The Community for Technology Leaders
RSS Icon
Issue No.10 - October (2008 vol.30)
pp: 1841-1857
Recently, the Non-Parametric (NP) Windows has been proposed to estimate the statistics of real 1D and 2D signals. NP Windows is accurate, because it is equivalent to sampling images at a high (infinite) resolution for an assumed interpolation model. This paper extends the proposed approach to consider joint distributions of image-pairs. Secondly, Green's Theorem is used to simplify the previous NP Windows algorithm. Finally, a resolution aware NP Windows algorithm is proposed, to improve robustness to relative scaling between an image-pair. Comparative testing of 2D image registration was performed using translation-only and affine transformations. Although more expensive than other methods, NP Windows frequently demonstrated superior performance for bias (distance between ground truth and global maximum) and frequency of convergence. Unlike other methods, the number of samples and histogram bin-size has little effect on NP Windows, and the prior selection of a kernel is not required.
Interpolation, Optimization, Distribution functions, Nonparametric statistics, Antialiasing, Image-based rendering, Image Processing and Computer Vision, Sampling, Signal processing
Timor Kadir, Nicholas Dowson, "Estimating the Joint Statistics of Images Using Nonparametric Windows with Application to Registration Using Mutual Information", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.30, no. 10, pp. 1841-1857, October 2008, doi:10.1109/TPAMI.2007.70832
[1] P. Viola and W. Wells, “Alignment by Maximization of Mutual Information,” Proc. Fifth Int'l Conf. Computer Vision, pp. 16-23, June 1995.
[2] A. Collignon, F. Maes, D. Delaere, D. Vandermeulen, P. Suetens, and G. Marchal, “Automated Multimodality Image Registration Based on Information Theory,” Information Processing in Medical Imaging, pp. 263-374, Kluwer Academic, 1995.
[3] C. Studholme, D. Hill, and D. Hawkes, “Automated 3D Registration of Truncated MR and CT Images of the Head,” Proc. British Machine Vision Conf., pp. 27-36, Sept. 1995.
[4] P. Viola and W. Wells, “Alignment by Maximization of Mutual Information,” Int'l J. Computer Vision, vol. 24, no. 2, pp. 137-154, 1997.
[5] F. Maes, D. Vandermeulen, and P. Seutens, “Comparative Evaluation of Multiresolution Optimization Strategies for Multimodality Image Registration by Maximization of Mutual Information,” Medical Image Analysis, vol. 3, no. 4, pp. 272-286, Apr. 1999.
[6] F. Maes, D. Vandermeulen, and P. Suetens, “Medical Image Registration Using Mutual Information,” Proc. IEEE, vol. 91, no. 10, pp. 1699-1722, 2003.
[7] E. Loutas, N. Nikolaidis, and I. Pitas, “A Mutual Information Approach to Articulated Object Tracking,” Proc. IEEE Int'l Symp. Circuits and Systems, vol. 2, pp. 672-675, May 2003.
[8] R. Moddemeijer, “On Estimation of Entropy and Mutual Information of Continuous Distributions,” Signal Processing, vol. 16, pp. 233-248, 1989.
[9] E. Parzen, “On Estimation of a Probability Density Function and Mode,” Annals of Math. Statistics, vol. 33, no. 3, pp. 1065-1076, Sept. 1962.
[10] P. Thevenaz and M. Unser, “Optimization of Mutual Information for Multi-Resolution Image Registration,” IEEE Trans. Image Processing, vol. 9, no. 12, pp. 2083-2099, Dec. 2000.
[11] F. Maes, A. Collignon, D. Vandermeulen, G. Marchal, and P. Suetens, “Multimodality Image Registration by Maximization of Mutual Information,” IEEE Trans. Medical Imaging, vol. 16, no. 2, pp. 187-198, Apr. 1997.
[12] H. Chen and P. Varshney, “Mutual Information-Based CT-MR Brain Image Registration Using Generalised Partial Volume Joint Histogram Estimation,” IEEE Trans. Medical Imaging, vol. 22, no. 9, pp. 1111-1119, Sept. 2003.
[13] E. D'Agostino, F. Maes, D. Vandermeulen, and P. Suetens, “An Information Theoretic Approach for Non-Rigid Image Registration Using Voxel Class Probabilities,” Medical Image Analysis, vol. 10, pp. 413-430, 2006.
[14] J. Pluim, J. Maintz, and M. Viergever, “Interpolation Artefacts in Mutual Information-Based Image Registration,” Computer Vision and Image Understanding, vol. 77, pp. 211-232, 2000.
[15] T. Kadir and M. Brady, “Estimating Statistics in Arbitrary Regions of Interest,” Proc. 16th British Machine Vision Conf., vol. 2, pp. 589-598, Sept. 2005.
[16] T. Kadir and M. Brady, “Nonparametric Estimation of Probability Distributions from Sampled Signals,” technical report, Robotics Research Laboratory, July 2005.
[17] I. Matthews, T. Ishikawa, and S. Baker, “The Template Update Problem,” Proc. 14th British Machine Vision Conf., Sept. 2003.
[18] T. Kaneko and O. Hori, “Template Update Criterion for Template Matching of Image Sequences,” Proc. 16th Int'l Conf. Pattern Recognition, vol. 2, pp. 1-5, Aug. 2002.
[19] A. Rajwade, A. Banerjee, and A. Rangarajan, “A New Method of Probability Density Estimation with Application to Mutual Information Based Image Registration,” Proc. IEEE Int'l Conf. Computer Vision and Pattern Recognition, June 2006.
[20] T. Cover and J. Thomas, Elements of Information Theory. Wiley & Sons, 1991.
[21] C. Shannon, “A Mathematical Theory of Communication,” The Bell System Technical J., vol. 27, pp. 379-423, July-Oct. 1948.
[22] A. Papoulis and S.U. Pillai, Probability, Random Variables, and Stochastic Processes, third ed., pp. 124-148. McGraw-Hill, 1991.
[23] J.C. Morrison, “Fast Anti-Aliasing Polygon Scan Conversion,” Graphics Gems, A.S. Glassner, ed., pp. 63-83, Morgan Kaufmann, June 1990.
[24] P.S. Heckbert, “Generic Convex Polygon Scan Conversion and Clipping,” Graphics Gems, A.S. Glassner, ed., pp. 84-86, Morgan Kaufmann, June 1990.
[25] C.A. Shaffer and C.D. Feustel, “Exact Computation of 2D Intersections,” Graphics Gems III, D. Kirk, ed., pp. 188-192, Morgan Kaufmann, June 1994.
[26] E.W. Weisstein, “Polygon: Area,” http://mathworld.wolfram. comPolygonArea.html , Aug. 2007.
[27] CRC Standard Mathematical Tables, 28th ed., W.H. Beyer, ed., pp.123-124. CRC Press, 1987.
[28] W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes in C, second ed. Cambridge Univ. Press, 1992.
[29] R.-S. Kwan, A. Evans, and G. Pike, “MRI Simulation-Based Evaluation of Image Processing and Classification Methods,” IEEE Trans. Medical Imaging, vol. 18, no. 11, pp. 1085-1097, Nov. 1999.
[30] S. Baker and I. Matthews, “Lucas-Kanade 20 Years On: A Unifying Framework Part 1,” Technical Report CMU-RI-TR-02-16, Robotics Inst., Carnegie Mellon Univ., July 2002.
33 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool