CSDL Home IEEE Transactions on Pattern Analysis & Machine Intelligence 2009 vol.31 Issue No.03 - March

Subscribe

Issue No.03 - March (2009 vol.31)

pp: 475-491

Ajit Rajwade , University of Florida, Gainesville

Arunava Banerjee , Univeristy of Florida, Gainesville

Anand Rangarajan , University of Florida, Gainesville

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TPAMI.2008.97

ABSTRACT

We present a new, geometric approach for determining the probability density of the intensity values in an image. We drop the notion of an image as a set of discrete pixels, and assume a piecewise-continuous representation. The probability density can then be regarded as being proportional to the area between two nearby isocontours of the image surface. Our paper extends this idea to joint densities of image pairs. We demonstrate the application of our method to affine registration between two or more images using information theoretic measures such as mutual information. We show cases where our method outperforms existing methods such as simple histograms, histograms with partial volume interpolation, Parzen windows, etc. under fine intensity quantization for affine image registration under significant image noise. Furthermore, we demonstrate results on simultaneous registration of multiple images, as well as for pairs of volume datasets, and show some theoretical properties of our density estimator. Our approach requires the selection of only an image interpolant. The method neither requires any kind of kernel functions (as in Parzen windows) which are unrelated to the structure of the image in itself, nor does it rely on any form of sampling for density estimation.

INDEX TERMS

computer vision, pattern recognition

CITATION

Ajit Rajwade, Arunava Banerjee, Anand Rangarajan, "Probability Density Estimation Using Isocontours and Isosurfaces: Applications to Information-Theoretic Image Registration",

*IEEE Transactions on Pattern Analysis & Machine Intelligence*, vol.31, no. 3, pp. 475-491, March 2009, doi:10.1109/TPAMI.2008.97REFERENCES

- [1] J. Beirlant, E. Dudewicz, L. Györfi, and E.C. van der Meulen, “Nonparametric Entropy Estimation: An Overview,”
Int'l J. Math. and Statistical Sciences, vol. 6, no. 1, pp. 17-39, June 1997.- [2] J. Boes and C. Meyer, “Multi-Variate Mutual Information for Registration,”
Proc. Second Int'l Conf. Medical Image Computing and Computer-Assisted Intervention (MICCAI '99), pp. 606-612, 1999.- [5] J. Costa and A. Hero, “Entropic Graphs for Manifold Learning,”
Proc. 37th Asilomar Conf. Signals, Systems and Computers, vol. 1, pp.316-320, 2003.- [6] T. Cover and J. Thomas,
Elements of Information Theory. Wiley-Interscience, 1991.- [7] M. de Berg, M. van Kreveld, M. Overmars, and O. Schwarzkopf,
Computational Geometry: Algorithms and Applications. Springer, 1997.- [8] L. Devroye, L. Gyorfi, and G. Lugosi,
A Probabilistic Theory of Pattern Recognition. Springer, 1996.- [9] T. Downie and B. Silverman, “A Wavelet Mixture Approach to the Estimation of Image Deformation Functions,”
Sankhya Series B, vol. 63, pp. 181-198, 2001.- [10] N. Dowson, R. Bowden, and T. Kadir, “Image Template Matching Using Mutual Information and NP-Windows,”
Proc. 18th Int'l Conf. Pattern Recognition (ICPR '06), vol. 2, pp. 1186-1191, 2006.- [11] W. Feller, “On the Kolmogorov-Smirnov Limit Theorems for Empirical Distributions,”
The Annals of Math. Statistics, vol. 19, no. 2, pp. 177-189, 1948.- [12] E. Hadjidemetriou, M. Grossberg, and S. Nayar, “Histogram Preserving Image Transformations,”
Int'l J. Computer Vision, vol. 45, no. 1, pp. 5-23, 2001.- [13] T. Kadir and M. Brady, “Estimating Statistics in Arbitrary Regions of Interest,”
Proc. British Machine Vision Conf. (BMVC '05), pp. 589-598, 2005.- [14] B. Karaçali, “Information Theoretic Deformable Registration Using Local Image Information,”
Int'l J. Computer Vision, vol. 72, no. 3, pp. 219-237, 2007.- [15] M. Leventon and W.E.L. Grimson, “Multi-Modal Volume Registration Using Joint Intensity Distributions,”
Proc. First Int'l Conf. Medical Image Computing and Computer-Assisted Intervention (MICCAI '98), pp. 1057-1066, 1998.- [16] B. Ma, A. Hero, J. Gorman, and O. Michel, “Image Registration with Minimum Spanning Tree Algorithm,”
Proc. IEEE Int'l Conf. Image Processing (ICIP '00), vol. 1, pp. 481-484, 2000.- [19] E. Parzen, “On Estimation of a Probability Density Function and Mode,”
Annals of Math. Statistics, vol. 33, pp. 1065-1076, 1962.- [23] A. Rajwade, A. Banerjee, and A. Rangarajan, “Continuous Image Representations Avoid the Histogram Binning Problem in Mutual Information Based Image Registration,”
Proc. Third IEEE Int'l Symp. Biomedical Imaging (ISBI '06), pp. 840-843, 2006.- [24] A. Rajwade, A. Banerjee, and A. Rangarajan, “New Method of Probability Density Estimation with Application to Mutual Information Based Image Registration,”
Proc. IEEE Conf. Computer Vision and Pattern Recognition (CVPR '06), vol. 2, pp. 1769-1776, 2006.- [27] M. Sabuncu and P. Ramadge, “Gradient Based Optimization of an EMST Image Registration Function,”
Proc. IEEE Int'l Conf. Acoustics, Speech, and Signal Processing (ICASSP '05), vol. 2, pp.253-256, 2005.- [29] B. Silverman,
Density Estimation for Statistics and Data Analysis. Chapman and Hall, 1986.- [31] Tina Is No Acronym (TINA) Image Database, Univ. of Manchester and Univ. of Sheffield, UK, http://www.tina-vision.netilib.php, 2008.
- [32] P. Viola and W.M. Wells, “Alignment by Maximization of Mutual Information,”
Int'l J. Computer Vision, vol. 24, no. 2, pp. 137-154, 1997.- [33] C. Yang, R. Duraiswami, N. Gumerov, and L. Davis, “Improved Fast Gauss Transform and Efficient Kernel Density Estimation,”
Proc. Ninth IEEE Int'l Conf. Computer Vision (ICCV '03), vol. 1, pp.464-471, 2003.- [34] J. Zhang and A. Rangarajan, “Affine Image Registration Using a New Information Metric,”
Proc. IEEE Conf. Computer Vision and Pattern Recognition (CVPR '04), vol. 1, pp. 848-855, 2004.- [35] J. Zhang and A. Rangarajan, “Multimodality Image Registration Using an Extensible Information Metric,”
Proc. 19th Int'l Conf. Information Processing in Medical Imaging (IPMI '05), pp. 725-737, 2005. |