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 present an estimation-theoretic approach to curve evolution for the Mumford-Shah problem. By viewing an active contour as the set of discontinuities in the Mumford-Shah problem, we may use the corresponding functional to determine gradient descent evolution equations to deform the active contour. In each gradient descent step, we solve a corresponding optimal estimation problem, connecting t...

Ionisation in collisions of alpha particles with hydrogen atoms has been investigated for impact energies lying between 2 and 900 keV amu-l. The multistate semiclassical impact parameter model with a two-centre expansion in travelling atomic orbitals was employed. The computed ionisation cross sections are, in particular in the low-energy region, in good agreement with the recent experimental d...

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The aim of this paper is to provide a formal link between an oscillatory neural model, whose phase is represented by a difference equation, and the Mumford and Shah functional. A Riemannian metric is induced by the pattern of neural connections, and in this setting the difference equation is studied. Its Euler–Lagrange operator Γ-converges as the dimension of the grid tends to 0 to the Mumford ...