Non-Rigid Shape Correspondence of Physically Based Deformations

The registration of non-rigidly deforming shapes is a fundamental problem in the area of Graphics and Computational Geometry. One of the applications of shape registration is to facilitate 3D model retrieval; after alignment it becomes easier to compare shapes since the correspondences between their elements is known. Many existing methods have been proposed for computing shape correspondence [van Kaick et al., 2011, Tam et al., 2013, Sahillioğlu, 2019]. These approaches assume surface deformations to be simple (i.e., primarily piece-wise rigid) and contain low degrees of non-isometry. Presently, there are currently few public datasets that challenge these concepts, providing complex real-world deformations. Few benchmarking datasets suitably consider the different types of extreme deformation that an object may undergo in real-life, and typically only consider synthetic or near-isometric deformations.

This motivates our track which provides a new benchmark that consists of real-life shapes that undergo varying types of complex deformation. The findings of this track will be presented at the Workshop on 3D Object Retrieval in Graz, Austria, 4-5 September 2020 and is in collaboration with Eurographics (pending) and Elsevier.

To participate in this track, please register by emailing DykeRM@cardiff.ac.uk

For queries, contact the corresponding organiser at roberto-marco.dyke@inria.fr

• March 16, 2020: Participant submit results for this track, participants must also include a short description of their method, submitted to DykeRM@cardiff.ac.uk.
• March 03, 2020: This track is finished, and results are included in a track report are submitted for review.

• Roberto M. Dyke — Cardiff University, UK.
• Feng Zhou — Beihang University, China.
• Yu-Kun Lai — Cardiff University, UK.
• Paul L. Rosin — Cardiff University, UK.

Participants are provided a copy of the dataset. Participants are to find the correspondence between each partial scan and the one watertight scan. As well as their results, participants will be asked to also submit a description of the method used. Participants should mention any changes made to internal parameters between scans pairs.

The quality of shape correspondence will be evaluated by the organisers automatically using normalised geodesics to measure the distance between the ground-truth and predicted correspondence. Similarly to other shape correspondence benchmarks [Cosmo et al., 2016, Lähner et al., 2016], we will evaluate the correspondence quality of each method using the approach of Kim et al. [2011]. We shall use the following measurements to help evaluate the performance of each method:

• For methods that complete all scan pairs, an overall error measurement will be based on the number of correspondences within a normalised geodesic threshold, this will be used to plot cumulative error curves;
• Similarly, three plots (one for each type of interal material) of cumulative error curves showing the percentage of matches within a variable geodesic distance will be plotted.

Let be a pair of correspondences between the surface of a partial scan and the surface of the full scan , the normalised geodesic error between the predicted correspondence and the ground-truth position on surface is measured as:

For methods that produce a sparse correspondence, we shall interpolate their result and measure the predicted correspondence against the ground truth.

Participants must match all partial scans to the full scan. A short description of the algorithm/method used must be included with a submission. Either dense or sparse vertex-to-face correspondences for each scan pair may be submitted. Participants should email a zipped file containing their results to DykeRM@cardiff.ac.uk. If participants are unable send their results directly via email, e.g., because the file is too large, they may share their results via other platforms.

Like Cosmo et al. [2016], for each scan pair, participants shall give the correspondence for each vertex on a partial scan to a barycentric co-ordinate on the surface of the full scan in a four column file, as follows:

• Each row represents the vertex on the target scan (i.e., the ith row = the ith vertex).
• The first column contains a one-based index of the triangle on the source shape that the matched point is predicted to lie on. Points that participants fail to match should use the index value -1.
• The second, third and fourth columns represent the barycentric weights of the matched point.

The diagram below illustrates how the predicted correspondence is represented on surface as a barycentric co-ordinate on a face of .

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F. Bogo, J. Romero, M. Loper, and M. J. Black. FAUST: Dataset and evaluation for 3D mesh registration. In Proceedings IEEE Conf. on Computer Vision and Pattern Recognition. IEEE, 2014. doi: 10.1109/CVPR.2014.491.

L. Cosmo, E. Rodolà, M. M. Bronstein, A. Torsello, D. Cremers, and Y. Sahillioğlu. Partial matching of deformable shapes. In Proceedings of the Eurographics 2016 Workshop on 3D Object Retrieval, 3DOR'16, Goslar, Germany, 2016. ISBN 978-3-03868-004-8. doi: 10.2312/3dor.20161089.

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Z. Lähner, E. Rodolà, M. M. Bronstein, D. Cremers, O. Burghard, L. Cosmo, A. Dieckmann, R. Klein, and Y. Sahillioğlu. Matching of Deformable Shapes with Topological Noise. In Eurographics Workshop on 3D Object Retrieval, 2016. ISBN 978-3-03868-004-8. doi: 10.2312/3dor.20161088.

Y. Sahillioğlu. Recent advances in shape correspondence. The Visual Computer, September 2019. doi:10.1007/s00371-019-01760-0.

G. K. L. Tam, Z. Cheng, Y. Lai, F. C. Langbein, Y. Liu, D. Marshall, R. R. Martin, X. Sun, and P. L. Rosin. Registration of 3d point clouds and meshes: A survey from rigid to nonrigid. IEEE Transactions on Visualization and Computer Graphics, 19(7):1199-1217, July 2013. ISSN 1077-2626. doi: 10.1109/TVCG.2012.310.

O. van Kaick, H. Zhang, G. Hamarneh, and D. Cohen-Or. A survey on shape correspondence. Computer Graphics Forum, 30(6):1681-1707, 2011. doi: 10.1111/j.1467-8659.2011.01884.x.

@inproceedings {Dyke:2020:track.a,
 booktitle = {Eurographics Workshop on 3D Object Retrieval},
 editor = {Schreck, Tobias and Theoharis, Theoharis and Pratikakis, Ioannis and Spagnuolo, Michela and Veltkamp, Remco C.},
 title = {{SHREC 2020 Track}: Non-rigid Shape Correspondence of Physically-Based Deformations},
 author = {Dyke, Roberto M. and Zhou, Feng and Lai, Yu-Kun and Rosin, Paul L. and Guo, Daoliang and Li, Kun and Marin, Riccardo and Yang, Jingyu},
 year = {2020},
 publisher = {The Eurographics Association},
 ISSN = {1997-0471},
 ISBN = {978-3-03868-126-7},
 DOI = {10.2312/3dor.20201161}
}