Galiano Casas, GonzaloRamírez Díaz, IvánSchiavi, Emanuele2025-01-242025-01-242020-10-15Galiano, G., Ramírez, I., & Schiavi, E. (2020). Non-convex non-local reactive flows for saliency detection and segmentation. Journal of Computational and Applied Mathematics, 377, 112873.0377-0427https://hdl.handle.net/10115/62399The first author has been supported by the Spanish MCI Project MTM2017-87162-P. The second and the last authors’ research have been partially supported by the Spanish Government research funding ref. MINECO/FEDER TIN2015-69542-C2-1 and the Banco de Santander and Universidad Rey Juan Carlos, Spain Funding Program for Excellence Research Groups ref. “Computer Vision and Image Processing (CVIP)”We propose and numerically solve a new variational model for automatic saliency detection and segmentation in digital images. Using a non-local framework we consider a family of edge preserving functions combined with a new quadratic saliency detection term. Such a term defines a constrained bilateral obstacle problem for image classification driven by p-Laplacian operators, including the so-called hyper-Laplacian case (0< p< 1). As an application the related non-convex non-local reactive flows are considered for glioblastoma segmentation in magnetic resonance fluid-attenuated inversion recovery (MRI-Flair) images. A fast convolutional kernel based approximated solution is computed. The numerical experiments show that the non-convexity related to the hyper-Laplacian operators provokes sparseness of the non-local gradients and provides better results in terms of the standard metrics when the parameter p decreases.enVariational methodsNon-local image processingAutomatic saliency detectionMRI-flair glioblastoma segmentationArticlehttps://doi.org/10.1016/j.cam.2020.112873info:eu-repo/semantics/closedAccess