Self-Crossing Detection and Location for Parametric Active Contours

Department of Electrical and Computer Engineering, BostonUniversity, Boston, MA 02115, USA.
IEEE Transactions on Image Processing (Impact Factor: 3.63). 02/2012; 21(7):3150-6. DOI: 10.1109/TIP.2012.2188808
Source: PubMed


Active contours are very popular tools for video tracking and image segmentation. Parameterized contours are used due to their fast evolution and have become the method of choice in the Sobolev context. Unfortunately, these contours are not easily adaptable to topological changes, and they may sometimes develop undesirable loops, resulting in erroneous results. To solve such topological problems, one needs an algorithm for contour self-crossing detection. We propose a simple methodology via simple techniques from differential topology. The detection is accomplished by inspecting the total net change of a given contour's angle, without point sorting and plane sweeping. We discuss the efficient implementation of the algorithm. We also provide algorithms for locating crossings by angle considerations and by plotting the four-connected lines between the discrete contour points. The proposed algorithms can be added to any parametric active-contour model. We show examples of successful tracking in real-world video sequences by Sobolev active contours and the proposed algorithms and provide ideas for further research.

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    • "In (Nakhmani & Tannenbaum, 2012), a constant number of nodes is set, and the removed nodes are replaced but in the most sparse regions. When an active contour is used to approximate complex shapes, for instance the one presented in Figure 1, it is difficult to assume a constant number of nodes. "
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    • "In publication [7], self–crossings are removed based on calculated angle values between neighbouring nodes, calculated slopes of consecutive segments and with the use of four–connected line interpolation. In publication [7], a certain constant number of nodes of the active contour approximating the moving object in a video image sequence is assumed, and the removed nodes are replaced in the most sparse regions . When segmenting shapes in medical images, which are frequently very complex, it is difficult to assume a constant number of nodes, so there is unfortunately no single solution for all possible applications . "
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