A variational formulation for segmenting desired objects in color images

This paper presents a new variational formulation for detecting interior and exterior boundaries of desired object(s) in color images. The classical level set methods can handle changes in topology, but can not detect interior boundaries. The Chan-Vese model can detect the interior and exterior boundaries of all objects, but cannot detect the boundaries of desired object(s) only. Our method combines the advantages of both methods. In our algorithm, a discrimination function on whether a pixel belongs to the desired object(s) is given. We define a modified Chan-Vese functional and give the corresponding evolution equation. Our method also improves the classical level set method by adding a penalizing term in the energy functional so that the calculation of the signed distance function and re-initialization can be avoided. The initial curve and the stopping function are constructed based on that discrimination function. The initial curve locates near the boundaries of the desired object(s), and converges to the boundaries efficiently. In addition, our algorithm can be implemented by using only simple central difference scheme, and no upwind scheme is needed. This algorithm has been applied to real images with a fast and accurate result. The existence of the minimizer to the energy functional is proved in the Appendix A.