A 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. Each gradient descent step involves solving a corresponding optimal estimation problem which connects the Mumford-Shah functional and our curve evolution implementation with the theory of boundary-value stochastic processes. The resulting active contour model, therefore, inherits the attractive ability of the Mumford-Shah technique to generate, in a coupled manner, both a smooth reconstruction of the image and a segmentation as well. We demonstrate applications of our method to problems in which data quality is spatially varying and to problems in which sets of pixel measurements are missing. Final...

• Type: Conference
• Year: 2000
• Where: CVPR
• Authors: Andy Tsai, Anthony J. Yezzi, Alan S. Willsky
• Keywords: Computer Vision, Curve Evolution Implementation, Curve Evolution Perspective, CVPR 2000, Gradient Descent Equation, Gradient Descent Step, Optimal Estimation Problem