A class of constrained clustering algorithms for object boundary extraction

Boundary extraction is a key task in many image analysis operations. This paper describes a class of constrained clustering algorithms for object boundary extraction that includes several well-known algorithms proposed in different fields (deformable models, constrained clustering, data ordering, and traveling salesman problems). The algorithms belonging to this class are obtained by the minimization of a cost function with two terms: a quadratic regularization term and an image-dependent term defined by a set of weighting functions. The minimization of the cost function is achieved by lowpass filtering the previous model shape and by attracting the model units toward the centroids of their attraction regions. To define a new algorithm belonging to this class, the user has to specify a regularization matrix and a set of weighting functions that control the attraction of the model units toward the data. The usefulness of this approach is twofold: it provides a unified framework for many existing algorithms in pattern recognition and deformable models, and allows the design of new recursive schemes.

[1]  John F. Canny,et al.  A Computational Approach to Edge Detection , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[2]  J. MacQueen.  Some methods for classification and analysis of multivariate observations , 1967 .

[3]  Theodosios Pavlidis,et al.  Algorithms for Shape Analysis of Contours and Waveforms , 1980, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[4]  Mubarak Shah,et al.  A Fast algorithm for active contours and curvature estimation , 1992, CVGIP Image Underst..

[5]  Jorge S. Marques,et al.  Unified approach to snakes, elastic nets and Kohonen maps , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[6]  Laurent D. Cohen.  Auxiliary variables for deformable models , 1995, Proceedings of IEEE International Conference on Computer Vision.

[7]  J. C. Dunn,et al.  A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Compact Well-Separated Clusters , 1973 .

[8]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[9]  Charles W. Therrien,et al.  Discrete Random Signals and Statistical Signal Processing , 1992 .

[10]  Timothy F. Cootes,et al.  Active Shape Models-Their Training and Application , 1995, Comput. Vis. Image Underst..

[11]  James C. Bezdek,et al.  A Convergence Theorem for the Fuzzy ISODATA Clustering Algorithms , 1980, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[12]  T. Poggio,et al.  Ill-Posed Problems and Regularization Analysis in Early Vision , 1984 .

[13]  Frank Fallside,et al.  An adaptive training algorithm for back propagation networks , 1987 .

[14]  D Marr,et al.  Theory of edge detection , 1979, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[15]  Geoffrey E. Hinton,et al.  Combining two methods of recognizing hand-printed digits , 1992 .

[16]  Dana H. Ballard,et al.  Generalizing the Hough transform to detect arbitrary shapes , 1981, Pattern Recognit..

[17]  Tai Sing Lee,et al.  Region competition: unifying snakes, region growing, energy/Bayes/MDL for multi-band image segmentation , 1995, Proceedings of IEEE International Conference on Computer Vision.

[18]  Rachid Deriche.  Fast Algorithms for Low-Level Vision , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[19]  Azriel Rosenfeld,et al.  Compact Object Recognition Using Energy-Function-Based Optimization , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[20]  Andrew Blake,et al.  Dynamic contours: real-time active splines , 1993 .

[21]  William R. Uttal,et al.  A Particle System Model for Combining Edge Information from Multiple Segmentation Modules , 1994, CVGIP Graph. Model. Image Process..

[22]  W. T. Tucker,et al.  Convergence theory for fuzzy c-means: Counterexamples and repairs , 1987, IEEE Transactions on Systems, Man, and Cybernetics.

[23]  D. J. Burr,et al.  An improved elastic net method for the traveling salesman problem , 1988, IEEE 1988 International Conference on Neural Networks.

[24]  Jorge S. Marques,et al.  Exploiting the common structure of some edge linking algorithms: an experimental study , 1995, Proceedings., International Conference on Image Processing.

[25]  Michael J. Black,et al.  The outlier process: unifying line processes and robust statistics , 1994, 1994 Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[26]  K. Schulten,et al.  Kohonen's self-organizing maps: exploring their computational capabilities , 1988, IEEE 1988 International Conference on Neural Networks.

[27]  Richard Durbin,et al.  An analogue approach to the travelling salesman problem using an elastic net method , 1987, Nature.

[28]  Richard Szeliski,et al.  An Analysis of the Elastic Net Approach to the Traveling Salesman Problem , 1989, Neural Computation.

[29]  Geoffrey C. Fox,et al.  Constrained Clustering as an Optimization Method , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[30]  Martin Fodslette Meiller.  A Scaled Conjugate Gradient Algorithm for Fast Supervised Learning , 1993 .

[31]  Gérard G. Medioni,et al.  Simultaneous segmentation and approximation of complex patterns , 1994, 1994 Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[32]  Bernard Widrow,et al.  The "Rubber-Mask" Technique I. Pattern Measurement and Analysis , 1973 .

[33]  Alan L. Yuille,et al.  Re ion COm et it ion: Unifying Snakes,Region Growing, inergy/Bayes P MDL for Multi-band Image Segmentation , 1995 .

[34]  Teuvo Kohonen,et al.  The self-organizing map , 1990 .

[35]  Alan L. Yuille,et al.  Deformable templates , 1993 .

[36]  Anders Krogh,et al.  Introduction to the theory of neural computation , 1994, The advanced book program.

[37]  David J. Burr,et al.  Elastic Matching of Line Drawings , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[38]  R. Gray,et al.  Vector quantization , 1984, IEEE ASSP Magazine.

[39]  Martin Fodslette Møller,et al.  A scaled conjugate gradient algorithm for fast supervised learning , 1993, Neural Networks.

[40]  Masahiko Yachida,et al.  A Versatile Machine Vision System for Complex Industrial Parts , 1977, IEEE Transactions on Computers.

[41]  Laurent D. Cohen,et al.  Finite-Element Methods for Active Contour Models and Balloons for 2-D and 3-D Images , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[42]  Laurent D. Cohen,et al.  On active contour models and balloons , 1991, CVGIP Image Underst..

[43]  Richard Szeliski,et al.  Tracking with Kalman snakes , 1993 .

[44]  M. Møller.  A Scaled Conjugate Gradient Algorithm for Fast Supervised Learning , 1990 .

[45]  Demetri Terzopoulos,et al.  Regularization of Inverse Visual Problems Involving Discontinuities , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[46]  Ramesh C. Jain,et al.  Using Dynamic Programming for Solving Variational Problems in Vision , 1990, IEEE Trans. Pattern Anal. Mach. Intell..