Abstract
What does it mean for a deforming object to be “moving” (see Fig.1)? 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-equivalent shapes using region-based methods, and to simultaneously approximate and register structures in grey-scale 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.
This research is supported in part by NSF grant IIS-9876145, ARO grant DAAD19-99-1-0139 and Intel grant 8029.
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Soatto, S., Yezzi, A.J. (2002). DEFORMOTION Deforming Motion, Shape Average and the Joint Registration and Segmentation of Images. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds) Computer Vision — ECCV 2002. ECCV 2002. Lecture Notes in Computer Science, vol 2352. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47977-5_3
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