  We propose and numerically solve a new variational model for automatic
saliency detection 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 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). The related non-convex non-local reactive
flows are then considered and applied 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 how the non-convexity related to the hyperLaplacian operators
provides monotonically better results in terms of the standard metrics.
