International Journal of Computer Vision

, Volume 53, Issue 2, pp 153–167

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

  • Anthony J. Yezzi
  • Stefano Soatto

DOI: 10.1023/A:1023048024042

Cite this article as:
Yezzi, A.J. & Soatto, S. International Journal of Computer Vision (2003) 53: 153. doi:10.1023/A:1023048024042


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.

shape segmentation motion registration 

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Anthony J. Yezzi
    • 1
  • Stefano Soatto
    • 2
  1. 1.Georgia Institute of TechnologyAtlantaUSA
  2. 2.University of CaliforniaLos AngelesUSA