A variational framework for active and adaptative segmentation of vector valued images

Much effort has been made in integrating different information in a variational framework to segment images. Recent works on curve propagation were able to incorporate stochastic information (see Paragios, N. and Deriche, R., J. Visual Commun. and Image Representation, 2002; Zhu, S. and Yuille, A., 1996) and prior knowledge on shapes (see Cremers, D. et al., 2002; Rousson M. and Paragios, N., 2002). The information inserted in these studies is most of the time extracted offline. Meanwhile, other approaches have proposed to extract region information during the segmentation process itself (see Chan, T. et al., 2000; Jehan-Besson, S. et al., 2002; Yezzi, A. et al., 1999). Following these new approaches and extending the work of Paragios and Deriche to vector-valued images, we propose an entirely variational framework to approach the segmentation problem. Both the image partition and the statistical parameters for each region are unknown. After a brief reminder on recent segmenting methods, we present a variational formulation obtained from a Bayesian model. After that, we show two different differentiations driving to the same evolution equations. Detailed studies on gray and color images of the 2-phase case follow. We finish with an application to tracking which shows the benefits of our dynamic framework.