The Mumford-Shah conjecture in image processing
Runge Property and Multiplicity of Solutions for Elliptic Equations in IRN with a Monotone Nonlinearity.
On a variational theory of image amodal completion
Segmentation of images by variational methods: a constructive approach.
A homotopy method for solving an equation of the type
Traffic plans.
In recent research in the optimization of transportation networks, the problem was formalized as finding the optimal paths to transport a measure y+ onto a measure y- with the same mass. This approach is realistic for simple good distribution networks (water, electric power,. ..) but it is no more realistic when we want to specify who goes where, like in the mailing problem or the optimal urban traffic network problem. In this paper, we present a new framework generalizing the former approathes...
Image Interpolation
We discuss possible algorithms for interpolating data given in a set of curves and/or points in the plane. We propose a set of basic assumptions to be satisfied by the interpolation algorithms which lead to a set of models in terms of possibly degenerate elliptic partial differential equations. The Absolute Minimal Lipschitz Extension model (AMLE) is singled out and studied in more detail. We show experiments suggesting a possible application, the restoration of images with poor dynamic range. We...
Connected components of sets of finite perimeter and applications to image processing
This paper contains a systematic analysis of a natural measure theoretic notion of connectedness for sets of finite perimeter in , introduced by H. Federer in the more general framework of the theory of currents. We provide a new and simpler proof of the existence and uniqueness of the decomposition into the so-called -connected components. Moreover, we study carefully the structure of the essential boundary of these components and give in particular a reconstruction formula of a set of finite...
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