Related papers: Face numbers of down-sets
Face recognition has been widely studied due to its importance in different applications; however, most of the proposed methods fail when face images are occluded or captured under illumination and pose variations. Recently several low-rank…
As the features from the traditional Local Binary Patterns (LBP) and Local Directional Patterns (LDP) are found to be ineffective for face recognition, we have proposed a new approach derived on the basis of Information sets whereby the…
In the field of mathematics, a purely combinatorial equivalent to a simplicial complex, or more generally, a down-set, is an abstract structure known as a family of sets. This family is closed under the operation of taking subsets, meaning…
Deep learning technology has enabled successful modeling of complex facial features when high quality images are available. Nonetheless, accurate modeling and recognition of human faces in real world scenarios `on the wild' or under adverse…
A new notion of face relative interior for convex sets in topological real vector spaces is introduced in this work. Face relative interior is grounded in the facial structure, and may capture the geometry of convex sets in topological…
In this study, we consider the positive cluster complex, a full subcomplex of a cluster complex the vertices of which are all non-initial cluster variables. In particular, we provide a formula for the difference in face vectors of positive…
The scale and complexity of modern data sets and the limitations associated with testing large numbers of hypotheses underline the need for feature selection methods. Spectral techniques rank features according to their degree of…
Several recent papers have examined a rational polyhedron $P_m$ whose integer points are in bijection with the numerical semigroups (cofinite, additively closed subsets of the non-negative integers) containing $m$. A combinatorial…
Given two combinatorial identities proved earlier, a new set of variations of these combinatorial identities is listed and proved with the integral representation method. Some identities from literature are shown to be special cases of…
This paper describes the homology of various simplicial complexes associated to set families from combinatorial number theory, including primitive sets, pairwise coprime sets, product-free sets, and coprime-free sets. We present a condition…
Simplicial complexes are a popular tool used to model higher-order interactions between elements of complex social and biological systems. In this paper, we study some combinatorial aspects of a class of simplicial complexes created by a…
Hybrid approach has a special status among Face Recognition Systems as they combine different recognition approaches in an either serial or parallel to overcome the shortcomings of individual methods. This paper explores the area of Hybrid…
A combinatorial methods are used to investigate some properties of certain generalized Stirling numbers, including explicit formula and recurrence relations. Furthermore, an expression of these numbers with symmetric function is deduced.
In the beginning stage, face verification is done using easy method of geometric algorithm models, but the verification route has now developed into a scientific progress of complicated geometric representation and matching process. In…
Generating faithful visualizations of human faces requires capturing both coarse and fine-level details of the face geometry and appearance. Existing methods are either data-driven, requiring an extensive corpus of data not publicly…
We introduce notions of combinatorial blowups, building sets, and nested sets for arbitrary meet-semilattices. This gives a common abstract framework for the incidence combinatorics occurring in the context of De Concini-Procesi models of…
A standard assumption in the study of logarithmic structures is "fineness", but this assumption is not preserved by intersections, fiber products, and more general limits. We explain how a coherent logarithmic scheme $X$ has a natural…
We give a survey on the recent results and problems on the face enumeration of flag complexes and flag simplicial spheres, with an emphasis on the characterization of face vectors of flag complexes, several lower-bound type of conjectures…
There are a large number of theorems detailing the homological properties of the Stanley--Reisner ring of a simplicial complex. Here we attempt to generalize some of these results to the case of a simplicial poset. By investigating the…
Facial feature detection from facial images has attracted great attention in the field of computer vision. It is a nontrivial task since the appearance and shape of the face tend to change under different conditions. In this paper, we…