Elastic Alignment of Triangular Surface Meshes

• Published in: International journal of computer vision Vol. 126; no. 11; pp. 1220 - 1244
• Main Authors: Sánta, Zsolt, Kato, Zoltan
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.11.2018; Springer; Springer Nature B.V
• Subjects: Artificial Intelligence; Brain; Computational efficiency; Computer graphics; Computer Imaging; Computer Science; Computing time; Deformation; Feature extraction; Formability; Image Processing and Computer Vision; Integral equations; Linear functions; Pattern Recognition; Pattern Recognition and Graphics; Thin plates; Vision; Vision systems; Elastic alignment; Correspondence-less registration; Triangular surface mesh; Thin plate spline
• ISSN: 0920-5691; 1573-1405
• DOI: 10.1007/s11263-018-1084-4

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.