Arias, P.; Ballester, C.; Coll, B.; Mazón, J. M.; Provenzi, E. The contribution of Vicent Caselles to the world of mathematics and its application to image processing. (Catalan. English summary) Zbl 1404.35001 Butll. Soc. Catalana Mat. 33, No. 1, 5-41 (2018). 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 Keywords:functional analysis; total variation; nonlinear PDEs; image processing; contour detection; inpainting; color theory Biographic References: Caselles, Vicent PDFBibTeX XMLCite \textit{P. Arias} et al., Butll. Soc. Catalana Mat. 33, No. 1, 5--41 (2018; Zbl 1404.35001) Full Text: DOI