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.

我们提出并数值解决了一种新的变分模型，用于自动显着性检测和数字图像分割。使用非局部框架，我们考虑了一系列边缘保留功能，并结合了新的二次显着性检测项。这个术语定义了受约束的双边障碍问题，用于图像分类，由$p$-拉普拉斯算子，包括所谓的超拉普拉斯案（$0<p<\mathrm{1个}$）。作为一种应用，在磁共振流体衰减倒置恢复（MRI-Flair）图像中考虑了有关胶质母细胞瘤分割的相关非凸非局部反应流。计算基于快速卷积核的近似解。数值实验表明，与超拉普拉斯算子有关的非凸性引起了非局部梯度的稀疏性，并且当参数为$p$ 减少。