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Friedrich, F.* ; Demaret, L. ; Führ, H. ; Wicker, K.*

Efficient moment computation over polygonal domains with an application to rapid wedgelet approximation.

SIAM J. Sci. Comput. 29, 842-863 (2007)
DOI
Open Access Green as soon as Postprint is submitted to ZB.
Many algorithms in image processing rely on the computation of sums of pixel values over a large variety of subsets of the image domain. This includes the computation of image moments for pattern recognition purposes, or adaptive smoothing and regression methods, such as wedgelets. In the. rst part of the paper, we present a general method which allows the fast computation of sums over a large class of polygonal domains. The approach relies on the idea of considering polygonal domains with a fixed angular resolution, combined with an efficient implementation of a discrete version of Green's theorem. The second part deals with the application of the new methodology to a particular computational problem, namely wedgelet approximation. Our technique results in a speedup of O(10(3)) by comparison to preexisting implementations. A further attractive feature of our implementation is the instantaneous access to the full scale of wedgelet minimizers. We introduce a new scheme that replaces the locally constant regression underlying wedgelets by basically arbitrary local regression models. Due to the speedup obtained by the techniques explained in the. rst part, this scheme is computationally efficient and at the same time much more flexible than previously suggested methods such as wedgelets or platelets. In the final section we present numerical experiments showing the increase in speed and flexibility.
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Publication type Article: Journal article
Document type Scientific Article
Corresponding Author
Keywords wedgelets; platelets; image approximation; image moments; polygonal domains; discrete Green's theorem; digital lines
ISSN (print) / ISBN 1064-8275
e-ISSN 1095-7197
Journal SIAM Journal on Scientific Computing
Quellenangaben Volume: 29, Issue: 2, Pages: 842-863 Article Number: , Supplement: ,
Publisher Society for Industrial and Applied Mathematics (SIAM)
Non-patent literature Publications
Reviewing status Peer reviewed
Institute(s) Institute of Biomathematics and Biometry (IBB)