Higher-order nonlinear priors for surface reconstruction

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Publication Type Journal Article
School or College College of Engineering
Department Electrical & Computer Engineering
Creator Tasdizen, Tolga; Whitaker, Ross T.
Title Higher-order nonlinear priors for surface reconstruction
Date 2004
Description Abstract-For surface reconstruction problems with noisy and incomplete range data, a Bayesian estimation approach can improve the overall quality of the surfaces. The Bayesian approach to surface estimation relies on a likelihood term, which ties the surface estimate to the input data, and the prior, which ensures surface smoothness or continuity. This paper introduces a new high-order, nonlinear prior for surface reconstruction. The proposed prior can smooth complex, noisy surfaces, while preserving sharp, geometric features, and it is a natural generalization of edge-preserving methods in image processing, such as anisotropic diffusion. An exact solution would require solving a fourth-order partial differential equation (PDE), which can be difficult with conventional numerical techniques. Our approach is to solve a cascade system of two second-order PDEs, which resembles the original fourth-order system. This strategy is based on the observation that the generalization of image processing to surfaces entails filtering the surface normals. We solve one PDE for processing the normals and one for refitting the surface to the normals. Furthermore, we implement the associated surface deformations using level sets. Hence, the algorithm can accommodate very complex shapes with arbitrary and changing topologies. This paper gives the mathematical formulation and describes the numerical algorithms. We also show results using range and medical data.
Type Text
Publisher Institute of Electrical and Electronics Engineers (IEEE)
Volume 26
Issue 7
First Page 878
Last Page 891
Language eng
Bibliographic Citation Tasdizen, T., & Whitaker, R. T. (2004). Higher-order nonlinear priors for surface reconstruction. IEEE Transactions on Pattern Analysis and Machine Intelligence, 26(7), 878-91. July.
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Identifier ir-main,15185
ARK ark:/87278/s6n01qrb
Setname ir_uspace
ID 703545
Reference URL https://collections.lib.utah.edu/ark:/87278/s6n01qrb
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