Mumford-shah regularizer with spatial coherence

Erdem, Erkut
Sancar-Yilmaz, Aysun
Tarı, Zehra Sibel
As recently discussed by Bar, Kiryati, and Sochen in [3], the Ambrosio-Tortorelli approximation of the Mumford-Shah functional de-Lines an extended line process regularization where the regularizer has an additional constraint introduced by the term rho vertical bar del v vertical bar(2). This term mildly forces some spatial organization by demanding that the edges are smooth. However, it does not force spatial coherence such as edge direction compatibility or edge connectivity, as in the traditional edge detectors such as Canny. Using the connection between regularization and diffusion filters, we incorporate further spatial structure into the regularization process of the Mumford-Shah model. The new model combines smoothing; edge detection and edge linking steps of the traditional approach to boundary detection. Importance of spatial coherence is best observed if the image noise is salt and pepper like. Proposed approach is able to deal with difficult noise cases without using non-smooth cost functions such as L-1 in the data fidelity or regularizer.


BASKAL, S; ERIS, A (Springer Science and Business Media LLC, 1994-06-01)
Backlund transformations for harmonic maps are described as the action of the structure group on harmonic one-forms or as gauge transformations of the soliton connection constructed via embedding the configuration manifold into a flat space. As an illustration, Baicklund transformations for maps from M2 to the Poincare upper half-plane and for maps determining stationary vacuum gravitational fields with axial symmetry are obtained.
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We extend the post-processing implementation of a projection based variational multiscale (VMS) method with proper orthogonal decomposition (POD) to flows governed by double diffusive convection. In the method, the stabilization terms are added to momentum equation, heat and mass transfer equations as a completely decoupled separate steps. The theoretical analyses are presented. The results are verified with numerical tests on a benchmark problem.
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Erdem, Erkut; Tarı, Zehra Sibel (Springer Science and Business Media LLC, 2008-7-24)
We present a simple and robust feature preserving image regularization by letting local region measures modulate the diffusivity. The purpose of this modulation is to disambiguate low level cues in early vision. We interpret the Ambrosio-Tortorelli approximation of the Mumford-Shah model as a system with modulatory feedback and utilize this interpretation to integrate high level information into the regularization process. The method does not require any prior model or learning; the high level information i...
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In this paper, we consider the null controllability of 1-d heat equation endowed with Robin's boundary conditions, when the operator - d(2)/dx(2) has positive eigenvalues and try to find sufficient conditions for building switching controls. In [1], the author developed a first analysis of this problem with Dirichlet's boundary conditions and obtain sufficient conditions for switching controls. We firstly consider 1-d heat system endowed with two controls. Then we try to build switching control strategies g...
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Citation Formats
E. Erdem, A. Sancar-Yilmaz, and Z. S. Tarı, “Mumford-shah regularizer with spatial coherence,” Ischia, Italy, 2007, vol. 4485, Accessed: 00, 2020. [Online]. Available: