A Geometric-Functional-Based Image Segmentation and Inpainting

Abstract

Abstract. 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.

Geometric Approach to Measure-Based Metric in Image Segmentation

“…Likewise one may consider the implementation of this geometric approach in other image processing and computer vision tasks. In fact, we have illustrated it also in the context of inpainting [29,30].…”

“…The possible application of the above approach may be image restoration, especially denoising-we implemented it in case of one-dimensional signals, see [28]. Eventually, the proposed change allows us to replace the deterministic data by a random one and include also the case of missing data (inpainting, see [29] and [30]). …”