Non-convex non-local reactive flows for saliency detection and segmentation

Abstract

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.