Geometric Approach to Measure-Based Metric in Image Segmentation

The Mumford-Shah functional and related algorithms for image segmentation involve a tradeoff between a two-dimensional image structure and one-dimensional parametric curves (contours) that surround objects or distinct regions in the image. We propose an alternative functional that is independent of parameterization; it is a geometric functional given in terms of the surfaces representing the data and image in the feature space. The I"-convergence technique is combined with the minimal surfaces theory to yield a global generalization of the Mumford-Shah segmentation function.