Shape Distributions of Nonlinear Dynamical Systems for Video-Based Inference

Vinay Venkataraman, Pavan Turaga

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


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.

Original languageEnglish (US)
Article number7415965
Pages (from-to)2531-2543
Number of pages13
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number12
StatePublished - Dec 1 2016


  • Action modeling
  • Dynamical scene analysis
  • action and gesture recognition
  • chaos theory
  • largest Lyapunov exponent
  • movement quality assessment
  • shape distribution

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics


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