Hyperbolic Harmonic Mapping for Surface Registration

Rui Shi, Wei Zeng, Zhengyu Su, Jian Jiang, Hanna Damasio, Zhonglin Lu, Yalin Wang, Shing Tung Yau, Xianfeng Gu

Research output: Contribution to journalArticle

11 Scopus citations

Abstract

Automatic computation of surface correspondence via harmonic map is an active research field in computer vision, computer graphics and computational geometry. It may help document and understand physical and biological phenomena and also has broad applications in biometrics, medical imaging and motion capture industries. Although numerous studies have been devoted to harmonic map research, limited progress has been made to compute a diffeomorphic harmonic map on general topology surfaces with landmark constraints. This work conquers this problem by changing the Riemannian metric on the target surface to a hyperbolic metric so that the harmonic mapping is guaranteed to be a diffeomorphism under landmark constraints. The computational algorithms are based on Ricci flow and nonlinear heat diffusion methods. The approach is general and robust. We employ our algorithm to study the constrained surface registration problem which applies to both computer vision and medical imaging applications. Experimental results demonstrate that, by changing the Riemannian metric, the registrations are always diffeomorphic and achieve relatively high performance when evaluated with some popular surface registration evaluation standards.

Original languageEnglish (US)
Article number7469384
Pages (from-to)965-980
Number of pages16
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Volume39
Issue number5
DOIs
StatePublished - May 1 2017

Keywords

  • harmonic mapping
  • hyperbolic geometry
  • Surface matching and registration

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics

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  • Cite this

    Shi, R., Zeng, W., Su, Z., Jiang, J., Damasio, H., Lu, Z., Wang, Y., Yau, S. T., & Gu, X. (2017). Hyperbolic Harmonic Mapping for Surface Registration. IEEE Transactions on Pattern Analysis and Machine Intelligence, 39(5), 965-980. [7469384]. https://doi.org/10.1109/TPAMI.2016.2567398