相关论文: Singularity degree of non-facially exposed faces

Given a polyhedron (planar, $3$-connected graph) $G$, we investigate its common neighbourhood graph con($G$). For cubic ($3$-regular) polyhedra, we show that the planarity of con($G$) depends on the number of odd faces of $G$, and on their…

We prove a formula for the polar degree of projective hypersurfaces in terms of the Milnor data of the singularities, extending to 1-dimensional singularities the Dimca-Papadima result for isolated singularities. We discuss the…

The purpose of this paper is to study low degree points on plane curves. We prove results analogous to those of Debarre and Klassen for singular plane curves with a finite number $\delta$ of ordinary nodes/cusps, where $\delta$ is bounded…

The paper is devoted to a study of the cone $\cop$ of copositive matrices. Based on the known from semi-infinite optimization concept of immobile indices, we define zero and minimal zero vectors of a subset of the cone $\cop$ and use them…

Let $\mathcal{A}$ be a mathematical structure with an additional relation $R$. We are interested in the degree spectrum of $R$, either among computable copies of $\mathcal{A}$ when $(\mathcal{A},R)$ is a "natural" structure, or (to make…

Recognizing facial expressions from static images or video sequences is a widely studied but still challenging problem. The recent progresses obtained by deep neural architectures, or by ensembles of heterogeneous models, have shown that…

We prove that the determinantal complexity of a hypersurface of degree $d > 2$ is bounded below by one more than the codimension of the singular locus, provided that this codimension is at least $5$. As a result, we obtain that the…

This paper investigates the geometry and singularities of parallel surfaces of cuspidal cross caps, the fundamental non-front frontal singularities. We establish a criterion for the degeneracy of the distance squared function in terms of…

This article investigates the notions of exposed points and (exposed) faces in the matrix convex setting. Matrix exposed points in finite dimensions were first defined by Kriel in 2019. Here this notion is extended to matrix convex sets in…

Slater's condition -- existence of a "strictly feasible solution" -- is a common assumption in conic optimization. Without strict feasibility, first-order optimality conditions may be meaningless, the dual problem may yield little…

The discrete KdV (dKdV) equation, the pinnacle of discrete integrability, is often thought to possess the singularity confinement property because it confines on an elementary quadrilateral. Here we investigate the singularity structure of…

Face images appeared in multimedia applications, e.g., social networks and digital entertainment, usually exhibit dramatic pose, illumination, and expression variations, resulting in considerable performance degradation for traditional face…

"Frontalization" is the process of synthesizing frontal facing views of faces appearing in single unconstrained photos. Recent reports have suggested that this process may substantially boost the performance of face recognition systems.…

Faces manifest large variations in many aspects, such as identity, expression, pose, and face styling. Therefore, it is a great challenge to disentangle and extract these characteristics from facial images, especially in an unsupervised…

This is a survey article on recognition problem of frontal singularities. We specify geometrically several frontal singularities and then we solve the recognition problem of such singularities, giving explicit normal forms. We combine the…

Face clustering is a promising way to scale up face recognition systems using large-scale unlabeled face images. It remains challenging to identify small or sparse face image clusters that we call hard clusters, which is caused by the…

Some face recognition methods are designed to utilize geometric information extracted from depth sensors to overcome the weaknesses of single-image based recognition technologies. However, the accurate acquisition of the depth profile is an…

In domains where computational resources and labeled data are limited, such as in robotics, deep networks with millions of weights might not be the optimal solution. In this paper, we introduce a connectivity scheme for pyramidal…

Explicit formulas determining the dimension and the degree of the singular subscheme of hypersurfaces in ${\mathbb P}^n$ are given in terms of the graded Betti numbers of the minimal free resolution of the corresponding Jacobian algebra.…

We investigate singularities of all parallel surfaces to a given regular surface. In generic context, the types of singularities of parallel surfaces are cuspidal edge, swallowtail, cuspidal lips, cuspidal beaks, cuspidal butterfly and…