Active Contours and Mumford-Shah Segmentation Based on Level Sets

IntroductionThe basic idea in active contour models orsnakes is to evolve a curve,subject to constraintsfrom a given image,in order to detect objects inthat image.For instance,starting with a curvearound the object to be detected,the curve movestoward its interior normal and has to stop on theboundary of the object.LetΩ be a bounded open subset of R2 ,with Ω its boundary. Let u0 ∶Ω→ R be a given image,and C( s)∶ 0 ,1 ]→ R2 be a parameterized curve. Inthe classical snakes and active…

Active Contours and Mumford-Shah Segmentation Based on Level Sets

This paper is to detect regions (objects) boundaries, also to isolate and extract individual components from a medical image. This can be done using an active contours to detect regions in a given image, based on techniques of curve evolution, Mumford Shah functional for segmentation and level sets. The paper classified the images into different intensity regions based on Markov random field, then detected regions whose boundaries are not necessarily defined by gradient by minimizing an energy of Mumford Shah functional for segmentation which can be seen as a particular case of the minimal partition problem. In the level set formulation, the problem becomes a mean curvature flow like evolving the active contour, which will stop on the desired boundary. The stopping term does not depend on the gradient of the image, as in the classical active contour and the initial curve of level set can be anywhere in the image, and interior contours are automatically detected. The final image segmentation is one closed boundary per actual region in the image.