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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 367086, 13 pages
Research Article

Implicit Active Contour Model with Local and Global Intensity Fitting Energies

1College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
2School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, China

Received 19 December 2012; Accepted 28 March 2013

Academic Editor: Oluwole Daniel Makinde

Copyright © 2013 Xiaozeng Xu and Chuanjiang He. 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 new active contour model which integrates a local intensity fitting (LIF) energy with an auxiliary global intensity fitting (GIF) energy. The LIF energy is responsible for attracting the contour toward object boundaries and is dominant near object boundaries, while the GIF energy incorporates global image information to improve the robustness to initialization of the contours. The proposed model not only can provide desirable segmentation results in the presence of intensity inhomogeneity but also allows for more flexible initialization of the contour compared to the RSF and LIF models, and we give a theoretical proof to compute a unique steady state regardless of the initialization; that is, the convergence of the zero-level line is irrespective of the initial function. This means that we can obtain the same zero-level line in the steady state, if we choose the initial function as a bounded function. In particular, our proposed model has the capability of detecting multiple objects or objects with interior holes or blurred edges.