图像分割-不用边界表达的动态轮廓线算法.pptVIP

Variational Image Segmentation Models -A Brief Introduction Basic Assumptions Active Contours Contour representation Model Description Euler-Lagrange Equation (Level Set Formulation) Why Level Set? 图像分割－不用边界表达的动态轮廓线算法 经典的图像分割算法（如snakes）都需要将图像的边界特殊表示，然后计算其长度等进行优化，而实际上边界的长度可以用数学表达式表示 定义Heaviside函数 图像分割－不用边界表达的动态轮廓线算法 其导数为 则边界的长度可以表示为 这样无边界表达的优化方程为 图像分割－不用边界表达的动态轮廓线算法 试验结果 Summery For active contours Alignment term Weighted region Minimal Variance Geodesic Active Contour Summery Image segmentation Data Driven Recognition Driven Two standard object extraction methods Interactive Graph cuts [BoykovJolly ‘01] Discrete formulation Computes min-cuts on N-D grid-graphs Graph cuts (simple example à la BoykovJolly, ICCV’01) Cut Metric on grids can approximate Euclidean Metric A relation between… Level Sets Graph Cuts [OsherSethian’88,…] [Greig et. al.’89, Ishikawa et. al.’98, BVZ’98,…] Grabcut * Smoothness Elasticity Internal Energy Edge Penalty (”Function (“g func External Energy Level Set Deformation Mean Curvature Balloon Force Computing geodesics and minimal surfaces via graph cuts (ICCV 03) Yuri Boykov, Siemens Research, Princeton, NJ joint work with Vladimir Kolmogorov, Cornell University, Ithaca, NY Geodesic active contours [Caselles et.al. ‘97, Yezzi et.al ‘97] Continuous formulation Computes geodesics in image- based N-D Riemannian spaces Geo-cuts Minimal geometric artifacts Solved via local variational technique (level sets) Possible metrication errors Global minima Geodesics and minimal surfaces The shortest curve between two points is a geodesic Riemannian metric (space varying, tensor D(p)) Geodesic contours use image-based Riemannian metric Euclidian metric (constant) A B A B Generalizes to 3D (minimal surfaces) distance map distance map n-links s t a cut hard constraint hard constraint Minimum cost cut can be computed in pol