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

DOI：10.3770/j.issn:2095-2651.2013.03.001

 作者 单位 Lavdie RADA Centre for Mathematical Imaging Techniques and Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, United Kingdom 陈柯 Centre for Mathematical Imaging Techniques and Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, United Kingdom

Variational models provide reliable formulation for segmentation of features and their boundaries in an image, following the seminal work of Mumford-Shah (1989, Commun. Pure Appl.\,Math.) on dividing a general surface into piecewise smooth sub-surfaces. 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.

Variational models provide reliable formulation for segmentation of features and their boundaries in an image, following the seminal work of Mumford-Shah (1989, Commun. Pure Appl.\,Math.) on dividing a general surface into piecewise smooth sub-surfaces. 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.