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.