Regularization of Discrete Contour by Willmore Energy

We propose a novel approach to reconstruct shapes from digital data. Contrarily to most methods, reconstructed shapes are smooth with a well-defined curvature field and have the same digitization as the input data: the range of application we have in mind is especially post-processing to image segme...

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Bibliographic Details
Published in:Journal of mathematical imaging and vision 2011-06, Vol.40 (2), p.214-229
Main Authors: Bretin, E., Lachaud, J.-O., Oudet, É.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Computer Science
Image Processing and Computer Vision
Mathematical Methods in Physics
Mathematics
Numerical Analysis
Signal,Image and Speech Processing
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Summary:We propose a novel approach to reconstruct shapes from digital data. Contrarily to most methods, reconstructed shapes are smooth with a well-defined curvature field and have the same digitization as the input data: the range of application we have in mind is especially post-processing to image segmentation where labelled regions are digital objects. For this purpose, we introduce three new algorithms to regularize digital contours based on the minimization of Willmore energy: our first algorithm is based on tools coming from discrete geometry, the second is related to convex geometry while the third approach is a constrained phase field minimization. The three algorithms are described in details and the convergence of the phase field approach is investigated. We present a comparative evaluation of all three methods, in terms of the accuracy of curvature estimators and computation time.
ISSN:0924-9907
1573-7683
DOI:10.1007/s10851-010-0257-8