Recognizing human actions in 3-D video sequences is an important open problem that is currently at the heart of many research domains including surveillance, natural interfaces and rehabilitation. However, the design and development of models for action recognition that are both accurate and efficient is a challenging task due to the variability of the human pose, clothing and appearance. In this paper, we propose a new framework to extract a compact representation of a human action captured through a depth sensor, and enable accurate action recognition. The proposed solution develops on fitting a human skeleton model to acquired data so as to represent the 3-D coordinates of the joints and their change over time as a trajectory in a suitable action space. Thanks to such a 3-D joint-based framework, the proposed solution is capable to capture both the shape and the dynamics of the human body, simultaneously. The action recognition problem is then formulated as the problem of computing the similarity between the shape of trajectories in a Riemannian manifold. Classification using k-nearest neighbors is finally performed on this manifold taking advantage of Riemannian geometry in the open curve shape space. Experiments are carried out on four representative benchmarks to demonstrate the potential of the proposed solution in terms of accuracy/latency for a low-latency action recognition. Comparative results with state-of-the-art methods are reported.

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, and so on. This framework is shown to be promising from both-empirical and theoretical-perspectives. In terms of the empirical evaluation, our results match or improve upon 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.

In this paper, we propose a method for three-dimensional (3D)-model indexing based on two-dimensional (2D) views, which we call adaptive views clustering (AVC). The goal of this method is to provide an "optimal" selection of 2D views from a 3D model, and a probabilistic Bayesian method for 3D-model retrieval from these views. The characteristic view selection algorithm is based on an adaptive clustering algorithm and uses statistical model distribution scores to select the optimal number of views. Starting from the fact that all views do not have equal importance, we also introduce a novel Bayesian approach to improve the retrieval. Finally, we present our results and compare our method to some state-of-the-art 3D retrieval descriptors on the Princeton 3D Shape Benchmark database and a 3D-CAD-models database supplied by the car manufacturer Renault

We study shapes of facial surfaces for the purpose of face recognition. The main idea is to 1) represent surfaces by unions of level curves, called facial curves, of the depth function and 2) compare shapes of surfaces implicitly using shapes of facial curves. The latter is performed using a differential geometric approach that computes geodesic lengths between closed curves on a shape manifold. These ideas are demonstrated using a nearest-neighbor classifier on two 3D face databases: Florida State University and Notre Dame, highlighting a good recognition performance