A variational formulation for segmenting desired objects in color images

  • Authors:

  • Ling Pi;Chaomin Shen;Fang Li;Jinsong Fan

  • Affiliations:

  • Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, PR China;Joint Laboratory for Imaging Science and Technology, Department of Computer Science, East China Normal University, Shanghai 200062, PR China;Department of Mathematics, East China Normal University, Shanghai 200062, PR China and Department of Mathematics, Southwest University, Chongqing 400715, PR China;Department of Mathematics, East China Normal University, Shanghai 200062, PR China and School of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang Province 325000, PR Chin ...

  • Venue:
  • Image and Vision Computing
  • Year:
  • 2007

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Abstract

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.