Shape Distributions of Nonlinear Dynamical Systems for Video-Based Inference

Vinay Venkataraman, Pavan Turaga

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

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
Volume38
Issue number12
DOIs
StatePublished - Dec 1 2016

Fingerprint

Nonlinear dynamical systems
Nonlinear Dynamical Systems
Time series
Motion Capture
Gesture recognition
Patient rehabilitation
Rössler System
Shape Representation
Action Recognition
Gesture Recognition
Activity Recognition
Dynamical systems
Lorenz System
Quality Assessment
Experimental Validation
Rehabilitation
Dynamical Model
Stroke
Descriptors
Nonlinear Model

Keywords

  • action and gesture recognition
  • Action modeling
  • chaos theory
  • Dynamical scene analysis
  • 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

Cite this

Shape Distributions of Nonlinear Dynamical Systems for Video-Based Inference. / Venkataraman, Vinay; Turaga, Pavan.

In: IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 38, No. 12, 7415965, 01.12.2016, p. 2531-2543.

Research output: Contribution to journalArticle

@article{cf01b15d26ee4fe1b9f2c7c3fa4fd845,
title = "Shape Distributions of Nonlinear Dynamical Systems for Video-Based Inference",
abstract = "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.",
keywords = "action and gesture recognition, Action modeling, chaos theory, Dynamical scene analysis, largest Lyapunov exponent, movement quality assessment, shape distribution",
author = "Vinay Venkataraman and Pavan Turaga",
year = "2016",
month = "12",
day = "1",
doi = "10.1109/TPAMI.2016.2533388",
language = "English (US)",
volume = "38",
pages = "2531--2543",
journal = "IEEE Transactions on Pattern Analysis and Machine Intelligence",
issn = "0162-8828",
publisher = "IEEE Computer Society",
number = "12",

}

TY - JOUR

T1 - Shape Distributions of Nonlinear Dynamical Systems for Video-Based Inference

AU - Venkataraman, Vinay

AU - Turaga, Pavan

PY - 2016/12/1

Y1 - 2016/12/1

N2 - 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.

AB - 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.

KW - action and gesture recognition

KW - Action modeling

KW - chaos theory

KW - Dynamical scene analysis

KW - largest Lyapunov exponent

KW - movement quality assessment

KW - shape distribution

UR - http://www.scopus.com/inward/record.url?scp=84995596456&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84995596456&partnerID=8YFLogxK

U2 - 10.1109/TPAMI.2016.2533388

DO - 10.1109/TPAMI.2016.2533388

M3 - Article

AN - SCOPUS:84995596456

VL - 38

SP - 2531

EP - 2543

JO - IEEE Transactions on Pattern Analysis and Machine Intelligence

JF - IEEE Transactions on Pattern Analysis and Machine Intelligence

SN - 0162-8828

IS - 12

M1 - 7415965

ER -