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Brenti and Welker have shown that for any simplicial complex X, the face vectors of successive barycentric subdivisions of X have roots which converge to fixed values depending only on the dimension of X. We improve and generalize this…
State-of-the-art face recognition algorithms are able to achieve good performance when sufficient training images are provided. Unfortunately, the number of facial images is limited in some real face recognition applications. In this paper,…
In this paper, we share our experience in designing a convolutional network-based face detector that could handle faces of an extremely wide range of scales. We show that faces with different scales can be modeled through a specialized set…
In recent years, deep face recognition methods have demonstrated impressive results on in-the-wild datasets. However, these methods have shown a significant decline in performance when applied to real-world low-resolution benchmarks like…
We fully generalize a previously-developed computational geometry tool [1] to perform large-scale simulations of arbitrary two-dimensional faceted surfaces $z = h(x,y)$. Our method uses a three-component facet/edge/junction storage model,…
Feature descriptors involved in image processing are generally manually chosen and high dimensional in nature. Selecting the most important features is a very crucial task for systems like facial expression recognition. This paper…
This paper introduces an algebraic combinatorial approach to simplicial cone decompositions, a key step in solving inhomogeneous linear Diophantine systems and counting lattice points in polytopes. We use constant term manipulation on the…
To produce cartographic maps, simplification is typically used to reduce complexity of the map to a legible level. With schematic maps, however, this simplification is pushed far beyond the legibility threshold and is instead constrained by…
In this paper, we propose a novel face alignment method that trains deep convolutional network from coarse to fine. It divides given landmarks into principal subset and elaborate subset. We firstly keep a large weight for principal subset…
We consider $N$-way data arrays and low-rank tensor factorizations where the time mode is coded as a sparse linear combination of temporal elements from an over-complete library. Our method, Shape Constrained Tensor Decomposition (SCTD) is…
Homomorphic encryption (HE) is a privacy-preserving technique that enables computation directly over ciphertext. Unfortunately, a key challenge for HE is that implementations can be impractically slow and have limits on computation that can…
Face recognition and identification is a very important application in machine learning. Due to the increasing amount of available data, traditional approaches based on matricization and matrix PCA methods can be difficult to implement.…
The objective of this work is to learn a compact embedding of a set of descriptors that is suitable for efficient retrieval and ranking, whilst maintaining discriminability of the individual descriptors. We focus on a specific example of…
The success of most advanced facial expression recognition works relies heavily on large-scale annotated datasets. However, it poses great challenges in acquiring clean and consistent annotations for facial expression datasets. On the other…
In this paper a novel efficient method for representation of facial action units by encoding an image sequence as a fourth-order tensor is presented. The multilinear tensor-based extension of the biased discriminant analysis (BDA)…
Mixed Boolean-Arithmetic (MBA) obfuscation is a common technique used to transform simple expressions into semantically equivalent but more complex combinations of boolean and arithmetic operators. Its widespread usage in DRM systems,…
We consider the ubiquitous technique of VByte compression, which represents each integer as a variable length sequence of bytes. The low 7 bits of each byte encode a portion of the integer, and the high bit of each byte is reserved as a…
Weighted simplicial complexes (WSCs) are powerful tools for describing weighted cloud data or networks with weighted nodes. In this paper, we propose a novel approach to study WSCs via the concept of polarization. Polarization of a WSC…
A good clustering algorithm can discover natural groupings in data. These groupings, if used wisely, provide a form of weak supervision for learning representations. In this work, we present Clustering-based Contrastive Learning (CCL), a…
We propose a method to address challenges in unconstrained face detection, such as arbitrary pose variations and occlusions. First, a new image feature called Normalized Pixel Difference (NPD) is proposed. NPD feature is computed as the…