Emanuele Schiavi

Iván Ramírez, Gonzalo Galiano, Emanuele Schiavi

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.

Gonzalo Galiano, Emanuele Schiavi, Julián Velasco

We study the existence and uniqueness of solutions of a nonlinear integro-differential problem which we reformulate introducing the notion of the decreasing rearrangement of the solution. A dimensional reduction of the problem is obtained and a detailed analysis of the properties of the solutions of the model is provided. Finally, a fast numerical method is devised and implemented to show the performance of the model when typical image processing tasks such as filtering and segmentation are performed.