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

“Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks”の学習報告

On robust estimation of the location parameter

Principal Component Analysis (PCA) is perhaps the most prominent learning tool for dimensionality reduction in pattern recognition and computer vision. However, the ? 2-norm employed by standard PCA is not robust to outliers. In this paper, we propose a kernel PCA method for fast and robust PCA, which we call Euler-PCA (e-PCA). In particular, our algorithm utilizes a robust dissimilarity measure based on the Euler representation of complex numbers. We show that Euler-PCA retains PCA's desirable properties while suppressing outliers. Moreover, we formulate Euler-PCA in an incremental learning framework which allows for efficient computation. In our experiments we apply Euler-PCA to three different computer vision applications for which our method performs comparably with other state-of-the-art approaches.

/pdf/euler-principal-component-analysis-23b11o057g.pdf

Euler Principal Component Analysis

In this paper, a modified class of support vector machines (SVMs) inspired from the optimization of Fisher's discriminant ratio is presented, the so-called minimum class variance SVMs (MCVSVMs). The MCVSVMs optimization problem is solved in cases in which the training set contains less samples that the dimensionality of the training vectors using dimensionality reduction through principal component analysis (PCA). Afterward, the MCVSVMs are extended in order to find nonlinear decision surfaces by solving the optimization problem in arbitrary Hilbert spaces defined by Mercer's kernels. In that case, it is shown that, under kernel PCA, the nonlinear optimization problem is transformed into an equivalent linear MCVSVMs problem. The effectiveness of the proposed approach is demonstrated by comparing it with the standard SVMs and other classifiers, like kernel Fisher discriminant analysis in facial image characterization problems like gender determination, eyeglass, and neutral facial expression detection.

/pdf/minimum-class-variance-support-vector-machines-1qt5fhqzmu.pdf

Minimum Class Variance Support Vector Machines

In this paper, the principles of sparse signal representation theory are explored in order to perform facial expressions recognition from frontal views. Motivated by the success such methods have demonstrated in the face recognition problem, we formulate the feature extraction procedure in order to achieve facial expression recognition as an l 1 optimization problem. We show that the straightforward application of these methods to expressive images imposes certain difficulties. The use of difference images (i.e., the images that are derived from the subtraction of the neutral image from the expressive one) for sparse facial expression representations is justified. The use of expressive facial grids for similar tasks is also studied. Finally, the robustness of the proposed representations under facial image occlusion is shown and the efficacy of the proposed method in a series of experiments is demonstrated.

/pdf/sparse-representations-for-facial-expressions-recognition-3hpxgc851f.pdf

Sparse representations for facial expressions recognition via l 1 optimization

The de facto algorithm for facial landmark estimation involves running a face detector with a subsequent deformable model fitting on the bounding box. This encompasses two basic problems: 1) the detection and deformable fitting steps are performed independently, while the detector might not provide the best-suited initialization for the fitting step, and 2) the face appearance varies hugely across different poses, which makes the deformable face fitting very challenging and thus distinct models have to be used (e.g., one for profile and one for frontal faces). In this paper, we propose the first, to the best of our knowledge, joint multi-view convolutional network to handle large pose variations across faces in-the-wild, and elegantly bridge face detection and facial landmark localization tasks. The existing joint face detection and landmark localization methods focus only on a very small set of landmarks. By contrast, our method can detect and align a large number of landmarks for semi-frontal (68 landmarks) and profile (39 landmarks) faces. We evaluate our model on a plethora of datasets including the standard static image datasets such as IBUG, 300W, COFW, and the latest Menpo Benchmark for both semi-frontal and profile faces. A significant improvement over the state-of-the-art methods on deformable face tracking is witnessed on the 300VW benchmark. We also demonstrate state-of-the-art results for face detection on FDDB and MALF datasets.

Joint Multi-View Face Alignment in the Wild

Three-dimensional Morphable Models (3DMMs) are powerful statistical tools for representing the 3D surfaces of an object class. In this context, we identify an interesting question that has previously not received research attention: is it possible to combine two or more 3DMMs that (a) are built using different templates that perhaps only partly overlap, (b) have different representation capabilities and (c) are built from different datasets that may not be publicly-available? In answering this question, we make two contributions. First, we propose two methods for solving this problem: i. use a regressor to complete missing parts of one model using the other, ii. use the Gaussian Process framework to blend covariance matrices from multiple models. Second, as an example application of our approach, we build a new head and face model that combines the variability and facial detail of the LSFM with the full head modelling of the LYHM. The resulting combined model achieves state-of-the-art performance and outperforms existing head models by a large margin. Finally, as an application experiment, we reconstruct full head representations from single, unconstrained images by utilizing our proposed large-scale model in conjunction with the Face-Warehouse blendshapes for handling expressions.

https://openaccess.thecvf.com/content_CVPR_2019/papers/Ploumpis_Combining_3D_Morphable_Models_A_Large_Scale_Face-And-Head_Model_CVPR_2019_paper.pdf

Stefanos Zafeiriou

Papers

Euler Principal Component Analysis

Minimum Class Variance Support Vector Machines

Sparse representations for facial expressions recognition via l 1 optimization

Joint Multi-View Face Alignment in the Wild

Combining 3D Morphable Models: A Large Scale Face-And-Head Model