Non-convex non-local flows for saliency detection

TL;DR

This paper introduces a novel non-convex non-local variational model for saliency detection and applies it to medical image segmentation, demonstrating improved results through a fast convolutional solution.

Contribution

It develops a new variational framework using non-local, non-convex operators for saliency detection and medical image segmentation, with an efficient numerical solution.

Findings

Non-convex hyper-Laplacian operators improve saliency detection accuracy.

The proposed method outperforms standard metrics in MRI glioblastoma segmentation.

A fast convolutional kernel approach enables practical computation.

Abstract

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.