Deformotion: Deforming Motion, Shape Average and the Joint Registration and Approximation of Structures in Images

  • Authors:

  • Anthony J. Yezzi;Stefano Soatto

  • Affiliations:

  • Georgia Institute of Technology, Atlanta, GA 30332, USA. ayezzi@ece.gatech.edu;University of California, Los Angeles, CA 90095, USA. soatto@ucla.edu

  • Venue:
  • International Journal of Computer Vision
  • Year:
  • 2003

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Abstract

What does it mean for a deforming object to be “moving”? How can we separate the overall motion (a finite-dimensional group action) from the more general deformation (a diffeomorphism)? In this paper we propose a definition of motion for a deforming object and introduce a notion of “shape average” as the entity that separates the motion from the deformation. Our definition allows us to derive novel and efficient algorithms to register non-identical shapes using region-based methods, and to simultaneously approximate and align structures in greyscale images. We also extend the notion of shape average to that of a “moving average” in order to track moving and deforming objects through time. The algorithms we propose extend prior work on landmark-based matching to smooth curves, and involve the numerical integration of partial differential equations, which we address within the framework of level set methods.