Image segmentation and smoothing via partial differential equations

Özmen, Neslihan
In image processing, partial differential equation (PDE) based approaches have been extensively used in segmentation and smoothing applications. The Perona-Malik nonlinear diffusion model is the first PDE based method used in the image smoothing tasks. Afterwards the classical Mumford-Shah model was developed to solve both image segmentation and smoothing problems and it is based on the minimization of an energy functional. It has numerous application areas such as edge detection, motion analysis, medical imagery, object tracking etc. The model is a way of finding a partition of an image by using a piecewise smooth representation of the image. Unfortunately numerical procedures for minimizing the Mumford-Shah functional have some difficulties because the problem is non convex and it has numerous local minima, so approximate approaches have been proposed. Two such methods are the Ambrosio-Tortorelli approximation and the Chan-Vese active contour method. Ambrosio and Tortorelli have developed a practical numerical implementation of the Mumford-Shah model which based on an elliptic approximation of the original functional. The Chan-Vese model is a piecewise constant generalization of the Mumford-Shah functional and it is based on level set formulation. Another widely used image segmentation technique is the “Active Contours (Snakes)” model and it is correlated with the Chan-Vese model. In this study, all these approaches have been examined in detail. Mathematical and numerical analysis of these models are studied and some experiments are performed to compare their performance.


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Citation Formats
N. Özmen, “Image segmentation and smoothing via partial differential equations,” M.S. - Master of Science, Middle East Technical University, 2009.