where Ω ⊂ R2 is a bounded open set (the image domain), H1 denotes the one-dimensional Hausdorff measure, and g ∈ L∞(Ω) is the input image. The functional has to be minimized over all closed sets C ⊂ Ω and all u ∈ C1(Ω \ C). The function u represents a denoised approximation of the input image g, and C represents the set of boundaries of the segmentation. The Mumford and Shah variational model c...

We deal with the Ambrosio-Tortorelli approximation of the well-known Mumford-Shah functional to model quasi-static crack propagation in brittle materials. We employ anisotropic mesh adaptation to efficiently capture the crack path. Aim of this work is to investigate the numerical sensitivity of the crack behavior to the parameters involved in both the physical model and in the adaptive procedure.

In this paper, we propose an active contour algorithm for object detection in vectorvalued images (such as RGB or multispectral). The model is an extension of the scalar Chan–Vese algorithm to the vector-valued case [1]. The model minimizes a Mumford–Shah functional over the length of the contour, plus the sum of the fitting error over each component of the vector-valued image. Like the Chan–Ve...

Magnetic resonance elastography (MRE) noninvasively images the propagation of mechanical waves within soft tissues. The elastic properties of soft tissues can then be quantified from MRE wave snapshots. Various algorithms have been proposed to obtain their inversion for soft tissue elasticity. Anomalies are assumed to be discernible in the elasticity map. We propose a new elastic level set mode...

Human vision works equally well in a large dynamic range of light intensities, from only a few photons to typical midday sunlight. Contributing to such remarkable flexibility is a famous law in perceptual (both visual and aural) psychology and psychophysics known as Weber’s Law. There has been a great deal of efforts in mathematical biology as well to simulate and interpret the law in the cellu...

In this paper, we propose a new model for active contours to detect objects in a given image, based on techniques of curve evolution, Mumford-Shah functional for segmentation and level sets. Our model can detect objects whose boundaries are not necessarily defined by gradient. The model is a combination between more classical active contour models using mean curvature motion techniques, and the...

This paper is the first part of an ongoing project aimed at providing a local minimality criterion, based on a second variation approach, for the triple point configurations of the Mumford-Shah functional.