There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

One of the main challenges in feature learning using Deep Convolutional Neural Networks (DCNNs) for large-scale face recognition is the design of appropriate loss functions that can enhance the discriminative power. Centre loss penalises the distance between deep features and their corresponding class centres in the Euclidean space to achieve intra-class compactness. SphereFace assumes that the linear transformation matrix in the last fully connected layer can be used as a representation of the class centres in the angular space and therefore penalises the angles between deep features and their corresponding weights in a multiplicative way. Recently, a popular line of research is to incorporate margins in well-established loss functions in order to maximise face class separability. In this paper, we propose an Additive Angular Margin Loss (ArcFace) to obtain highly discriminative features for face recognition. The proposed ArcFace has a clear geometric interpretation due to its exact correspondence to geodesic distance on a hypersphere. We present arguably the most extensive experimental evaluation against all recent state-of-the-art face recognition methods on ten face recognition benchmarks which includes a new large-scale image database with trillions of pairs and a large-scale video dataset. We show that ArcFace consistently outperforms the state of the art and can be easily implemented with negligible computational overhead. To facilitate future research, the code has been made available.

/pdf/arcface-additive-angular-margin-loss-for-deep-face-7vvlem659h.pdf

ArcFace: Additive Angular Margin Loss for Deep Face Recognition

The PASCAL Visual Object Classes Challenge

Automated analysis of human affective behavior has attracted increasing attention from researchers in psychology, computer science, linguistics, neuroscience, and related disciplines. However, the existing methods typically handle only deliberately displayed and exaggerated expressions of prototypical emotions despite the fact that deliberate behaviour differs in visual appearance, audio profile, and timing from spontaneously occurring behaviour. To address this problem, efforts to develop algorithms that can process naturally occurring human affective behaviour have recently emerged. Moreover, an increasing number of efforts are reported toward multimodal fusion for human affect analysis including audiovisual fusion, linguistic and paralinguistic fusion, and multi-cue visual fusion based on facial expressions, head movements, and body gestures. This paper introduces and surveys these recent advances. We first discuss human emotion perception from a psychological perspective. Next we examine available approaches to solving the problem of machine understanding of human affective behavior, and discuss important issues like the collection and availability of training and test data. We finally outline some of the scientific and engineering challenges to advancing human affect sensing technology.

A Survey of Affect Recognition Methods: Audio, Visual, and Spontaneous Expressions

In this paper, we exploit the advantages of tensorial representations and propose several tensor learning models for regression. The model is based on the canonical/parallel-factor decomposition of tensors of multiple modes and allows the simultaneous projections of an input tensor to more than one direction along each mode. Two empirical risk functions are studied, namely, the square loss and e-insensitive loss functions. The former leads to higher rank tensor ridge regression (TRR), and the latter leads to higher rank support tensor regression (STR), both formulated using the Frobenius norm for regularization. We also use the group-sparsity norm for regularization, favoring in that way the low rank decomposition of the tensorial weight. In that way, we achieve the automatic selection of the rank during the learning process and obtain the optimal-rank TRR and STR. Experiments conducted for the problems of head-pose, human-age, and 3-D body-pose estimations using real data from publicly available databases, verified not only the superiority of tensors over their vector counterparts but also the efficiency of the proposed algorithms.

Tensor Learning for Regression

https://ibug.doc.ic.ac.uk/media/uploads/documents/pat_rec_2008.pdf

Texture and shape information fusion for facial expression and facial action unit recognition

The methods introduced so far regarding discriminant non-negative matrix factorization (DNMF) do not guarantee convergence to a stationary limit point. In order to remedy this limitation, a novel DNMF method is presented that uses projected gradients. The proposed algorithm employs some extra modifications that make the method more suitable for classification tasks. The usefulness of the proposed technique to frontal face verification and facial expression recognition problems is demonstrated.

A Novel Discriminant Non-Negative Matrix Factorization Algorithm With Applications to Facial Image Characterization Problems

In this article, we present the Menpo 2D and Menpo 3D benchmarks, two new datasets for multi-pose 2D and 3D facial landmark localisation and tracking. In contrast to the previous benchmarks such as 300W and 300VW, the proposed benchmarks contain facial images in both semi-frontal and profile pose. We introduce an elaborate semi-automatic methodology for providing high-quality annotations for both the Menpo 2D and Menpo 3D benchmarks. In Menpo 2D benchmark, different visible landmark configurations are designed for semi-frontal and profile faces, thus making the 2D face alignment full-pose. In Menpo 3D benchmark, a united landmark configuration is designed for both semi-frontal and profile faces based on the correspondence with a 3D face model, thus making face alignment not only full-pose but also corresponding to the real-world 3D space. Based on the considerable number of annotated images, we organised Menpo 2D Challenge and Menpo 3D Challenge for face alignment under large pose variations in conjunction with CVPR 2017 and ICCV 2017, respectively. The results of these challenges demonstrate that recent deep learning architectures, when trained with the abundant data, lead to excellent results. We also provide a very simple, yet effective solution, named Cascade Multi-view Hourglass Model, to 2D and 3D face alignment. In our method, we take advantage of all 2D and 3D facial landmark annotations in a joint way. We not only capitalise on the correspondences between the semi-frontal and profile 2D facial landmarks but also employ joint supervision from both 2D and 3D facial landmarks. Finally, we discuss future directions on the topic of face alignment.

https://link.springer.com/content/pdf/10.1007/s11263-018-1134-y.pdf

The Menpo Benchmark for Multi-pose 2D and 3D Facial Landmark Localisation and Tracking

The progress we are currently witnessing in many computer vision applications, including automatic face analysis, would not be made possible without tremendous efforts in collecting and annotating large scale visual databases. To this end, we propose 4DFAB, a new large scale database of dynamic high-resolution 3D faces (over 1,800,000 3D meshes). 4DFAB contains recordings of 180 subjects captured in four different sessions spanning over a five-year period. It contains 4D videos of subjects displaying both spontaneous and posed facial behaviours. The database can be used for both face and facial expression recognition, as well as behavioural biometrics. It can also be used to learn very powerful blendshapes for parametrising facial behaviour. In this paper, we conduct several experiments and demonstrate the usefulness of the database for various applications. The database will be made publicly available for research purposes.

/pdf/4dfab-a-large-scale-4d-database-for-facial-expression-33woeptefq.pdf

Irene Kotsia

Papers

Tensor Learning for Regression

Texture and shape information fusion for facial expression and facial action unit recognition

A Novel Discriminant Non-Negative Matrix Factorization Algorithm With Applications to Facial Image Characterization Problems

The Menpo Benchmark for Multi-pose 2D and 3D Facial Landmark Localisation and Tracking

4DFAB: A Large Scale 4D Database for Facial Expression Analysis and Biometric Applications