Abstract-We propose a novel geometric framework for analyzing 3D faces, with the specific goals of comparing, matching, and averaging their shapes. Here we represent facial surfaces by radial curves emanating from the nose tips and use elastic shape analysis of these curves to develop a Riemannian framework for analyzing shapes of full facial surfaces. This representation, along with the elastic Riemannian metric, seems natural for measuring facial deformations and is robust to challenges such as large facial expressions (especially those with open mouths), large pose variations, missing parts, and partial occlusions due to glasses, hair, etc. This framework is shown to be promising from both -empirical and theoretical -perspectives. In terms of the empirical evaluation, our results match or improve the state-of-the-art methods on three prominent databases: FRGCv2, GavabDB, and Bosphorus, each posing a different type of challenge. From a theoretical perspective, this framework allows for formal statistical inferences, such as the estimation of missing facial parts using PCA on tangent spaces and computing average shapes.

We study the problem of classifying actions of human subjects using depth movies generated by Kinect or other depth sensors. Representing human body as dynamical skeletons, we study the evolution of their (skeletons’) shapes as trajectories on Kendall’s shape manifold. The action data is typically corrupted by large variability in execution rates within and across subjects and, thus, causing major problems in statistical analyses. To address that issue, we adopt a recently-developed framework of Su et al. [1], [2] to this problem domain. Here, the variable execution rates correspond to re-parameterizations of trajectories, and one uses a parameterization-invariant metric for aligning, comparing, averaging, and modeling trajectories. This is based on a combination of transported square-root vector fields (TSRVFs) of trajectories and the standard Euclidean norm, that allows computational efficiency. We develop a comprehensive suite of computational tools for this application domain: smoothing and denoising skeleton trajectories using median filtering, up- and down-sampling actions in time domain, simultaneous temporal-registration of multiple actions, and extracting invertible Euclidean representations of actions. Due to invertibility these Euclidean representations allow both discriminative and generative models for statistical analysis. For instance, they can be used in a SVM-based classification of original actions, as demonstrated here using MSR Action-3D, MSR Daily Activity and 3D Action Pairs datasets. Using only the skeletal information, we achieve state-of-the-art classification results on these datasets.

Methods to recognize humans' facial expressions have been proposed mainly focusing on 2D still images and videos. In this paper, the problem of person-independent facial expression recognition is addressed using the 3D geometry information extracted from the 3D shape of the face. To this end, a completely automatic approach is proposed that relies on identifying a set of facial keypoints, computing SIFT feature descriptors of depth images of the face around sample points defined starting from the facial keypoints, and selecting the subset of features with maximum relevance. Training a Support Vector Machine (SVM) for each facial expression to be recognized, and combining them to form a multi-class classifier, an average recognition rate of 78.43% on the BU-3DFE database has been obtained. Comparison with competitor approaches using a common experimental setting on the BU-3DFE database shows that our solution is capable of obtaining state of the art results. The same 3D face representation framework and testing database have been also used to perform 3D facial expression retrieval (i.e., retrieve 3D scans with the same facial expression as shown by a target subject), with results proving the viability of the proposed solution.

In this paper, the problem of person-independent facial expression recognition is addressed on 3D shapes. To this end, an original approach is proposed that computes SIFT descriptors on a set of facial landmarks of depth images, and then selects the subset of most relevant features. Using SVM classification of the selected features, an average recognition rate of 77.5% on the BU-3DFE database has been obtained. Comparative evaluation on a common experimental setup, shows that our solution is able to obtain state of the art results.

In this paper we explore the use of shapes of elastic radial curves to model 3D facial deformations, caused by changes in facial expressions. We represent facial surfaces by indexed collections of radial curves on them, emanating from the nose tips, and compare the facial shapes by comparing the shapes of their corresponding curves. Using a past approach on elastic shape analysis of curves, we obtain an algorithm for comparing facial surfaces. We also introduce a quality control module which allows our approach to be robust to pose variation and missing data. Comparative evaluation using a common experimental setup on GAVAB dataset, considered as the most expression-rich and noise-prone 3D face dataset, shows that our approach outperforms other state-of-the-art approaches.

We utilize ideas from two growing but disparate ideas in computer vision-shape analysis using tools from differential geometry and feature selection using machine learning-to select and highlight salient geometrical facial features that contribute most in 3D face recognition and gender classification. Firstly, a large set of geometries curve features are extracted using level sets (circular curves) and streamlines (radial curves) of the Euclidean distance functions of the facial surface; together they approximate facial surfaces with arbitrarily high accuracy. Then, we use the well-known Adaboost algorithm for feature selection from this large set and derive a composite classifier that achieves high performance with a minimal set of features. This greatly reduced set, consisting of some level curves on the nose and some radial curves in the forehead and cheeks regions, provides a very compact signature of a 3D face and a fast classification algorithm for face recognition and gender selection. It is also efficient in terms of data storage and transmission costs. Experimental results, carried out using the FRGCv2 dataset, yield a rank-1 face recognition rate of 98% and a gender classification rate of 86%.

In this paper, we propose a novel space-time geometric representation of human landmark configurations and derive tools for comparison and classification. We model the temporal evolution of landmarks as parametrized trajectories on the Riemannian manifold of positive semidefinite matrices of fixed-rank. Our representation has the benefit to bring naturally a second desirable quantity when comparing shapes -the spatial covariance -in addition to the conventional affine-shape representation. We derived then geometric and computational tools for rate-invariant analysis and adaptive re-sampling of trajectories, grounding on the Riemannian geometry of the underlying manifold. Specifically, our approach involves three steps: (1) landmarks are first mapped into the Riemannian manifold of positive semidefinite matrices of fixed-rank to build time-parameterized trajectories; (2) a temporal warping is performed on the trajectories, providing a geometry-aware (dis-)similarity measure between them; (3) finally, a pairwise proximity function SVM is used to classify them, incorporating the (dis-)similarity measure into the kernel function. We show that such representation and metric achieve competitive results in applications as action recognition and emotion recognition from 3D skeletal data, and facial expression recognition from videos. Experiments have been conducted on several publicly available up-to-date benchmarks.In this document, we provide the mathematical preliminaries to our approach. We also give further details on the conducted experiments and the reported results.

International audienceIn this paper we address the problem of 3D facial expression recognition. We propose a local geometric shape analysis of facial surfaces coupled with machine learning techniques for expression classification. A computation of the length of the geodesic path between corresponding patches, using a Riemannian framework, in a shape space provides a quantitative information about their similarities. These measures are then used as inputs to several classification methods. The experimental results demonstrate the effectiveness of the proposed approach. Using Multi-boosting and Support Vector Machines (SVM) classifiers, we achieved 98.81% and 97.75% recognition average rates, respectively, for recognition of the six prototypical facial expressions on BU-3DFE database. A comparative study using the same experimental setting shows that the suggested approach outperforms previous work