This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
A Generic Grouping Algorithm and Its Quantitative Analysis
February 1998 (vol. 20 no. 2)
pp. 168-185

Abstract—This paper presents a generic method for perceptual grouping quality. The grouping method is fairly general: It may be used the grouping of various types of data features, and to incorporate different grouping cues operating over feature sets of different sizes. The proposed method is divided into two parts: constructing a graph representation of the available perceptual grouping evidence, and then finding the "best" partition of the graph into groups. The first stage includes a cue enhancement procedure, which integrates the information available from multifeature cues into very reliable bifeature cues. Both stages are implemented using known statistical tools such as Wald's SPRT algorithm and the Maximum Likelihood criterion. The accompanying theoretical analysis of this grouping criterion quantifies intuitive expectations and predicts that the expected grouping quality increases with cue reliability. It also shows that investing more computational effort in the grouping algorithm leads to better grouping results. This analysis, which quantifies the grouping power of the Maximum Likelihood criterion, is independent of the grouping domain. To our best knowledge, such an analysis of a grouping process is given here for the first time. Three grouping algorithms, in three different domains, are synthesized as instances of the generic method. They demonstrate the applicability and generality of this grouping method.

[1] E.H. Adelson and J.Y.A. Wang, "Representing Moving Images With Layers," Technical Report 279, Massachusetts Institute of Tech nology, May 1994.
[2] A. Amir, "A Quantitative Approach to Perceptual Grouping in Computer Vision," DSc dissertation, Technion-IIT, Dept. of Computer Science, June 1997.
[3] A. Amir and M. Lindenbaum, "The Construction and Analysis of a Generic Grouping Algorithm," Technical Report CIS-9418, Technion, Israel, Nov. 1994.
[4] A. Amir and M. Lindenbaum, “Grouping-Based Nonadditive Verification,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 20, no. 2, pp. 186-192, Feb. 1998.
[5] A. Amir and M. Lindenbaum, "Quantitative Analysis of Grouping Processes," ECCV-96, vol. 1, pp. 371-384,Cambridge, 1996.
[6] C. Brautigam, J. Garding, and J.-O. Eklundh, "Seeing the Obvious," Technical Report CVAP193, KTH, Mar. 1996.
[7] D.T. Clemens, "Region-Based Feature Interpretation for Recognizing 3D Models in 2D Images," PhD dissertation, Massachusetts Institute of Technology, Dept. of Electrical Eng. and Computer Science, June 1991.
[8] I.J. Cox, J.M. Rehg, and S. Hingorani, "A Bayesian Mulitple-Hypothesis Approach to Edge Grouping and Contour Segmentation," IJCV, vol. 11, no. 1, pp. 5-24, 1993.
[9] J.H. Fridman, J.L. Bentley, and R.A. Finkel, "An Algorithm for Finding Best Matches in Logarithmic Expected Time," ACM Trans. Mathematical Software, vol. 3, no. 3, pp. 209-226, Sept. 1977.
[10] D. Geman,S. Geman,C. Graffigne,, and P. Dong,“Boundary detection by constrained optimization,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, no. 7, pp. 609-628, July 1990.
[11] I.E. Gordon, Theories of Visual Perception, first ed. John Wiley and Sons, 1989.
[12] W.E.L. Grimson, Object Recognition by Computer: The Role of Geometric Constraints, first ed. Cambridge, Mass.: Massachusetts Institute of Technology Press, 1990.
[13] W.E.L. Grimson and D.P. Huttenlocher, “On the Verification of Hypothesized Matches in Model-Based Recognition,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 12, pp. 1201-1213, 1991.
[14] G. Guy and G. Medioni, "Perceptual Grouping Using Global Saliency-Enhancing Operators," Proc. Int'l Conf. Pattern Recognition '92, vol. 1, pp. 99-103, 1992.
[15] P. Havaldar, G. Medioni, and F. Stein, "Extraction of Groups for Recognition," ECCV-94, pp. 251-261,Stockholm, 1994.
[16] L. Herault and R. Horaud, “Figure Ground Discrimination: A Combinatorial Optimization Method,” IEEE Tran. Pattern Analysis and Machine Intelligence, vol. 15, no. 9, pp. 899-914, Sept. 1993.
[17] D.W. Jacobs, "The Use of Grouping in Visual Object Recognition," PhD dissertation, Massachusetts Institute of Technology, Dept. of Electrical Eng. and Computer Science, June 1988.
[18] D.W. Jacobs, "Robust and Efficient Detection of Salient Convex Groups," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 18, pp. 23-37, Jan. 1996.
[19] D.W. Jacobs and C. Chennubhotla, "Finding Structurally Consistent Motion Correspondences," Proc. Int'l Conf. Pattern Recognition '94, vol. 1, pp. 650-653,Jerusalem, 1994.
[20] M. Lindenbaum, "On the Amount of Information Required for Object Recognition," CIS Report 9329, Technion, Nov.1993 (revised July 1995). A shorter version appeared in Proc. Int'l Conf. Pattern Recognition, pp. 726-729, 1994.
[21] D.G. Lowe, Perceptual Organization and Visual Recognition. Kluwer Academic Pub., 1985.
[22] D.W. Matula, "Graph Theoretic Techniques for Cluster Analysis Algorithms," V. Ryzin, ed., Classification and Clustering, pp. 95-129. Academic Press, 1977.
[23] R. Mohan and R. Nevatia, “Using Perceptual Organization to Extract 3-D Structures,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 11, pp. 1,121-1,139, Nov. 1989.
[24] E.M. Palmer, Graphical Evolution, Series in Discrete Mathematics. John Wiley and Sons, 1985.
[25] P. Parent and S.W. Zucker, “Trace Inference, Curvature Consistency and Curve Detection,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 8, pp. 823-839, 1989.
[26] E. Saund, “Labeling of Curvilinear Structure Across Scales By Token Grouping,” Proc. Conf. Computer Vision and Pattern Recognition, pp. 257-263, 1992.
[27] A. Sha'ashua and S. Ullman, “Structural Saliency: The Detection of Globally Salient Structures Using a Locally Connected Network,” Proc. Int'l Conf. Computer Vision, pp. 321-327, 1988.
[28] A. Sha'ashua and S. Ullman, "Grouping Contours by Iterated Pairing Network," Neural Information Processing Systems (NIPS), vol. 3, 1990.
[29] L.G. Shapiro and R.M. Haralick, "Decomposition of Two-Dimensional Shapes by Graph-Theoretic Clustering," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 1, no. 1, pp. 10-20, Jan. 1979.
[30] L.S. Shapiro, "Affine Analysis of Image Sequences," PhD dissertation, Univ. of Oxford, 1994.
[31] R. Sitaraman and A. Rosenfeld, "Probabilistic Analysis of Two Stage Matching," Pattern Recognition, vol. 22, no. 3, pp. 331-343, 1989.
[32] M. Tuceryan, A.K. Jain, and N. Ahuja, "Supervised Classification of Early Perceptual Structure in Dot Patterns, " Proc. Int'l Conf. Pattern Recognition '92, pp. 88-91, 1992.
[33] G. Vosselman, "Relational Matching," Lecture Notes in Computer Science, third ed. Springer, 1992.
[34] A. Wald, "Sequencial Analysis," Wiley Publications in Statistics, third ed. Wiley, 1947 (1952).
[35] R. Weiss and M. Boldt, "Geometric Grouping Applied to Straight Lines," Computer Vision and Pattern Recognition, pp. 489-495, 1986.
[36] M. Wertheimer, "Laws of Organization in Perceptual Forms," W. D. Ellis, ed., A Source Book of Gestalt Psychology, pp. 71-88, 1950.
[37] A.P. Witkin and J.M. Tenenbaum, "On the Role of Structure in Vision," J. Beck, B. Hope, and A. Rosenfeld, eds., Human and Machine Vision, pp. 481-543. Academic Press, 1983.
[38] Z. Wu and R. Leahy, “An Optimal Graph Theoretic Approach to Data Clustering: Theory and Its Application to Image Segmentation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 15, no. 11, pp. 1,101-1,113, Nov. 1993.
[39] A. Zisserman, J.L. Mundy, D.A. Forsyth, J. Liu, N. Pillow, C. Rothwell, and S. Utcke, “Class-Based Grouping in Perspective Images,” Proc. Fifth Int'l Conf. Computer Vision, pp. 183-188, June 1995.
[40] S.W. Zucker, "Computational and Psychophysical Experiments in Grouping: Early Orientation Selection," J. Beck, B. Hope, and A. Rosenfeld, eds., Human and Machine Vision, pp. 545-567. Academic Press, Feb. 1983.

Index Terms:
Perceptual grouping, grouping analysis, graph clustering, maximum likelihood, Wald's SPRT, performance prediction, generic grouping algorithm.
Citation:
Arnon Amir, Michael Lindenbaum, "A Generic Grouping Algorithm and Its Quantitative Analysis," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 20, no. 2, pp. 168-185, Feb. 1998, doi:10.1109/34.659934
Usage of this product signifies your acceptance of the Terms of Use.