View-Invariant Analysis of Cyclic Motion

  • Authors:

  • Steven M. Seitz;Charles R. Dyer

  • Affiliations:

  • Department of Computer Sciences, University of Wisconsin, Madison, WI 53706. E-mail: seitz@cs.wisc.edu, dyer@cs.wisc.edu;Department of Computer Sciences, University of Wisconsin, Madison, WI 53706. E-mail: seitz@cs.wisc.edu, dyer@cs.wisc.edu

  • Venue:
  • International Journal of Computer Vision
  • Year:
  • 1997

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Abstract

This paper presents a general framework for image-based analysis of3D repeating motions that addresses two limitations in the state ofthe art. First, the assumption that a motion be perfectly even fromone cycle to the next is relaxed. Real repeating motions tend not tobe perfectly even, i.e., the length of a cycle varies through timebecause of physically important changes in the scene. Ageneralization of period is defined for repeatingmotions that makes this temporal variation explicit. Thisrepresentation, called the period trace, is compact and purelytemporal, describing the evolution of an object or scene withoutreference to spatial quantities such as position or velocity. Second,the requirement that the observer be stationary is removed. Observermotion complicates image analysis because an object that undergoes a3D repeating motion will generally not produce a repeating sequenceof images. Using principles of affine invariance, we derive necessaryand sufficient conditions for an image sequence to be the projectionof a 3D repeating motion, accounting for changes in viewpoint andother camera parameters. Unlike previous work in visual invariance,however, our approach is applicable to objects and scenes whosemotion is highly non-rigid. Experiments on realimage sequences demonstrate how the approach may be used to detectseveral types of purely temporal motion features, relating to motiontrends and irregularities. Applications to athletic and medicalmotion analysis are discussed.