L'aportació de Vicent Caselles al món de les matemàtiques i l'aplicació al processament d'imatges Authors Coloma Ballester i Nicolau Pablo Arias Bartomeu Coll i Vicens José M. Manzón Ruiz Edoardo Provenzi Abstract 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 non-linear 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. Downloads Text complet (Català) Published 2018-07-16 How to Cite Ballester i Nicolau, C., Arias, P., Coll i Vicens, B., Manzón Ruiz, J. M., & Provenzi, E. (2018). L’aportació de Vicent Caselles al món de les matemàtiques i l’aplicació al processament d’imatges. Butlletí De La Societat Catalana De Matemàtiques, 33(1), 5–41. Retrieved from https://revistes.iec.cat/index.php/BSCM/article/view/99828.003 More Citation Formats ACM ACS APA ABNT Chicago Harvard IEEE MLA Turabian Vancouver Download Citation Endnote/Zotero/Mendeley (RIS) BibTeX Issue Vol. 33 No. 1 (2018) Section Articles License The intellectual property of articles belongs to the respective authors.On submitting articles for publication to the journal Butlletí de la Societat Catalana de Matemàtiques, authors accept the following terms:Authors assign to Societat Catalana de Matemàtiques (a subsidiary of Institut d’Estudis Catalans) the rights of reproduction, communication to the public and distribution of the articles submitted for publication to Butlletí de la Societat Catalana de Matemàtiques.Authors answer to Societat Catalana de Matemàtiques for the authorship and originality of submitted articles.Authors are responsible for obtaining permission for the reproduction of all graphic material included in articles.Societat Catalana de Matemàtiques declines all liability for the possible infringement of intellectual property rights by authors.The contents published in the journal, unless otherwise stated in the text or in the graphic material, are subject to a Creative Commons Attribution-NonCommercial-NoDerivs (by-nc-nd) 3.0 Spain licence, the complete text of which may be found at https://creativecommons.org/licenses/by-nc-nd/3.0/es/deed.en. Consequently, the general public is authorised to reproduce, distribute and communicate the work, provided that its authorship and the body publishing it are acknowledged, and that no commercial use and no derivative works are made of it.The journal Butlletí de la Societat Catalana de Matemàtiques is not responsible for the ideas and opinions expressed by the authors of the published articles.