Sharp geometric requirements in the Wachspress interpolation error estimate

Geometric conditions on general polygons are given in [9] in order to guarantee the error estimate for interpolants built from generalized barycentric coordinates, and the question about identifying sharp geometric restrictions in this setting is proposed. In this work, we address the question when the construction is made by using Wachspress coordinates. We basically show that the imposed conditionsbounded aspect ratio property(barp),maximum angle condition(MAC) andminimum edge length property(melp) are actually equivalent to (MAC, melp), and if any of these conditions is not satisfied, then there is no guarantee that the error estimate is valid. In this sense, (MAC) and (melp) can be regarded as sharp geometric requirements in the Wachspress interpolation error estimate.

An error estimate in image processing

International audience A new interpolation error estimate for a finite element method for image processing is proved in this paper. The suggested scheme is based on the Raviart-Thomas one, extended to a non linear formulation. The numerical trials run confirm the accuracy of the restoration algorithm.