This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Design Considerations for Generic Grouping in Vision
April 2003 (vol. 25 no. 4)
pp. 445-457

Abstract—Grouping in vision can be seen as the process that organizes image entities into higher-level structures. Despite its importance, there is little consistency in the statement of the grouping problem in literature. In addition, most grouping algorithms in vision are inspired on a specific technique, rather than being based on desired characteristics, making it cumbersome to compare the behavior of various methods. This paper discusses six precisely formulated considerations for the design of generic grouping algorithms in vision: proper definition, invariance, multiple interpretations, multiple solutions, simplicity and robustness. We observe none of the existing algorithms for grouping in vision meet all the considerations. We present a simple algorithm as an extension of a classical algorithm, where the extension is based on taking the considerations into account. The algorithm is applied to three examples: grouping point sets, grouping poly-lines, and grouping flow-field vectors. The complexity of the greedy algorithm is {\cal{O}}(n{\cal O}_G) , where {\cal{O}}_G is the complexity of the grouping measure.

[1] N. Ahuja and M. Tuceryan, “Extraction of Early Perceptual Structure in Dot Patterns: Integrating Region, Boundary, and Gestalt,” Computer Vision, Graphics, and Image Processing, vol. 48, pp. 304-356, 1989.
[2] M.N. Murty, A.K. Jain, and P.J. Flynn, “Data Clustering: A Review,” ACM Computing Surveys, vol. 31, no. 3, pp. 264-323, 1999.
[3] A. Amir and M. Lindenbaum, “A Generic Grouping Algorithm and Its Quantitative Analysis,” IEEE Tran. Pattern Analysis and Machine Intelligence, vol. 20, no. 2, pp. 168-185, Feb. 1998.
[4] J. August and S.W. Zucker, “The Curve Indicator Random Field: Curve Organization Via Edge Correlation,” Perceptual Organization for Artificial Vision Systems, K. Boyer and S. Sarkar, eds., pp. 265-288, Boston: Kluwer Academic, Jan. 2000.
[5] M. Boldt, R. Weiss, and E. Riseman, “Token-Based Extraction of Straight Lines,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 6, pp. 1581-1595, June 1989.
[6] S. Casadei and S.K. Mitter, “Hierarchical Image Segmentation-Detection of Regular Curves in a Vector Graph,” Int'l J. Computer Vision, vol. 27, no. 3, 1998.
[7] I.J. Cox, J.M. Rehg, and S. Hingorani, “A Bayesian Multi-Hypothesis Approach to Edge Grouping and Contour Segmentation,” Int'l J. Computer Vision, vol. 11, no. 1, pp. 5-24, 1993.
[8] J. Dolan and R. Weiss, “Perceptual Grouping of Curved Lines,” Proc. Image Understanding Workshop, pp. 1135-1145, 1989.
[9] R. Duda, P. Hart, and D. Stork, Pattern Classification. New York: John Wiley&Sons, 2001.
[10] J.H. Elder and S.W. Zucker, “Evidence for Boundary-Specific Grouping,” Vision Research, vol. 38, no. 1, pp. 143-152, 1998.
[11] E.A. Engbers and A.W.M. Smeulders, “Requirements for Generic Grouping in Vision and an Algorithm,” ISIS Technical Report Series 2001-17, Univ. of Amsterdam, 2001.
[12] M.A. Fischler and R.C. Bolles, “Perceptual Organization and Curve Partitioning,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 8, pp. 100-105, 1986.
[13] W.E.L. Grimson, "The Combinatorics of Heuristic Search Termination for Object Recognition in Cluttered Environments," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 9, pp. 920-935, Sept. 1991.
[14] 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.
[15] G. Guy and G. Medioni, “Inference of Surfaces, 3D Curves, and Junctions from Sparse, Noisy, 3D Data,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 11, pp. 1265-1277, Nov. 1997.
[16] D.W. Jacobs, “Grouping for Recognition,” MIT AI Memo 1177, 1989.
[17] 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.
[18] A.K. Jain and R.C. Dubes, Algorithms for Clustering Data. Englewood Cliffs, N.J.: Prentice Hall, 1988.
[19] N. Jardine and R. Sibson, Mathematical Taxonomy. London: Wiley, 1971.
[20] A. Jonk and A.W.M. Smeulders, “An Axiomatic Approach to Clustering Line-Segments,” Proc. Third Int'l Conf. Document Analysis and Recognition, pp. 386-389, 1995.
[21] G. Kanizsa, Organization in Vision. Preager, 1979.
[22] R. Krishnapuram and J.M. Keller, “A Possibilistic Approach to Clustering,” IEEE Fuzzy Systems, vol. 1, no. 2, pp. 98-110, 1993.
[23] N. Kruger, “Collinearity and Parallelism Are Statistically Significant Second-Order Relations of Complex Cell Responses,” Neural Processing Letters, vol. 8, pp. 117-129, 1998.
[24] G.N. Lance and W.T. Williams, “Computer Programs for Hierarchical Polythetic Classification,” Computer J., vol. 9, pp. 60-64, 1966.
[25] G.N. Lance and W.T. Williams, “A General Theory of Classificatory Sorting Strategies: I. Hierarchical Systems,” Computer J., vol. 9, pp. 373-380, 1966.
[26] G.N. Lance and W.T. Williams, “A General Theory of Classificatory Sorting Strategies: II. Clustering Systems,” Computer J., vol. 10, pp. 271-277, 1967.
[27] D.G. Lowe, “Perceptual Organization and Visual Recognition,” PhD thesis, Stanford Univ., 1984.
[28] S.Y. Lu and K.S. Fu, “A Sentence to Sentence Clustering Procedure for Pattern Analysis,” IEEE Trans. System, Man, and Cybernetics, vol. 8, pp. 381-389, 1978.
[29] D. Marr, Vision. San Francisco: W.H. Freeman and Company, 1982.
[30] J. McQueen, “Some Methods for Classification and Analysis of Multivariate Observations,” Proc. Fifth Berkeley Symp. Math. Statistics and Probability, pp. 281-297, 1967.
[31] R. Mohan and R. Nevatia, "Perceptual Organization for Scene Segmentation and Description," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, no. 6, pp. 616-635, June 1992.
[32] R.M. Needham, “A Method for Using Computers in Information Classification,” Proc. IFIP Congress '62, C.M. Popplewel, ed., pp. 284-287, 1962.
[33] M. Nitzberg, D. Mumford, and T. Shiota, “Filtering, Segmentation and Depth Filtering, Segmentation and Depth,” Lecture Notes in Computer Science, vol. 662, 1993.
[34] 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.
[35] J. Princen, J. Illingworth, and J. Kittler, “A Hierarchical Approach to Line Extraction Based on the Hough Transform,” Computer Vision, Graphics, and Image Processing, vol. 52, pp. 57-77, 1990.
[36] I. Rock, The Logic of Perception. MIT Press, 1983.
[37] E.H. Ruspini, “A New Approach to Clustering,” Information and Control, vol. 15, pp. 22-32, 1969.
[38] S. Santini and R. Jain, “Similarity Measures,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 9, pp. 871-883, Sept. 1999.
[39] S. Sarkar and K.L. Boyer, "Integration, Inference, and Management of Spatial Information Using Bayesian Networks: Perceptual Organization," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 15, no. 3, pp. 256-274, Mar. 1993. Special Section on Probabilistic Reasoning.
[40] S. Sarkar and K.L. Boyer, “Perceptual Organization in Computer Vision: A Review and a Proposal for a Classificatory Structure,” IEEE Trans. Systems, Man, and Cybernetics, vol. 23, no. 2, pp. 382-399, 1993.
[41] E. Saund, “Identifying Salient Circular Arcs on Curves,” CVGIP: Image Understanding, vol. 58, no. 3, pp. 327-337, 1993.
[42] I. Sethi and A.K. Jain, Artificail Neural Networks and Pattern Recognition: Old an New Connections, I. Sethi and A.K. Jain, eds., Elsevier Science, 1991.
[43] R. Weiss and M. Boldt, “Geometric Grouping Applied to Straight Lines,” Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, pp. 489-495, 1986.
[44] A. Witkin and J. Tenenbaum, “On the Role of Structure in Vision,” Human and Machine Vision, J. Beck, B. Hope, and A. Rozenfeld, eds. pp. 481-543, Academic Press, 1983.
[45] A.P. Witkin and J.M. Tenenbaum, “What Is Perceptual Organization For?” Proc. Eighth Int'l Joint Conf. Artificial Intelligence, pp. 1023-1026, 1983.
[46] W.E. Wright, “A Formalization of Cluster Analysis,” Pattern Recognition, vol. 5, pp. 273-282, 1973.
[47] 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.
[48] J. Xiao, Z. Yang, and S. Ma, “Some General Grouping Principles: Line Perception From Points as an Example,” Proc. 14th Int'l Conf. Pattern Recognition, A.K. Jain, S. Venkatesh, and B.C. Lovell, eds., pp. 1825-1828, 1998.
[49] C.T. Zahn, “Graph-Theoretical Methods for Detecting and Describing Gestalt Clusters,” IEEE Trans. Computers, vol. 20, pp. 68-86, 1971.
[50] S.W. Zucker, “The Diversity of Perceptual Grouping,” Vision, Brain, and Cooperative Computation, M.A. Arbib and A.R. Hanson, eds. pp. 231-262, Cambridge, Mass.: MIT Press, 1987.

Index Terms:
Grouping, design considerations, vision, perceptual grouping, clustering.
Citation:
Erik A. Engbers, Arnold W.M. Smeulders, "Design Considerations for Generic Grouping in Vision," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 25, no. 4, pp. 445-457, April 2003, doi:10.1109/TPAMI.2003.1190571
Usage of this product signifies your acceptance of the Terms of Use.