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...

The binary Mumford-Shah model is a widespread tool for image segmentation and can be considered as a basic model in shape optimization with a broad range of applications in computer vision, ranging from basic segmentation and labeling to object reconstruction. This paper presents robust a posteriori error estimates for a natural error quantity, namely the area of the non properly segmented regi...

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The Mumford-Shah functional has had a major impact on a variety of image analysis problems, including image segmentation and filtering, and, despite being introduced over two decades ago, it is still in widespread use. Present day optimization of the Mumford-Shah functional is predominated by active contour methods. Until recently, these formulations necessitated optimization of the contour by ...

As recently discussed by Bar, Kiryati, and Sochen in [3], the Ambrosio-Tortorelli approximation of the Mumford-Shah functional defines an extended line process regularization where the regularizer has an additional constraint introduced by the term ρ|∇v|. This term mildly forces some spatial organization by demanding that the edges are smooth. However, it does not force spatial coherence such a...

In this paper, an extension of Darbo?s fixed point theorem via the concept operators A(f;.) and ?-?-contractions in a Banach space has been presented. We illustrate that some conditions control functions ? can be omitted where they applied previously [Mohammadi et al., Mathematics, 2020, 8(4), 492]. As application, we study existence solutions for system fractional integral equations. Finally, ...