On the Statistical Interpretation of the Piecewise Smooth Mumford-Shah Functional
نویسندگان
چکیده
In region-based image segmentation, two models dominate the field: the Mumford-Shah functional and statistical approaches based on Bayesian inference. Whereas the latter allow for numerous ways to describe the statistics of intensities in regions, the first includes spatially smooth approximations. In this paper, we show that the piecewise smooth Mumford-Shah functional is a first order approximation of Bayesian a-posteriori maximization where region statistics are computed in local windows. This equivalence not only allows for a statistical interpretation of the full Mumford-Shah functional. Inspired by the Bayesian model, it also offers to formulate an extended Mumford-Shah functional that takes the variance of the data into account.
منابع مشابه
Real-Time Minimization of the Piecewise Smooth Mumford-Shah Functional
We propose an algorithm for efficiently minimizing the piecewise smooth Mumford-Shah functional. The algorithm is based on an extension of a recent primal-dual algorithm from convex to non-convex optimization problems. The key idea is to rewrite the proximal operator in the primal-dual algorithm using Moreau’s identity. The resulting algorithm computes piecewise smooth approximations of color i...
متن کاملEfficient Segmentation of Piecewise Smooth Images
We propose a fast and robust segmentation model for piecewise smooth images. Rather than modeling each region with global statistics, we introduce local statistics in an energy formulation. The shape gradient of this new functional gives a contour evolution controlled by local averaging of image intensities inside and outside the contour. To avoid the computational burden of a direct estimation...
متن کاملFast Segmentation for the Piecewise Smooth Mumford-Shah Functional
This paper is concerned with an improved algorithm based on the piecewise-smooth Mumford and Shah (MS) functional for an efficient and reliable segmentation. In order to speed up convergence, an additional force, at each time step, is introduced further to drive the evolution of the curves instead of only driven by the extensions of the complementary functions + u and − u . In our scheme, furth...
متن کاملA level set algorithm for minimizing the Mumford-Shah functional in image processing
We show how the piecewise-smooth Mumford-Shah segmentation problem [25] can be solved using the level set method of S. Osher and J. Sethian [26]. The obtained algorithm can be simultaneously used to denoise, segment, detect-extract edges, and perform active contours. The proposed model is also a generalization of a previous active contour model without edges, proposed by the authors in [12], an...
متن کاملA Curve Evolution Approach to Smoothing and Segmentation Using the Mumford-Shah Functional
In this work, we approach the classic Mumford-Shah problem from a curve evolution perspective. In particular, we let a given family of curves define the boundaries between regions in an image within which the data are modeled by piecewise smooth functions plus noise as in the standard Mumford-Shah functional. The gradient descent equation of this functional is then used to evolve the curve. Eac...
متن کامل