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Elastic Alignment of Triangular Surface Meshes

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Abstract

A novel region-based approach is proposed to find a thin plate spline map between a pair of deformable 3D objects represented by triangular surface meshes. The proposed method works without landmark extraction and feature correspondences. The aligning transformation is simply found by solving a system of integral equations. Each equation is generated by integrating a non-linear function over the object domains. We derive recursive formulas for the efficient computation of these integrals for open and closed surface meshes. Based on a series of comparative tests on a large synthetic dataset, our triangular mesh-based algorithm outperforms state of the art methods both in terms of computing time and accuracy. The applicability of the proposed approach has been demonstrated on the registration of 3D lung CT volumes, brain surfaces and 3D human faces.

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Acknowledgements

This research was partially supported by the NKFI-6 fund through Project K120366; the Research and Development Operational Programme for the project "Modernization and Improvement of Technical Infrastructure for Research and Development of J. Selye University in the Fields of Nanotechnology and Intelligent Space", ITMS 26210120042, co-funded by the European Regional Development Fund; the Agence Universitaire de la Francophonie (AUF) and the Romanian Institute for Atomic Physics (IFA), through the AUF-RO project NETASSIST. Lung images provided by Mediso Ltd., Budapest, Hungary. The MR brain data sets and their manual segmentations were provided by the Center for Morphometric Analysis at Massachusetts General Hospital and the face scans have been obtained from the Bosphorus Dataset (Savran et al. 2008).

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  1. Institute of Informatics, University of Szeged, Szeged, P.O. Box 652, 6701, Hungary

    Zsolt Sánta

  2. Department of Mathematics and Informatics, J. Selye University, Komárno, Slovakia

    Zoltan Kato

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Sánta, Z., Kato, Z. Elastic Alignment of Triangular Surface Meshes. Int J Comput Vis 126, 1220–1244 (2018). https://doi.org/10.1007/s11263-018-1084-4

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