Journal of Applied Mathematics
Volume 2012 (2012), Article ID 692589, 16 pages
Research Article

Convex Image Segmentation Model Based on Local and Global Intensity Fitting Energy and Split Bregman Method

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Received 8 September 2011; Accepted 20 November 2011

Academic Editor: Wenyu Sun

Copyright © 2012 Yunyun Yang and Boying Wu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We propose a convex image segmentation model in a variational level set formulation. Both the local information and the global information are taken into consideration to get better segmentation results. We first propose a globally convex energy functional to combine the local and global intensity fitting terms. The proposed energy functional is then modified by adding an edge detector to force the active contour to the boundary more easily. We then apply the split Bregman method to minimize the proposed energy functional efficiently. By using a weight function that varies with location of the image, the proposed model can balance the weights between the local and global fitting terms dynamically. We have applied the proposed model to synthetic and real images with desirable results. Comparison with other models also demonstrates the accuracy and superiority of the proposed model.