On a Variational Model for Selective Image Segmentation of Features with Infinite Perimeter  

作　　者：Lavdie RADA Ke CHEN 

机构地区：[1]Centre for Mathematical Imaging Techniques and Department of Mathematical Sciences, University of Liverpool,Liverpool L69 7ZL, United Kingdom

出　　处：《Journal of Mathematical Research with Applications》2013年第3期253-272,共20页数学研究及应用（英文版）

摘　　要：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 cen- tral idea of models based on this work is to minimize the length of feature＇s boundaries （i.e., 7-I1 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 ~：2 Lebesgue measure of the ~,-neighborhood of the boundaries. This paper presents a dual level set selective segmen- tation 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 cen- tral idea of models based on this work is to minimize the length of feature＇s boundaries （i.e., 7-I1 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 ~：2 Lebesgue measure of the ~,-neighborhood of the boundaries. This paper presents a dual level set selective segmen- tation 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.

关 键 词：image selective segmentation level set edge detection 2D image segmentation. 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术] TG580.6[自动化与计算机技术—计算机科学与技术]