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Xiao Han, Chenyang Xu, Jerry L. Prince, "A Topology Preserving Level Set Method for Geometric Deformable Models," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 25, no. 6, pp. 755768, June, 2003.  
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@article{ 10.1109/TPAMI.2003.1201824, author = {Xiao Han and Chenyang Xu and Jerry L. Prince}, title = {A Topology Preserving Level Set Method for Geometric Deformable Models}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {25}, number = {6}, issn = {01628828}, year = {2003}, pages = {755768}, doi = {http://doi.ieeecomputersociety.org/10.1109/TPAMI.2003.1201824}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Pattern Analysis and Machine Intelligence TI  A Topology Preserving Level Set Method for Geometric Deformable Models IS  6 SN  01628828 SP755 EP768 EPD  755768 A1  Xiao Han, A1  Chenyang Xu, A1  Jerry L. Prince, PY  2003 KW  Geometric deformable model KW  topology preservation KW  topological constraint KW  level set method KW  digital topology KW  simple points KW  active contours. VL  25 JA  IEEE Transactions on Pattern Analysis and Machine Intelligence ER   
Abstract—Active contour and surface models, also known as deformable models, are powerful image segmentation techniques. Geometric deformable models implemented using level set methods have advantages over parametric models due to their intrinsic behavior, parameterization independence, and ease of implementation. However, a long claimed advantage of geometric deformable models—the ability to automatically handle topology changes—turns out to be a liability in applications where the object to be segmented has a known topology that must be preserved. In this paper, we present a new class of geometric deformable models designed using a novel topologypreserving level set method, which achieves topology preservation by applying the simple point concept from digital topology. These new models maintain the other advantages of standard geometric deformable models including subpixel accuracy and production of nonintersecting curves or surfaces. Moreover, since the topologypreserving constraint is enforced efficiently through local computations, the resulting algorithm incurs only nominal computational overhead over standard geometric deformable models. Several experiments on simulated and real data are provided to demonstrate the performance of this new deformable model algorithm.
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