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Recently, deep learning methods have achieved superior performance for Polarimetric Synthetic Aperture Radar(PolSAR) image classification. Existing deep learning methods learn PolSAR data by converting the covariance matrix into a feature…

We introduce a novel diffusion-based spectral algorithm to tackle regression analysis on high-dimensional data, particularly data embedded within lower-dimensional manifolds. Traditional spectral algorithms often fall short in such…

We present an optimized conductance-based retina microcircuit simulator which transforms light stimuli into a series of graded and spiking action potentials through photo transduction. We use discrete retinal neuron blocks based on a…

Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…

We propose a new Riemannian gradient descent method for computing spherical area-preserving mappings of topological spheres using a Riemannian retraction-based framework with theoretically guaranteed convergence. The objective function is…

Sparsity-based representations have recently led to notable results in various visual recognition tasks. In a separate line of research, Riemannian manifolds have been shown useful for dealing with features and models that do not lie in…

Reformulating computer vision problems over Riemannian manifolds has demonstrated superior performance in various computer vision applications. This is because visual data often forms a special structure lying on a lower dimensional space…

We derive the leading asymptotic behavior and build a new series representation for the Fredholm determinant of integrable integral operators appearing in the representation of the time and distance dependent correlation functions of…

Recently, multiple formulations of vision problems as probabilistic inversions of generative models based on computer graphics have been proposed. However, applications to 3D perception from natural images have focused on low-dimensional…

Purpose: To investigate whether a vision-language foundation model can enhance undersampled MRI reconstruction by providing high-level contextual information beyond conventional priors. Methods: We proposed a semantic distribution-guided…

We consider coefficient bodies $\mathcal M_n$ for univalent functions. Based on the L\"owner-Kufarev parametric representation we get a partially integrable Hamiltonian system in which the first integrals are Kirillov's operators for a…

By adapting a technique of Molchanov, we obtain the heat kernel asymptotics at the sub-Riemannian cut locus, when the cut points are reached by an $r$-dimensional parametric family of optimal geodesics. We apply these results to the…

In a joint paper, Jean Petitot together with the authors of the present paper described the functional geometry of the visual cortex as the symplectization of a contact form to describe the family of cells sensitive to position, orientation…

Inference of space-time varying signals on graphs emerges naturally in a plethora of network science related applications. A frequently encountered challenge pertains to reconstructing such dynamic processes, given their values over a…

Geometrical optical illusions have been object of many studies due to the possibility they offer to understand the behaviour of low-level visual processing. They consist in situations in which the perceived geometrical properties of an…

We address the problem of fitting parametric curves on the Grassmann manifold for the purpose of intrinsic parametric regression. As customary in the literature, we start from the energy minimization formulation of linear least-squares in…

Many scientific problems require identifying a small set of covariates that are associated with a target response and estimating their effects. Often, these effects are nonlinear and include interactions, so linear and additive methods can…

Geometric representation learning in preserving the intrinsic geometric and topological properties for discrete non-Euclidean data is crucial in scientific applications. Previous research generally mapped non-Euclidean discrete data into…

Visual distortions of perceived lengths, angles, or forms, are generally known as "geometric-optical illusions" (GOI). In the present paper we focus on a class of GOIs where the distortion of a straight line segment (the "target" stimulus)…

Most of the traditional work on intrinsic image decomposition rely on deriving priors about scene characteristics. On the other hand, recent research use deep learning models as in-and-out black box and do not consider the well-established,…