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A Grouping Principle and Four Applications
April 2003 (vol. 25 no. 4)
pp. 508-513

Abstract—Wertheimer's theory suggests a general perception law according to which objects having a quality in common get perceptually grouped. The Helmholtz principle is a quantitative version of this general grouping law. It states that a grouping is perceptually “meaningful” if its number of occurrences would be very small in a random situation: Geometric structures are then characterized as large deviations from randomness. In two previous works, we have applied this principle to the detection of orientation alignments and boundaries in a digital image. In this paper, we show that the method is fully general and can be extended to a grouping by any quality. We treat as an illustration the alignments of objects, their grouping by color and by size, and the vicinity gestalt (clusters). Collaboration of the gestalt grouping laws and their pyramidal structure are illustrated in a case study.

[1] A. Almansa, A. Desolneux, and S. Vamech, “Vanishing Point Detection without Any A Priori Information,” vol. 25, no. 4, pp. 502-507, Apr. 2003.
[2] A. Desolneux, L. Moisan, and J.-M. Morel, “Meaningful Alignments,” Int'l J. Computer Vision, vol. 40, no. 1, pp. 7-23, 2000.
[3] A. Desolneux, L. Moisan, and J.M. Morel, “Edge Detection by Helmholtz Principle,” J. Math. Imaging and Vision, vol. 14, no. 3, pp. 271-284, 2001.
[4] A. Desolneux, L. Moisan, and J.-M. Morel, “Maximal Meaningful Events and Applications to Image Analysis,” Annals of Statistics, pending publication,http://www.cmla.ens-cachan.fr/Cmla/Publications 2000.
[5] F. Fleuret and D. Geman, “Coarse-to-Fine Face Detection,” Int'l J. Computer Vision, vol. 41, no. 1, pp. 85-107, 2001.
[6] D. Geman and B. Jedynak, “Model-Based Classification Trees,” IEEE Trans. Information Theory, vol. 47, no. 3, 2001.
[7] Y. Gousseau, “The Size of Objects in Natural Images,” PhD dissertation, UniversitéParis-Dauphine, 2000.
[8] G. Guy and G. Medioni, “Inferring Global Perceptual Contours from Local Features,” Int'l J. Computer Vision, vol. 20, pp. 113-133, 1996.
[9] G. Kanizsa, Grammatica del Vedere, Il Mulino, Bologna, 1980. Traduction française: La grammaire du voir, Diderot Editeur, Arts et Sciences, 1996.
[10] M. Kass, A. Witkin, and D. Terzopoulos, “Snakes: Active Contour Models,” Proc. First Int'l Computer Vision Conf., 1987.
[11] N. Kiryati, Y. Eldar, and A.M. Bruckstein, “A Probabilistic Hough Transform,” Pattern Recognition, vol. 24, no. 4, pp. 303-316, 1991.
[12] D.G. Lowe, Perceptual Organization and Visual Recognition. Boston: Kluwer Academic, 1985.
[13] 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.
[14] D. Shaked, O. Yaron, and N. Kiryati, “Deriving Stopping Rules for the Probabilistic Hough Transform by Sequential Analysis,” Computer Vision and Image Understanding, vol. 63, pp. 512-526, 1996.
[15] C.V. Stewart, “MINPRAN: A New Robust Estimator for Computer Vision,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, no. 10, pp. 925-938, Oct. 1995.
[16] M. Wertheimer, “Untersuchungen zur Lehre der Gestalt,” Psychologische Forschung, vol. 4, pp. 301-350, 1923.
[17] S.W. Zucker and C. David, “Points and End-Points: A Size-Spacing Constraint for Dot Grouping,” Perception, vol. 17, pp. 229-247, 1988.

Index Terms:
Gestalt grouping laws, a contrario probabilistic model, binomial law, number of false alarms, histogram modes, clusters, alignments.
Citation:
Agnès Desolneux, Lionel Moisan, Jean-Michel Morel, "A Grouping Principle and Four Applications," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 25, no. 4, pp. 508-513, April 2003, doi:10.1109/TPAMI.2003.1190576
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