Related papers: Facial Reduction and Partial Polyhedrality

We suppose the existence of an oracle which solves any semidefinite programming (SDP) problem satisfying Slater's condition simultaneously at its primal and dual sides. We note that such an oracle might not be able to directly solve general…

The model of low-dimensional manifold and sparse representation are two well-known concise models that suggest each data can be described by a few characteristics. Manifold learning is usually investigated for dimension reduction by…

Given a polyline on $n$ vertices, the polyline simplification problem asks for a minimum size subsequence of these vertices defining a new polyline whose distance to the original polyline is at most a given threshold under some distance…

Facial representation pre-training is crucial for tasks like facial recognition, expression analysis, and virtual reality. However, existing methods face three key challenges: (1) failing to capture distinct facial features and fine-grained…

We study the problem of decomposing a non-negative polynomial as an exact sum of squares (SOS) in the case where the associated semidefinite program is feasible but not strictly feasible (for example if the polynomial has real zeros).…

Facial Expression Recognition (FER) is crucial in many research domains because it enables machines to better understand human behaviours. FER methods face the problems of relatively small datasets and noisy data that don't allow classical…

3D Morphable Models (3DMMs) provide promising 3D face reconstructions in various applications. However, existing methods struggle to reconstruct faces with extreme expressions due to deficiencies in supervisory signals, such as sparse or…

Existing face-swapping methods often deliver competitive results in constrained settings but exhibit substantial quality degradation when handling extreme facial poses. To improve facial pose robustness, explicit geometric features are…

Non-negative matrix factorization (NMF) is a natural model of admixture and is widely used in science and engineering. A plethora of algorithms have been developed to tackle NMF, but due to the non-convex nature of the problem, there is…

The field of Automatic Facial Expression Analysis has grown rapidly in recent years. However, despite progress in new approaches as well as benchmarking efforts, most evaluations still focus on either posed expressions, near-frontal…

This paper develops a correspondence relating convex hulls of fractional functions with those of polynomial functions over the same domain. Using this result, we develop a number of new reformulations and relaxations for fractional…

Facial expression recognition is a challenging task when neural network is applied to pattern recognition. Most of the current recognition research is based on single source facial data, which generally has the disadvantages of low accuracy…

Qualification conditions (also termed constraint qualifications) help avoid pathological behavior at domain boundaries in convex analysis. By generalizing facial reduction from conic programming to general convex programs of the form $f(x)…

The objective of this work is to study weak infeasibility in second order cone programming. For this purpose, we consider a relaxation sequence of feasibility problems that mostly preserve the feasibility status of the original problem.…

Facial expression recognition (FER) is an important task in computer vision, having practical applications in areas such as human-computer interaction, education, healthcare, and online monitoring. In this challenging FER task, there are…

We consider minimizing an objective function subject to constraints defined by the intersection of lower-level sets of convex functions. We study two cases: (i) strongly convex and Lipschitz-smooth objective function and (ii) convex but…

Automated Facial Expression Recognition (FER) has remained a challenging and interesting problem. Despite efforts made in developing various methods for FER, existing approaches traditionally lack generalizability when applied to unseen…

Automatic face recognition is a research area with high popularity. Many different face recognition algorithms have been proposed in the last thirty years of intensive research in the field. With the popularity of deep learning and its…

We study partial fraction decompositions (PFDs) in several variables using tools from commutative algebra. We give criteria for when a rational function with poles on a hyperplane arrangement has a desirable PFD. Our criteria are obtained…

Probabilistic Face Embeddings (PFE) can improve face recognition performance in unconstrained scenarios by integrating data uncertainty into the feature representation. However, existing PFE methods tend to be over-confident in estimating…