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Dynamic Trees for Unsupervised Segmentation and Matching of Image Regions
November 2005 (vol. 27 no. 11)
pp. 1762-1777
We present a probabilistic framework—namely, multiscale generative models known as Dynamic Trees (DT)—for unsupervised image segmentation and subsequent matching of segmented regions in a given set of images. Beyond these novel applications of DTs, we propose important additions for this modeling paradigm. First, we introduce a novel DT architecture, where multilayered observable data are incorporated at all scales of the model. Second, we derive a novel probabilistic inference algorithm for DTs—Structured Variational Approximation (SVA)—which explicitly accounts for the statistical dependence of node positions and model structure in the approximate posterior distribution, thereby relaxing poorly justified independence assumptions in previous work. Finally, we propose a similarity measure for matching dynamic-tree models, representing segmented image regions, across images. Our results for several data sets show that DTs are capable of capturing important component-subcomponent relationships among objects and their parts, and that DTs perform well in segmenting images into plausible pixel clusters. We demonstrate the significantly improved properties of the SVA algorithm—both in terms of substantially faster convergence rates and larger approximate posteriors for the inferred models—when compared with competing inference algorithms. Furthermore, results on unsupervised object recognition demonstrate the viability of the proposed similarity measure for matching dynamic-structure statistical models.

[1] N.J. Adams, A.J. Storkey, Z. Ghahramani, and C.K. I. Williams, “MFDTs: Mean Field Dynamic Trees,” Proc. 15th Int'l Conf. Pattern Recognition, vol. 3, pp. 147-150, 2002.
[2] N.J. Adams, “Dynamic Trees: A Hierarchical Probabilistic Approach to Image Modeling,” PhD dissertation, Division of Informatics, Univ. of Edinburgh, Edinburgh, U.K., 2001.
[3] A.J. Storkey, “Dynamic Trees: A Structured Variational Method Giving Efficient Propagation Rules,” Proc. 16th Conf. Uncertainty in Artificial Intelligence, pp. 566-573, 2000.
[4] A.J. Storkey and C.K.I. Williams, “Image Modeling with Position-Encoding Dynamic Trees,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 25, no. 7, pp. 859-871, July 2003.
[5] X. Feng, C.K.I. Williams, and S.N. Felderhof, “Combining Belief Networks and Neural Networks for Scene Segmentation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 4, pp. 467-483, Apr. 2002.
[6] Z. Ying and D. Castanon, “Partially Occluded Object Recognition Using Statistical Models,” Int'l J. Computer Vision, vol. 49, no. 1, pp. 57-78, 2002.
[7] H. Schneiderman and T. Kanade, “Object Detection Using the Statistics of Parts,” Int'l J. Computer Vision, vol. 56, no. 3, pp. 151-177, 2004.
[8] B. Moghaddam, “Principal Manifolds and Probabilistic Subspaces for Visual Recognition,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 6, pp. 780-788, June 2002.
[9] G. Hermosillo, C. Chefd'Hotel, and O. Faugeras, “Variational Methods for Multimodal Image Matching,” Int'l J. Computer Vision, vol. 50, no. 3, pp. 329-343, 2002.
[10] H. Greenspan, J. Goldberger, and L. Ridel, “A Continuous Probabilistic Framework for Image Matching,” Computer Vision and Image Understanding, vol. 84, no. 3, pp. 384-406, 2001.
[11] D. DeMenthon, D. Doermann, and M.V. Stuckelberg, “Image Distance Using Hidden Markov Models,” Proc. 15th Int'l Conf. Pattern Recognition, vol. 3, pp. 143-146, 2000.
[12] B.H. Juang and L.R. Rabiner, “A Probabilistic Distance Measure for Hidden Markov Models,” AT&T Technical J., vol. 64, no. 2, pp. 391-408, 1985.
[13] M.C. Nechyba and Y. Xu, “Stochastic Similarity for Validating Human Control Strategy Models,” IEEE Trans. Robotic Automation, vol. 14, no. 3, pp. 437-451, 1998.
[14] H. Cheng and C.A. Bouman, “Multiscale Bayesian Segmentation Using a Trainable Context Model,” IEEE Trans. Image Processing, vol. 10, no. 4, pp. 511-525, 2001.
[15] H. Choi and R.G. Baraniuk, “Multiscale Image Segmentation Using Wavelet-Domain Hidden Markov Models,” IEEE Trans. Image Processing, vol. 10, no. 9, pp. 1309-1321, 2001.
[16] J.-M. Laferté, P. Pérez, and F. Heitz, “Discrete Markov Image Modeling and Inference on the Quadtree,” IEEE Trans. Image Processing, vol. 9, no. 3, pp. 390-404, 2000.
[17] M.I. Jordan, Z. Ghahramani, T.S. Jaakkola, and L.K. Saul, “An Introduction to Variational Methods for Graphical Models,” Machine Learning, vol. 37, no. 2, pp. 183-233, 1999.
[18] T.S. Jaakkola, “Tutorial on Variational Approximation Methods,” Advanced Mean Field Methods, M. Opper and D. Saad, eds., pp. 129-161, Cambridge, Mass.: MIT Press, 2000.
[19] B.J. Frey and N. Jojic, “Advances in Algorithms for Inference and Learning in Complex Probability Models for Vision,” IEEE Trans. Pattern Analysis and Machine Intelligence, 2004.
[20] M.K. Schneider, P.W. Fieguth, W.C. Karl, and A.S. Willsky, “Multiscale Methods for the Segmentation and Reconstruction of Signals and Images,” IEEE Trans. Image Processing, vol. 9, no. 3, pp. 456-468, 2000.
[21] J. Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, chapter 4. pp. 143-236, San Mateo, Calif.: Morgan Kaufamnn, 1988.
[22] W.W. Irving, P.W. Fieguth, and A.S. Willsky, “An Overlapping Tree Approach to Multiscale Stochastic Modeling and Estimation,” IEEE Trans. Image Processing, vol. 6, no. 11, pp. 1517-1529, 1997.
[23] J. Li, R.M. Gray, and R.A. Olshen, “Multiresolution Image Classification by Hierarchical Modeling with Two-Dimensional Hidden Markov Models,” IEEE Trans. Information Theory, vol. 46, no. 5, pp. 1826-1841, 2000.
[24] W.K. Konen, T. Maurer, and C. von der Malsburg, “A Fast Dynamic Link Matching Algorithm for Invariant Pattern Recognition,” Neural Networks, vol. 7, no. 6-7, pp. 1019-1030, 1994.
[25] A. Montanvert, P. Meer, and A. Rosenfield, “Hierarchical Image Analysis Using Irregular Tessellations,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 4, pp. 307-316, Apr. 1991.
[26] M. Aitkin and D.B. Rubin, “Estimation and Hypothesis Testing in Finite Mixture Models,” J. Royal Statisitcal Soc. B, vol. 47, no. 1, pp. 67-75, 1985.
[27] D.J.C. MacKay, “Introduction to Monte Carlo Methods,” Learning in Graphical Models (Adaptive Computation and Machine Learning), M.I. Jordan, ed., pp. 175-204, Cambridge, Mass.: MIT Press, 1999.
[28] R.M. Neal, “Probabilistic Inference Using Markov Chain Monte Carlo Methods,” Technical Report CRG-TR-93-1, Connectionist Research Group, Univ. of Toronto, 1993.
[29] D.J.C. MacKay, Information Theory, Inference, and Learning Algorithms, chapter 29, pp. 357-386, Cambridge, U.K.: Cambridge Univ. Press, 2003.
[30] T.M. Cover and J.A. Thomas, Elements of Information Theory. New York: Wiley Interscience Press, 1991.
[31] M. Mignotte, C. Collet, P. Perez, and P. Bouthemy, “Sonar Image Segmentation Using an Unsupervised Hierarchical MRF Model,” IEEE Trans. Image Processing, vol. 9, no. 7, pp. 1216-1231, 2000.
[32] C. D'Elia, G. Poggi, and G. Scarpa, “A Tree-Structured Markov Random Field Model for Bayesian Image Segmentation,” IEEE Trans. Image Processing, vol. 12, no. 10, pp. 1259-1273, 2003.
[33] D. Martin, C. Fowlkes, D. Tal, and J. Malik, “A Database of Human Segmented Natural Images and Its Application to Evaluating Segmentation Algorithms and Measuring Ecological Statistics,” Proc. Eighth Int'l Conf. Computer Vision, vol. 2, pp. 416-423, 2001.
[34] N.G. Kingsbury, “Complex Wavelets for Shift Invariant Analysis and Filtering of Signals,” J. Applied Computer Harmonic Analysis, vol. 10, no. 3, pp. 234-253, 2001.
[35] T. Lindeberg, “Scale-Space Theory: A Basic Tool for Analysing Structures at Different Scales,” J. Applied Statistics, vol. 21, no. 2, pp. 224-270, 1994.
[36] D.G. Lowe, “Distinctive Image Features from Scale-Invariant Keypoints,” Int'l J. Computer Vision, vol. 60, no. 2, pp. 91-110, 2004.

Index Terms:
Index Terms- Generative models, Bayesian networks, dynamic trees, variational inference, image segmentation, image matching, object recognition.
Citation:
Sinisa Todorovic, Michael C. Nechyba, "Dynamic Trees for Unsupervised Segmentation and Matching of Image Regions," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 27, no. 11, pp. 1762-1777, Nov. 2005, doi:10.1109/TPAMI.2005.219
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