18. Vandewalle, P., Susstrunk, S., Vetterli, M.: A frequency domain approach to registration of aliased images with application to super-resolution. EURASIP J. Adv. Signal Process. 2006, 071459 (2006). doi:10.1155/ASP/2006/71459

  19. Horn, B.K.P., Weldon Jr., E.J.: Direct methods for recovering motion. IJCV 2.1, 51–76 (1988)

    Article  Google Scholar 

  20. Goshtasby, A., Gage, S.H., Bartholic, J.F.: A two-stage cross correlation approach to template matching. IEEE PAMI 3, 374378 (1984)

    Google Scholar 

  21. Thevenaz, P., Ruttimann, U.E., Unser, M.: A pyramid approach to sub-pixel registration based on intensity. IEEE TIP 7(1), 2741 (1998)

    Google Scholar 

  22. Turcajova, R., Kautsky, J.: A hierarchical multiresolution technique for image registration. In: Proceedings of SPIE Mathematical Imaging: Wavelet Applications in Signal and Image Processing (1996)

  23. Antonini, M., Barlaud, M., Mathieu, P., et al.: Image coding using wavelet transform. IEEE TIP 1(2), 205220 (1992)

    Google Scholar 

  24. Davis, G.M., Nosratinia, A.: Wavelet-based image coding: an overview. In: Applied and Computational Control, Signals, and Circuits. Birkhäuser Boston (1999). doi:10.1007/978-1-4612-0571-5_8

  25. Ma, S., Yin, W., Zhang, Y. et al.: An efficient algorithm for compressed MR imaging using total variation and wavelets. In: IEEE CVPR, p. 18 (2008)

  26. Chen, H.M., Arora, M.K., Varshney, P.K.: Mutual information based image registration for remote sensing data. Int. J. Remote Sens. 24, 37013706 (2003)

    Google Scholar 

  27. Szeliski, R., Coughlan, J.: Hierarchical spline-based image registration. In: IEEE CVPR, pp. 194–201 (1994)

  28. Gong, M., Zhao, S., Jiao, L., et al.: A novel coarse-to-fine scheme for automatic image registration based on SIFT and mutual information. IEEE Trans. Geosci. Remote Sens. 52(7), 4328–4338 (2014)

    Article  Google Scholar 

  29. Ibn-Elhaj, E.: A robust hierarchical motion estimation algorithm in noisy image sequences in the bispectrum domain. SIViP 3(3), 291–302 (2009)

    Article  MATH  Google Scholar 

  30. Le Moigne, J., Campbell, W.J., Cromp, R.P.: An automated parallel image registration technique based on the correlation of wavelet features. Geosci. Remote Sens. IEEE Trans. 40(8), 18491864 (2002)

    Article  Google Scholar 

  31. Hong, G., Zhang, Y.: Wavelet-based image registration tech. for high-resolution remote sensing images. Comput. Geosci. 34(12), 17081720 (2008)

    Article  Google Scholar 

  32. Alam, M., Howlader, T., Rahman, S.M.M.: Entropy-based image registration method using the curvelet transform. SIViP 8(3), 491–505 (2014)

    Article  Google Scholar 

  33. Alnasser, M., Foroosh, H.: Phase-shifting for nonseparable 2-D Haar wavelets. IEEE TIP 17(7), 1061–1068 (2008)

    MathSciNet  Google Scholar 

  34. Donoho, D.L., Johnstone, I.M.: Ideal spatial adaptation by wavelet shrinkage. Biometrika 81(3), 425455 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  35. Mart, R., Reinelt, G.: Branch-and-bound. The linear ordering problem. Springer, p 85–94 (2011)

  36. URL http://vasc.ri.cmu.edu/idb/images/motion/

  37. URL http://www.soe.ucsc.edu/~milanfar/software/sr-datasets.html

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Authors and Affiliations

  1. Department of Computer Science, University of Central Florida, Orlando, FL, USA

    Vildan Atalay Aydin & Hassan Foroosh

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  1. Vildan Atalay Aydin
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  2. Hassan Foroosh
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Correspondence to Vildan Atalay Aydin.

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Aydin, V.A., Foroosh, H. In-band sub-pixel registration of wavelet-encoded images from sparse coefficients. SIViP 11, 1527–1535 (2017). https://doi.org/10.1007/s11760-017-1116-5

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