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A combinatorial solution to non-rigid 3D shape-to-image matching

Bernard, Florian ; Schmidt, Frank R ; Thunberg, Johan LU and Cremers, Daniel (2017) IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017 p.1000-1009
Abstract
We propose a combinatorial solution for the problem of non-rigidly matching a 3D shape to 3D image data. To this end, we model the shape as a triangular mesh and allow each triangle of this mesh to be rigidly transformed to achieve a suitable matching to the image. By penalising the distance and the relative rotation between neighbouring triangles our matching compromises between the image and the shape information. In this paper, we resolve two major challenges: Firstly, we address the resulting large and NP-hard combinatorial problem with a suitable graph-theoretic approach. Secondly, we propose an efficient discretisation of the unbounded 6-dimensional Lie group SE(3). To our knowledge this is the first combinatorial formulation for... (More)
We propose a combinatorial solution for the problem of non-rigidly matching a 3D shape to 3D image data. To this end, we model the shape as a triangular mesh and allow each triangle of this mesh to be rigidly transformed to achieve a suitable matching to the image. By penalising the distance and the relative rotation between neighbouring triangles our matching compromises between the image and the shape information. In this paper, we resolve two major challenges: Firstly, we address the resulting large and NP-hard combinatorial problem with a suitable graph-theoretic approach. Secondly, we propose an efficient discretisation of the unbounded 6-dimensional Lie group SE(3). To our knowledge this is the first combinatorial formulation for non-rigid 3D shape-to-image matching. In contrast to existing local (gradient descent) optimisation methods, we obtain solutions that do not require a good initialisation and that are within a bound of the optimal solution. We evaluate the proposed combinatorial method on the two problems of non-rigid 3D shape-to-shape and non-rigid 3D shape-to-image registration and demonstrate that it provides promising results. (Less)
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author
; ; and
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
Proceedings of the IEEE conference on computer vision and pattern recognition
pages
10 pages
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
conference name
IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017
conference location
Honolulu, United States
conference dates
2017-07-21 - 2017-07-26
external identifiers
  • scopus:85044294587
ISBN
978-1-5386-0457-1
DOI
10.1109/CVPR.2017.157
language
English
LU publication?
no
id
7a1aa50b-0bbd-4403-9d45-f5a25a911677
date added to LUP
2024-09-05 14:21:02
date last changed
2024-09-20 10:05:23
@inproceedings{7a1aa50b-0bbd-4403-9d45-f5a25a911677,
  abstract     = {{We propose a combinatorial solution for the problem of non-rigidly matching a 3D shape to 3D image data. To this end, we model the shape as a triangular mesh and allow each triangle of this mesh to be rigidly transformed to achieve a suitable matching to the image. By penalising the distance and the relative rotation between neighbouring triangles our matching compromises between the image and the shape information. In this paper, we resolve two major challenges: Firstly, we address the resulting large and NP-hard combinatorial problem with a suitable graph-theoretic approach. Secondly, we propose an efficient discretisation of the unbounded 6-dimensional Lie group SE(3). To our knowledge this is the first combinatorial formulation for non-rigid 3D shape-to-image matching. In contrast to existing local (gradient descent) optimisation methods, we obtain solutions that do not require a good initialisation and that are within a bound of the optimal solution. We evaluate the proposed combinatorial method on the two problems of non-rigid 3D shape-to-shape and non-rigid 3D shape-to-image registration and demonstrate that it provides promising results.}},
  author       = {{Bernard, Florian and Schmidt, Frank R and Thunberg, Johan and Cremers, Daniel}},
  booktitle    = {{Proceedings of the IEEE conference on computer vision and pattern recognition}},
  isbn         = {{978-1-5386-0457-1}},
  language     = {{eng}},
  pages        = {{1000--1009}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  title        = {{A combinatorial solution to non-rigid 3D shape-to-image matching}},
  url          = {{http://dx.doi.org/10.1109/CVPR.2017.157}},
  doi          = {{10.1109/CVPR.2017.157}},
  year         = {{2017}},
}