(English summary for the article

P. Arias, C. Ballester, B. Coll, J. M. Mazón i E. Provenzi. L’aportació de Vicent Caselles al món de les matemàtiques i l’aplicació al processament d’imatges. Butlletí de la Societat Catalana de Matemàtiques Vol. 33, núm. 1, 2018. Pàg. 5–41. DOI: 10.2436/20.2002.01.78 )

In this paper we review the most important contributions of Vicent Caselles to the field of mathematics and their applications to the image processing field. The contributions cover a broad panorama ranging, from basic research as is the case of his contributions to the field of non-linear PDEs and the analytical study of the total variation (TV) model to the sphere of the applications in the field of image processing. To some degree, the sections relate to the areas in which the participation was most significant; specifically, to the sphere of basic research part, the contributions to the study of the function of total variation, strongly degenerate quasilinear equations and flux limited porus media diffussion equations. With regard to applications in the field of image processing, we have chosen three topics in which Caselles contributed in a very significant way: the detection of contours, the problem of interpolation or “inpainting” and the mathematical formulation of color theory.

The full article, in Catalan, can found here