This paper presents a shape-theoretic framework for dynamical analysis of nonlinear dynamical systems which appear frequently in several video-based inference tasks. Traditional approaches to dynamical modeling have included linear and nonlinear methods with their respective drawbacks. A novel approach we propose is the use of descriptors of the shape of the dynamical attractor as a feature representation of nature of dynamics. The proposed framework has two main advantages over traditional approaches: a) representation of the dynamical system is derived directly from the observational data, without any inherent assumptions, and b) the proposed features show stability under different time-series lengths where traditional dynamical invariants fail. We illustrate our idea using nonlinear dynamical models such as Lorenz and Rossler systems, where our feature representations (shape distribution) support our hypothesis that the local shape of the reconstructed phase space can be used as a discriminative feature. Our experimental analyses on these models also indicate that the proposed framework show stability for different time-series lengths, which is useful when the available number of samples are small variable. The specific applications of interest in this paper are: 1) activity recognition using motion capture and RGBD sensors, 2) activity quality assessment for applications in stroke rehabilitation, and 3) dynamical scene classification. We provide experimental validation through action and gesture recognition experiments on motion capture and Kinect datasets. In all these scenarios, we show experimental evidence of the favorable properties of the proposed representation.
Human activity recognition is an important area of computer vision research. Its applications include surveillance systems, patient monitoring systems, and a variety of systems that involve interactions between persons and electronic devices such as human-computer interfaces. Most of these applications require an automated recognition of high-level activities, composed of multiple simple (or atomic) actions of persons. This article provides a detailed overview of various state-of-the-art research papers on human activity recognition. We discuss both the methodologies developed for simple human actions and those for high-level activities. An approach-based taxonomy is chosen that compares the advantages and limitations of each approach. Recognition methodologies for an analysis of the simple actions of a single person are first presented in the article. Space-time volume approaches and sequential approaches that represent and recognize activities directly from input images are discussed. Next, hierarchical recognition methodologies for high-level activities are presented and compared. Statistical approaches, syntactic approaches, and description-based approaches for hierarchical recognition are discussed in the article. In addition, we further discuss the papers on the recognition of human-object interactions and group activities. Public datasets designed for the evaluation of the recognition methodologies are illustrated in our article as well, comparing the methodologies' performances. This review will provide the impetus for future research in more productive areas. The ability to recognize humans and their activities by vision is key for a machine to interact intelligently and effortlessly with a human-inhabited environment. Because of many potentially important applications, “looking at people” is currently one of the most active application domains in computer vision. This survey identifies a number of promising applications and provides an overview of recent developments in this domain. The scope of this survey is limited to work on whole-body or hand motion; it does not include work on human faces. The emphasis is on discussing the various methodologies; they are grouped in 2-D approaches with or without explicit shape models and 3-D approaches. Where appropriate, systems are reviewed. We conclude with some thoughts about future directions.