Human activity recognition has drawn considerable attention recently in the field of computer vision due to the development of commodity depth cameras, by which the human activity is represented as a sequence of 3D skeleton postures. Assuming human body 3D joint locations of an activity lie on a manifold, the problem of recognizing human activity is formulated as the computation of activity manifold-manifold distance (AMMD). In this paper, we first design an efficient division method to decompose a manifold into ordered continuous maximal linear patches (CMLPs) that denote meaningful action snippets of the action sequence. Then the CMLP is represented by its position (average value of points) and the first principal component, which specify the major posture and main evolving direction of an action snippet, respectively. Finally, we compute the distance between CMLPs by taking both the posture and direction into consideration. Based on these preparations, an intuitive distance measure that preserves the local order of action snippets is proposed to compute AMMD. The performance on two benchmark datasets demonstrates the effectiveness of the proposed approach.
In this paper, we address the problem of classifying image sets for face recognition, where each set contains images belonging to the same subject and typically covering large variations. By modeling each image set as a manifold, we formulate the problem as the computation of the distance between two manifolds, called manifold-manifold distance (MMD). Since an image set can come in three pattern levels, point, subspace, and manifold, we systematically study the distance among the three levels and formulate them in a general multilevel MMD framework. Specifically, we express a manifold by a collection of local linear models, each depicted by a subspace. MMD is then converted to integrate the distances between pairs of subspaces from one of the involved manifolds. We theoretically and experimentally study several configurations of the ingredients of MMD. The proposed method is applied to the task of face recognition with image sets, where identification is achieved by seeking the minimum MMD from the probe to the gallery of image sets. Our experiments demonstrate that, as a general set similarity measure, MMD consistently outperforms other competing nondiscriminative methods and is also promisingly comparable to the state-of-the-art discriminative methods. In this paper, we learn explicit representations for dynamic shape manifolds of moving humans for the task of action recognition. We exploit locality preserving projections (LPP) for dimensionality reduction, leading to a low-dimensional embedding of human movements. Given a sequence of moving silhouettes associated to an action video, by LPP, we project them into a low-dimensional space to characterize the spatiotemporal property of the action, as well as to preserve much of the geometric structure. To match the embedded action trajectories, the median Hausdorff distance or normalized spatiotemporal correlation is used for similarity measures. Action classification is then achieved in a nearest-neighbor framework. To evaluate the proposed method, extensive experiments have been carried out on a recent dataset including ten actions performed by nine different subjects. The experimental results show that the proposed method is able to not only recognize human actions effectively, but also considerably tolerate some challenging conditions, e.g., partial occlusion, low-quality videos, changes in viewpoints, scales, and clothes; within-class variations caused by different subjects with different physical build; styles of motion; etc