A Geometric-Functional-Based Image Segmentation and Inpainting

The Mumford-Shah functional minimization, and related algorithms for image segmentation, involve a tradeoff between a twodimensional 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 which is given in terms of the geometry of surfaces representing the data and image in a feature space. The Γ -convergence technique is combined with the minimal surface theory in order to yield a global generalization of the Mumford-Shah segmentation functional.