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Mathematical Problems in Engineering
Volume 2016, Article ID 6098021, 10 pages
Research Article

Fractional Differentiation-Based Active Contour Model Driven by Local Intensity Fitting Energy

1Department of Precision Instrument, Tsinghua University, Beijing 100084, China
2College of Computer Science and Information Technology, Zhejiang Wanli University, Ningbo 315100, China

Received 28 October 2015; Revised 28 March 2016; Accepted 19 April 2016

Academic Editor: Weizhong Dai

Copyright © 2016 Ming Gu and Renfang Wang. 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.


A novel active contour model is proposed for segmentation images with inhomogeneity. Firstly, fractional order filter is defined by eight convolution masks corresponding to the image orientation in the eight compass directions. Then, the fractional order differentiation image is obtained and applied to the level set method. Secondly, we defined a new energy functional based on local image information and fractional order differentiation image; the proposed model not only can describe the input image more accurately but also can deal with intensity inhomogeneity. Local fitting term can enhance the ability of the model to deal with intensity inhomogeneity. The defined penalty term is used to reduce the occurrence of false boundaries. Finally, in order to eliminate the time-consuming step of reinitialization and ensure stable evolution of level set function, the Gaussian filtering method is used. Experiments on synthetic and real images show that the proposed model is efficient for images with intensity inhomogeneity and flexible to initial contour.