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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 508543, 16 pages
http://dx.doi.org/10.1155/2013/508543
Research Article

Fast Image Segmentation Based on Efficient Implementation of the Chan-Vese Model with Discrete Gray Level Sets

School of Management, Harbin Institute of Technology, Harbin 150001, China

Received 3 December 2012; Accepted 28 January 2013

Academic Editor: Clara Ionescu

Copyright © 2013 Songsong Li and Qingpu Zhang. 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.

Abstract

A new image segmentation based on fast implementation of the Chan-Vese model is proposed. This approach differs from previous methods in that we do not need to solve the Euler-Lagrange equation of the underlying variational problem. First, through experiments, we observe that for the smooth image segmentation, Chan-Vese model (CVM) can be simplified. Utilizing the Gaussian low pass filter, we pretreat the original image and regularize the level curves. Then, we calculate the energy directly on discrete gray level sets, find the minimizer of the energy, and obtain the segmentation results. We analyze the algorithm and prove that under discrete gray level sets, the global minimum of the energy is same as the one obtained by the previous methods. Another advantage of this method is that the reinitialization is not needed. Since there are at most 255 discrete gray level sets, the algorithm improves the computational speed dramatically. And the complexity of the algorithm is , where is the number of pixels in the image. So even for the large images, it is also very efficient. We apply our segmentation algorithm to synthetic and real world images to emphasize the performances of our model compared with other segmentation models.