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The contribution of Vicent Caselles to the world of mathematics and its application to image processing. (Catalan. English summary) Zbl 1404.35001

Summary: In this paper we review the most important contributions of Vicent Caselles to the field of mathematics and their application 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 nonlinear EDPs 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 chocked flow 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.

MSC:

35-03 History of partial differential equations
68-03 History of computer science
94-03 History of information and communication theory
01A70 Biographies, obituaries, personalia, bibliographies
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
68U10 Computing methodologies for image processing

Biographic References:

Caselles, Vicent
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