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Active contour models based on the level set method (LSM) are widely used in image segmentation. The major advantages of these models based on an LSM are topological flexibility and evolution robustness. However, topological flexibility is not always needed, and it could bring some negative effects for object extraction, such as extracting noise and non-objects. In this paper, a topological preservation method is proposed to constrain the evolution of contour. First, the modes of topological changes in geometric active contour models are analyzed. Second, on the basis of the modes of topological changes, the corresponding constraints are designed to keep the topology. To be specific, extracting objects with a known topology (such as k-connected objects) is viewed as a sparse representation problem under a set of basis functions. According to sparse representation, the increase or decrease of evolving contours' topology corresponds to those of the basis functions. Thus, a corresponding energy functional for topology preservation is defined based on basis functions. Finally, the proposed constraint is integrated into geometric active contour models, which is useful in extracting special objects. Experiments demonstrate that the proposed method improves the robustness of the performance of active contour models and can increase the accuracy in target object extraction.

A Topology Preserving Method of Evolving Contours Based on Sparsity Constraint for Object Segmentation