On the Performance of Connected Components Grouping

Grouping processes may benefit computationally when simple algorithms are used as part of the grouping process. In this paper we consider a common and extremely fast grouping process based on the connected components algorithm. Relying on a probabilistic model, we focus on analyzing the algorithm's performance. In particular, we derive the expected number of addition errors and the group fragmentation rate. We show that these performance figures depend on a few inherent and intuitive parameters. Furthermore, we show that it is possible to control the grouping process so that the performance may be chosen within the bounds of a given tradeoff. The analytic results are supported by implementing the algorithm and testing it on synthetic and real images.

[1]  David W. Jacobs,et al.  The Use of Grouping in Visual Object Recognition , 1988 .

[2]  James L. McClelland,et al.  B-Spline Contour Representation and Symmetry Detection , 1993 .

[3]  Steven W. Zucker,et al.  Curve-like sets, normal complexity, and representation , 1994, Proceedings of 12th International Conference on Pattern Recognition.

[4]  P. Erdos,et al.  On the evolution of random graphs , 1984 .

[5]  William Grimson,et al.  Object recognition by computer - the role of geometric constraints , 1991 .

[6]  Kim L. Boyer,et al.  Perceptual organization in computer vision: a review and a proposal for a classificatory structure , 1993, IEEE Trans. Syst. Man Cybern..

[7]  Donald Geman,et al.  Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images , 1984 .

[8]  K. Boyer,et al.  Perceptual Organization for Artificial Vision Systems , 2000 .

[9]  J. Hammersley,et al.  Percolation processes , 1957, Mathematical Proceedings of the Cambridge Philosophical Society.

[10]  R. Nevatia,et al.  Perceptual Organization for Scene Segmentation and Description , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[11]  Robert M. Haralick,et al.  Decomposition of Two-Dimensional Shapes by Graph-Theoretic Clustering , 1979, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[12]  A. Witkin,et al.  On the Role of Structure in Vision , 1983 .

[13]  David G. Lowe,et al.  Perceptual Organization and Visual Recognition , 2012 .

[14]  Radu Horaud,et al.  Figure-Ground Discrimination: A Combinatorial Optimization Approach , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[15]  Shimon Ullman,et al.  Recognizing solid objects by alignment with an image , 1990, International Journal of Computer Vision.

[16]  A. Amir,et al.  Quantitative Analysis of Grouping Processes , 1996, ECCV.

[17]  Béla Bollobás,et al.  Random Graphs , 1985 .

[18]  Michael Lindenbaum,et al.  A Generic Grouping Algorithm and Its Quantitative Analysis , 1998, IEEE Trans. Pattern Anal. Mach. Intell..

[19]  David W. Jacobs,et al.  Robust and Efficient Detection of Salient Convex Groups , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[20]  Robert M. Haralick,et al.  Random perturbation models for boundary extraction sequence , 1997, Machine Vision and Applications.

[21]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[22]  S. Redner,et al.  Introduction To Percolation Theory , 2018 .

[23]  B. Bollobás.  The evolution of random graphs , 1984 .

[24]  O DudaRichard,et al.  Use of the Hough transformation to detect lines and curves in pictures , 1972 .

[25]  David W. Jacobs,et al.  Space and Time Bounds on Indexing 3D Models from 2D Images , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[26]  Jitendra Malik,et al.  Normalized Cut and Image Segmentation , 1997 .

[27]  Kim L. Boyer,et al.  Guest Editors' Introduction: Perceptual Organization in Computer Vision: Status, Challenges, and Potential , 1999, Comput. Vis. Image Underst..

[28]  Shimon Ullman,et al.  Structural Saliency: The Detection Of Globally Salient Structures using A Locally Connected Network , 1988, [1988 Proceedings] Second International Conference on Computer Vision.