Garamendi, Juan FranciscoSchiavi, Emanuele2024-03-132024-03-132017Garamendi JF, Schiavi E. A multiclass anisotropic Mumford-Shah functional for segmentation of d-dimensional vectorial images. In: Imai F, Tremeau A, Braz J, editors. Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2017) (Volume 4: VISAPP); 2017 Feb 27 - Mar 1; Porto, Portugal. Setúbal: SciTePress; 2017. p. 468-75. DOI: 10.5220/00061278046804759789897582257http://hdl.handle.net/10230/59400Comunicació presentada a la 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2017), celebrada del 27 de febrer l'1 de març de 2017 a Porto, Portugal.We present a general model for multi-class segmentation of multi-channel digital images. It is based on the minimization of an anisotropic version of the Mumford-Shah energy functional in the class of piecewise constant functions. In the framework of geometric measure theory we use the concept of common interphases between regions (classes) and the value of the jump discontinuities of the (weak) solution between adjacent regions in order to define a minimal partition energy functional. The resulting problem is non-smooth and non-convex. Non-smoothness is dealt with highlighting the relationship of the proposed model with the well known Rudin, Osher and Fatemi model for image denoising when piecewise constant solutions (i.e partitions) are considered. Non-convexity is tackled with an optimal threshold of the ROF solution which we which generalize to multi-channel images through a probabilistic clustering. The optimal solution is then computed with a fixed point iteration. The result ing algorithm is described and results are presented showing the successful application of the method to Light Field (LF) images.application/pdfengCopyright 2015 by SCITEPRESS – Science and Technology Publications, Lda. Distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND).info:eu-repo/semantics/conferenceObjecthttp://dx.doi.org/10.5220/0006127804680475Multi-channelImage segmentationVariational methodsMumford-Shahinfo:eu-repo/semantics/openAccess