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

To study a deformation of a singularity taking into consideration their differential geometric properties, a form representing the deformation using only diffeomorphisms on the source space and isometries of the target space plays a crucial…

We obtain a recursive formula for the characteristic number of degree $d$ curves in $\mathbb{P}^2$ with prescribed singularities (of type $A_k$) that are tangent to a given line. The formula is in terms of the characteristic number of…

We investigate the geometric constraints imposed by low Morse index on minimal surfaces with Y-singularities, focusing on the classification of those with Morse index one. Our rigidity result establishes a partial uniqueness theorem,…

The conditions for a cuspidal edge, swallowtail and other fundamental singularities are given in the context of Lie sphere geometry. We then use these conditions to study the Lie sphere transformations of a surface.

The geometry of closed surfaces equipped with a Euclidean metric with finitely many conical points of arbitrary angle is studied. The main result is that the image of a non-closed geodesic has 0 distance from the set of conical points.…

The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research. However, recent work has shown that real-world data exhibits distinct…

Consider a face F in an arrangement of n Jordan curves in the plane, no two of which intersect more than s times. We prove that the combinatorial complexity of F is O(\lambda_s(n)), O(\lambda_{s+1}(n)), and O(\lambda_{s+2}(n)), when the…

We study geometric properties of linear strata of uni-singular curves. The singularities of closures of the strata are resolved and the resolutions are represent as projective bundles. This enables to study their geometry. In particular we…

A face recognition model is typically trained on large datasets of images that may be collected from controlled environments. This results in performance discrepancies when applied to real-world scenarios due to the domain gap between clean…

Deep convolutional neural networks (DCNNs) trained for face identification develop representations that generalize over variable images, while retaining subject (e.g., gender) and image (e.g., viewpoint) information. Identity, gender, and…

Given any polar pair of convex bodies we study its conjugate face maps and we characterize conjugate faces of non-exposed faces in terms of normal cones. The analysis is carried out using the positive hull operator which defines lattice…

In this work we investigate a novel approach to handle the challenges of face recognition, which includes rotation, scale, occlusion, illumination etc. Here, we have used thermal face images as those are capable to minimize the affect of…

We study the long-standing open problem of efficiently testing rectilinear planarity of series-parallel graphs (SP-graphs) in the variable embedding setting. A key ingredient behind the design of a linear-time testing algorithm for…

We present a minimalistic but effective neural network that computes dense facial correspondences in highly unconstrained RGB images. Our network learns a per-pixel flow and a matchability mask between 2D input photographs of a person and…

Human face images usually appear with wide range of visual scales. The existing face representations pursue the bandwidth of handling scale variation via multi-scale scheme that assembles a finite series of predefined scales. Such…

In this paper, we prove a similar result to the fundamental theorem of regular surfaces in classical differential geometry, which extends the classical theorem to the entire class of singular surfaces in Euclidean 3-space known as frontals.…

Neutron skins encode essential information about nuclear geometry, surface structure, and isovector response, yet a compact description across the nuclear chart remains elusive. We present an empirical analysis of neutron-excess surface…

Consider a rational projective curve C of degree d over an algebraically closed field k. There are n homogeneous forms g_1,...,g_n of degree d in B=k[x,y] which parameterize C in a birational, base point free, manner. We study the…

In this paper we study plus-one generated arrangements of conics and lines in the complex projective plane with simple singularities. We provide several degree-wise classification results that allow us to construct explicit examples of such…

The degree partition of a simple graph is its degree sequence rearranged in weakly decreasing order. The polytope of degree partitions (respectively, degree sequences) is the convex hull of all degree partitions (respectively, degree…