相关论文: Non-convex non-local flows for saliency detection

In this paper we are concerned with a class of optimization problems involving the $p(x)$-Laplacian operator, which arise in imaging and signal analysis. We study the well-posedness of this kind of problems in an amalgam space considering…

The different families of saliency methods, either based on contrastive signals, closed-form formulas mixing gradients with activations or on perturbation masks, all focus on which parts of an image are responsible for the model's…

Finding an $\epsilon$-stationary point of a nonconvex function with a Lipschitz continuous Hessian is a central problem in optimization. Regularized Newton methods are a classical tool and have been studied extensively, yet they still face…

Inversions of rotational splittings have shown that the surface layers and the so-called solar tachocline at the base of the convection zone are regions in which high radial gradients of the rotation rate occur. The usual regularization…

We present a novel approach for saliency prediction in images, leveraging parallel decoding in transformers to learn saliency solely from fixation maps. Models typically rely on continuous saliency maps, to overcome the difficulty of…

We present a new approach to the numerical upscaling for elliptic problems with rough diffusion coefficient at high contrast. It is based on the localizable orthogonal decomposition of $H^1$ into the image and the kernel of some novel…

Simplicial complexes are generalizations of graphs that describe higher-order network interactions among nodes in the graph. Network dynamics described by graph Laplacian flows have been widely studied in network science and control theory,…

This paper presents a novel p-adaptive, high-order mesh-free framework for the accurate and efficient simulation of fluid flows in complex geometries. High-order differential operators are constructed locally for arbitrary node…

Modeling magnitude Magnetic Resonance Images (MRI) rician denoising in a Bayesian or generalized Tikhonov framework using Total Variation (TV) leads naturally to the consideration of nonlinear elliptic equations. These involve the so called…

We extend the standard notion of self-concordance to non-convex optimization and develop a family of second-order algorithms with global convergence guarantees. In particular, two function classes -- \textit{weakly self-concordant}…

In imaging modalities recording diffraction data, the original image can be reconstructed assuming known phases. When phases are unknown, oversampling and a constraint on the support region in the original object can be used to solve a…

Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their…

Saliency detection is one of the most challenging problems in image analysis and computer vision. Many approaches propose different architectures based on the psychological and biological properties of the human visual attention system.…

Hyperbolic spaces have increasingly been recognized for their outstanding performance in handling data with inherent hierarchical structures compared to their Euclidean counterparts. However, learning in hyperbolic spaces poses significant…

Many studies regarding the vasculature of biological tissues involve the segmentation of the blood vessels in a sample followed by the creation of a graph structure to model the vasculature. The graph is then used to extract relevant…

In this paper, we study four nonlocal diffusion operators, including the fractional Laplacian, spectral fractional Laplacian, regional fractional Laplacian, and peridynamic operator. These operators represent the infinitesimal generators of…

Recently Brendle-Huisken introduced a fully nonlinear flow $G$. Their aim was to extend the surgery algorithm of Huisken-Sinestrari, into the Riemannian setting. The aim of this paper is to go through the details on how to perform neck…

The second eigenvalue of the Laplacian matrix and its associated eigenvector are fundamental features of an undirected graph, and as such they have found widespread use in scientific computing, machine learning, and data analysis. In many…

Since the early 2000s, computational visual saliency has been a very active research area. Each year, more and more new models are published in the main computer vision conferences. Nowadays, one of the big challenges is to find a way to…

This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears \& S\"uli [SIAM J.\ Numer.\ Anal.\…