Journal
INTERNATIONAL JOURNAL OF COMPUTER VISION
Volume 53, Issue 2, Pages 153-167Publisher
SPRINGER
DOI: 10.1023/A:1023048024042
Keywords
shape; segmentation; motion; registration
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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 nonidentical 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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