In this letter, a fast approach for curve reparametrization, called Fast Adaptive Reparamterization (FAR), is introduced. Instead of computing an optimal matching between two curves such as Dynamic Time Warping (DTW) and elastic distance-based approaches, our method is applied to each curve independently, leading to linear computational complexity. It is based on a simple replacement of the curve parameter by a variable invariant under specific variations of reparametrization. The choice of this variable is heuristically made according to the application of interest. In addition to being fast, the proposed reparametrization can be applied not only to curves observed in Euclidean spaces but also to feature curves living in Riemannian spaces. To validate our approach, we apply it to the scenario of human action recognition using curves living in the Riemannian product Special Euclidean space$\mathbb {SE}(3)^n$. The obtained results on three benchmarks for human action recognition (MSRAction3D, Florence3D, and UTKinect) show that our approach competes with state-of-the-art methods in terms of accuracy and computational cost.

In this paper, we propose a novel view-invariant action recognition method using a single monocular RGB camera. View-invariance remains a very challenging topic in 2D action recognition due to the lack of 3D information in RGB images. Most successful approaches make use of the concept of knowledge transfer by projecting 3D synthetic data to multiple viewpoints. Instead of relying on knowledge transfer, we propose to augment the RGB data by a third dimension by means of 3D skeleton estimation from 2D images using a CNN-based pose estimator. In order to ensure view-invariance, a pre-processing for alignment is applied followed by data expansion as a way for denoising. Finally, a Long-Short Term Memory (LSTM) architecture is used to model the temporal dependency between skeletons. The proposed network is trained to directly recognize actions from aligned 3D skeletons. The experiments performed on the challenging Northwestern-UCLA dataset show the superiority of our approach as compared to state-of-the-art ones.

In this paper, we introduce a deformation based representation space for curved shapes in . Given an ordered set of points sampled from a curved shape, the proposed method represents the set as an element of a finite dimensional matrix Lie group. Variation due to scale and location are filtered in a preprocessing stage, while shapes that vary only in rotation are identified by an equivalence relationship. The use of a finite dimensional matrix Lie group leads to a similarity metric with an explicit geodesic solution. Subsequently, we discuss some of the properties of the metric and its relationship with a deformation by least action. Furthermore, invariance to reparametrization or estimation of point correspondence between shapes is formulated as an estimation of sampling function. Thereafter, two possible approaches are presented to solve the point correspondence estimation problem. Finally, we propose an adaptation of k-means clustering for shape analysis in the proposed representation space. Experimental results show that the proposed representation is robust to uninformative cues, e.g., local shape perturbation and displacement. In comparison to state of the art methods, it achieves a high precision on the Swedish and the Flavia leaf datasets and a comparable result on MPEG-7, Kimia99 and Kimia216 datasets.

We propose a deformation-based representation for analyzing expressions from three-dimensional (3D) faces. A point cloud of a 3D face is decomposed into an ordered deformable set of curves that start from a fixed point. Subsequently, a mapping function is defined to identify the set of curves with an element of a high-dimensional matrix Lie group, specifically the direct product of SE(3). Representing 3D faces as an element of a high-dimensional Lie group has two main advantages. First, using the group structure, facial expressions can be decoupled from a neutral face. Second, an underlying non-linear facial expression manifold can be captured with the Lie group and mapped to a linear space, Lie algebra of the group. This opens up the possibility of classifying facial expressions with linear models without compromising the underlying manifold. Alternatively, linear combinations of linearised facial expressions can be mapped back from the Lie algebra to the Lie group. The approach is tested on the Binghamton University 3D Facial Expression (BU-3DFE) and the Bosphorus datasets. The results show that the proposed approach performed comparably, on the BU-3DFE dataset, without using features or extensive landmark points.

In this paper, we introduce a similarity metric for curved shapes that can be described, distinctively, by ordered points. The proposed method represents a given curve as a point in the deformation space, the direct product of rigid transformation matrices, such that the successive action of the matrices on a fixed starting point reconstructs the full curve. In general, both open and closed curves are represented in the deformation space modulo shape orientation and orientation preserving diffeomorphisms. The use of direct product Lie groups to represent curved shapes led to an explicit formula for geodesic curves and the formulation of a similarity metric between shapes by the L2-norm on the Lie algebra. Additionally, invariance to reparametrization or estimation of point correspondence between shapes is performed as an intermediate step for computing geodesics. Furthermore, since there is no computation of differential quantities on the curves, our representation is more robust to local perturbations and needs no pre-smoothing. We compare our method with the elastic shape metric defined through the square root velocity (SRV) mapping, and other shape matching approaches.

A statistical model for shapes in R2or R3is proposed. Shape modelling is a difficult problem mainly due to the non-linear nature of its space. Our approach considers curves as shape contours, and models their deformations with respect to a de-formable template shape. Contours are uniformly sampled into a discrete sequence of points. Hence, the deformation of a shape is formulated as an action of transformation matrices on each of these points. A parametrized stochastic model based on Markov process is proposed to model shape variability in the deformation space. The model's parameters are estimated from a labeled training dataset. Moreover, a similarity metric based on the Mahalanobis distance is proposed. Subsequently, the model has been successfully tested for shape recognition, synthesis, and retrieval.