Manifolds, Active Models, And Deformable Templates
Manifolds, Active Models, And Deformable Templates
To study shape we introduce manifolds and submanifolds examined in the continuum as the generators. Transformations are constructed which are built from the matrix groups and infinite products. This gives rise to many of the widely used structural models in image analysis often termed active models, essentially the deformable templates. These deformations are studied as both diffeomorphisms as well as immersions. A calculus is introduced based on transport theory for activating these deformable shapes by taking variations with respect to the matrix groups parameterizing them. Segmentation based on activating these manifolds is examined based on Gaussian random fields and variations with respect to the parameterizations.
Keywords: Brownian motion, Fourier transform, Gram-Schmidt orthogonalization, Hoffman brain phantom, Laplacian circulant boundary, PIE phantom, Wiener process
Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.
Please, subscribe or login to access full text content.
If you think you should have access to this title, please contact your librarian.
To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .
