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.
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Yezzi, A.J., Soatto, S. Deformotion: Deforming Motion, Shape Average and the Joint Registration and Approximation of Structures in Images. International Journal of Computer Vision 53, 153–167 (2003). https://doi.org/10.1023/A:1023048024042
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DOI: https://doi.org/10.1023/A:1023048024042