Shape collaborative representation with fuzzy energy based active contour model

This paper presents a fuzzy energy-based active contour model for image segmentation with shape prior based on collaborative representation of training shapes. In the paper, a fuzzy energy functional including a data term and a shape prior term is proposed. The data term relies on image information to guide the evolution of the contour. Meanwhile, the shape prior term constrains the evolving contour with respect to the priori shape to handle background clutter and object occlusion. Especially, in this study, the prior shape is represented as the combination of atoms in the shape dictionary based on collaborative representation. In particular, instead of using ℓ₁-norm regularization as in sparse representation, we utilize ℓ₂-regularized linear regression scheme which can obtain algebraic solution for the coding coefficients, and significantly reduces the computation time. The proposed model therefore can segment images with background clutter and object occlusion even when the training set includes shapes with large variation. In addition, the proposed shape collaborative representation model also takes less computational time compared to shape sparse representation approach. Experimental results on various images and comparisons with other models show the desired performances of the proposed model.