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Curvature-Based Regularization for Surface Approximation

Olsson, Carl LU and Boykov, Yuri (2012) IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2012 In 2012 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) p.1576-1583
Abstract
We propose an energy-based framework for approximating surfaces from a cloud of point measurements corrupted by noise and outliers. Our energy assigns a tangent plane to each (noisy) data point by minimizing the squared distances to the points and the irregularity of the surface implicitly defined by the tangent planes. In order to avoid the well-known "shrinking" bias associated with first-order surface regularization, we choose a robust smoothing term that approximates curvature of the underlying surface. In contrast to a number of recent publications estimating curvature using discrete (e. g. binary) labellings with triple-cliques we use higher-dimensional labels that allows modeling curvature with only pair-wise interactions. Hence,... (More)
We propose an energy-based framework for approximating surfaces from a cloud of point measurements corrupted by noise and outliers. Our energy assigns a tangent plane to each (noisy) data point by minimizing the squared distances to the points and the irregularity of the surface implicitly defined by the tangent planes. In order to avoid the well-known "shrinking" bias associated with first-order surface regularization, we choose a robust smoothing term that approximates curvature of the underlying surface. In contrast to a number of recent publications estimating curvature using discrete (e. g. binary) labellings with triple-cliques we use higher-dimensional labels that allows modeling curvature with only pair-wise interactions. Hence, many standard optimization algorithms (e. g. message passing, graph cut, etc) can minimize the proposed curvature-based regularization functional. The accuracy of our approach for representing curvature is demonstrated by theoretical and empirical results on synthetic and real data sets from multi-view reconstruction and stereo. (1) (Less)
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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
in
2012 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
pages
1576 - 1583
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
conference name
IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2012
external identifiers
  • wos:000309166201092
  • scopus:84866699265
ISSN
1063-6919
DOI
10.1109/CVPR.2012.6247849
language
English
LU publication?
yes
id
9db1ee80-3c35-4383-b8b6-cfd79c57ce52 (old id 3283289)
date added to LUP
2012-12-20 12:21:14
date last changed
2017-07-30 04:14:02
@inproceedings{9db1ee80-3c35-4383-b8b6-cfd79c57ce52,
  abstract     = {We propose an energy-based framework for approximating surfaces from a cloud of point measurements corrupted by noise and outliers. Our energy assigns a tangent plane to each (noisy) data point by minimizing the squared distances to the points and the irregularity of the surface implicitly defined by the tangent planes. In order to avoid the well-known "shrinking" bias associated with first-order surface regularization, we choose a robust smoothing term that approximates curvature of the underlying surface. In contrast to a number of recent publications estimating curvature using discrete (e. g. binary) labellings with triple-cliques we use higher-dimensional labels that allows modeling curvature with only pair-wise interactions. Hence, many standard optimization algorithms (e. g. message passing, graph cut, etc) can minimize the proposed curvature-based regularization functional. The accuracy of our approach for representing curvature is demonstrated by theoretical and empirical results on synthetic and real data sets from multi-view reconstruction and stereo. (1)},
  author       = {Olsson, Carl and Boykov, Yuri},
  booktitle    = {2012 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
  issn         = {1063-6919},
  language     = {eng},
  pages        = {1576--1583},
  publisher    = {IEEE--Institute of Electrical and Electronics Engineers Inc.},
  title        = {Curvature-Based Regularization for Surface Approximation},
  url          = {http://dx.doi.org/10.1109/CVPR.2012.6247849},
  year         = {2012},
}