Lavdie RADA,陈柯.On a Variational Model for Selective Image Segmentation of Features with Infinite Perimeter[J].数学研究及应用,2013,33(3):253~272 
On a Variational Model for Selective Image Segmentation of Features with Infinite Perimeter 
On a Variational Model for Selective Image Segmentation of Features with Infinite Perimeter 
投稿时间：20120405 最后修改时间：20130219 
DOI：10.3770/j.issn:20952651.2013.03.001 
中文关键词: image selective segmentation level set edge detection 2D image segmentation. 
英文关键词:image selective segmentation level set edge detection 2D image segmentation. 
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中文摘要: 
Variational models provide reliable formulation for segmentation of features and their boundaries in an image, following the seminal work of MumfordShah (1989, Commun. Pure Appl.\,Math.) on dividing a general surface into piecewise smooth subsurfaces. A central idea of models based on this work is to minimize the length of feature's boundaries (i.e., $\mathcal{H}^{1}$ Hausdorff measure). However there exist problems with irregular and oscillatory object boundaries, where minimizing such a length is not appropriate, as noted by Barchiesi et al. (2010, SIAM J. Multiscale Model. Simu.) who proposed to miminize $\mathcal{L}^{2}$ Lebesgue measure of the $\gamma$neighborhood of the boundaries. This paper presents a dual level set selective segmentation model based on Barchiesi et al. (2010) to automatically select a local feature instead of all global features. Our model uses two level set functions: a global level set which segments all boundaries, and the local level set which evolves and finds the boundary of the object closest to the geometric constraints. Using real life images with oscillatory boundaries, we show qualitative results demonstrating the effectiveness of the proposed method. 
英文摘要: 
Variational models provide reliable formulation for segmentation of features and their boundaries in an image, following the seminal work of MumfordShah (1989, Commun. Pure Appl.\,Math.) on dividing a general surface into piecewise smooth subsurfaces. A central idea of models based on this work is to minimize the length of feature's boundaries (i.e., $\mathcal{H}^{1}$ Hausdorff measure). However there exist problems with irregular and oscillatory object boundaries, where minimizing such a length is not appropriate, as noted by Barchiesi et al. (2010, SIAM J. Multiscale Model. Simu.) who proposed to miminize $\mathcal{L}^{2}$ Lebesgue measure of the $\gamma$neighborhood of the boundaries. This paper presents a dual level set selective segmentation model based on Barchiesi et al. (2010) to automatically select a local feature instead of all global features. Our model uses two level set functions: a global level set which segments all boundaries, and the local level set which evolves and finds the boundary of the object closest to the geometric constraints. Using real life images with oscillatory boundaries, we show qualitative results demonstrating the effectiveness of the proposed method. 
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