Lower bounds for invariant statistical models with applications to principal component analysis

This paper develops nonasymptotic information inequalities for the estimation of the eigenspaces of a covariance operator. These results generalize previous lower bounds for the spiked covariance model, and they show that recent upper bounds for models with decaying eigenvalues are sharp. The proof relies on lower bound techniques based on group invariance arguments which can also deal with a variety of other statistical models.Comment: 42 pages, to appear in Annales de l'Institut Henri Poincar\'e Probabilit\'es et Statistique

Bi-temporal 3D active appearance models with applications to unsupervised ejection fraction estimation

Rapid and unsupervised quantitative analysis is of utmost importance to ensure clinical acceptance of many examinations using cardiac magnetic resonance imaging (MRI). We present a framework that aims at fulfilling these goals for the application of left ventricular ejection fraction estimation in four-dimensional MRI. The theoretical foundation of our work is the generative two-dimensional Active Appearance Models by Cootes et al., here extended to bi-temporal, three-dimensional models. Further issues treated include correction of respiratory induced slice displacements, systole detection, and a texture model pruning strategy. Cross-validation carried out on clinical-quality scans of twelve volunteers indicates that ejection fraction and cardiac blood pool volumes can be estimated automatically and rapidly with accuracy on par with typical inter-observer variability. \u

Online learning and fusion of orientation appearance models for robust rigid object tracking

We introduce a robust framework for learning and fusing of orientation appearance models based on both texture and depth information for rigid object tracking. Our framework fuses data obtained from a standard visual camera and dense depth maps obtained by low-cost consumer depth cameras such as the Kinect. To combine these two completely different modalities, we propose to use features that do not depend on the data representation: angles. More specifically, our framework combines image gradient orientations as extracted from intensity images with the directions of surface normals computed from dense depth fields. We propose to capture the correlations between the obtained orientation appearance models using a fusion approach motivated by the original Active Appearance Models (AAMs). To incorporate these features in a learning framework, we use a robust kernel based on the Euler representation of angles which does not require off-line training, and can be efficiently implemented online. The robustness of learning from orientation appearance models is presented both theoretically and experimentally in this work. This kernel enables us to cope with gross measurement errors, missing data as well as other typical problems such as illumination changes and occlusions. By combining the proposed models with a particle filter, the proposed framework was used for performing 2D plus 3D rigid object tracking, achieving robust performance in very difficult tracking scenarios including extreme pose variations. © 2014 Elsevier B.V. All rights reserved

Robust Head-Pose Estimation Based on Partially-Latent Mixture of Linear Regressions

Head-pose estimation has many applications, such as social event analysis, human-robot and human-computer interaction, driving assistance, and so forth. Head-pose estimation is challenging because it must cope with changing illumination conditions, variabilities in face orientation and in appearance, partial occlusions of facial landmarks, as well as bounding-box-to-face alignment errors. We propose tu use a mixture of linear regressions with partially-latent output. This regression method learns to map high-dimensional feature vectors (extracted from bounding boxes of faces) onto the joint space of head-pose angles and bounding-box shifts, such that they are robustly predicted in the presence of unobservable phenomena. We describe in detail the mapping method that combines the merits of unsupervised manifold learning techniques and of mixtures of regressions. We validate our method with three publicly available datasets and we thoroughly benchmark four variants of the proposed algorithm with several state-of-the-art head-pose estimation methods.Comment: 12 pages, 5 figures, 3 table

Face tracking and pose estimation with automatic three-dimensional model construction

A method for robustly tracking and estimating the face pose of a person using stereo vision is presented. The method is invariant to identity and does not require previous training. A face model is automatically initialised and constructed online: a fixed point distribution is superposed over the face when it is frontal to the cameras, and several appropriate points close to those locations are chosen for tracking. Using the stereo correspondence of the cameras, the three-dimensional (3D) coordinates of these points are extracted, and the 3D model is created. The 2D projections of the model points are tracked separately on the left and right images using SMAT. RANSAC and POSIT are used for 3D pose estimation. Head rotations up to ±45° are correctly estimated. The approach runs in real time. The purpose of this method is to serve as the basis of a driver monitoring system, and has been tested on sequences recorded in a moving car.Ministerio de Educación y CienciaComunidad de Madri

Object recognition in infrared imagery using appearance-based methods

Abstract unavailable please refer to PD

Face recognition with image sets using manifold density divergence

In many automatic face recognition applications, a set of a person\u27s face images is available rather than a single image. In this paper, we describe a novel method for face recognition using image sets. We propose a flexible, semi-parametric model for learning probability densities confined to highly non-linear but intrinsically low-dimensional manifolds. The model leads to a statistical formulation of the recognition problem in terms of minimizing the divergence between densities estimated on these manifolds. The proposed method is evaluated on a large data set, acquired in realistic imaging conditions with severe illumination variation. Our algorithm is shown to match the best and outperform other state-of-the-art algorithms in the literature, achieving 94% recognition rate on average

Creating invariance to "nuisance parameters" in face recognition

A major goal for face recognition is to identify faces where the pose of the probe is different from the stored face. Typical feature vectors vary more with pose than with identity, leading to very poor recognition performance. We propose a non-linear many-to-one mapping from a conventional feature space to a new space constructed so that each individual has a unique feature vector regardless of pose. Training data is used to implicitly parameterize the position of the multi-dimensional face manifold by pose. We introduce a co-ordinate transform, which depends on the position on the manifold. This transform is chosen so that different poses of the same face are mapped to the same feature vector. The same approach is applied to illumination changes. We investigate different methods for creating features, which are invariant to both pose and illumination. We provide a metric to assess the discriminability of the resulting features. Our technique increases the discriminability of faces under unknown pose and lighting compared to contemporary methods