Optimized Conformal Surface Registration with Shape-based Landmark Matching

Ronald Lok Ming Lui University of California, Los Angeles Sheshadri Thiruvenkadam University of California, Los Angeles Yalin Wang University of California, Los Angeles Paul M. Thompson University of California, Los Angeles Tony F. Chan University of California, Los Angeles

Computational Geometry mathscidoc:1609.09038

SIAM Journal of Imaging Sciences, 3, (1), 52-78, 2010
Surface registration, which transforms different sets of surface data into one common reference space, is an important process which allows us to compare or integrate the surface data effectively. If a nonrigid transformation is required, surface registration is commonly done by parameterizing the surfaces onto a simple parameter domain, such as the unit square or sphere. In this work, we are interested in looking for meaningful registrations between surfaces through parameterizations, using prior features in the form of landmark curves on the surfaces. In particular, we generate optimized conformal parameterizations which match landmark curves exactly with shape-based correspondences between them. We propose a variational method to minimize a compound energy functional that measures the harmonic energy of the parameterization maps and the shape dissimilarity between mapped points on the landmark curves. The novelty is that the computed maps are guaranteed to align the landmark features consistently and give a shape-based diffeomorphism between the landmark curves. We achieve this by intrinsically modeling our search space of maps as flows of smooth vector fields that do not flow across the landmark curves. By using the local surface geometry on the curves to define a shape measure, we compute registrations that ensure consistent correspondences between anatomical features. We test our algorithm on synthetic surface data. An application of our model to medical imaging research is shown, using experiments on brain cortical surfaces, with anatomical (sulcal) landmarks delineated, which show that our computed maps give a shape-based alignment of the sulcal curves without significantly impairing conformality. This ensures correct averaging and comparison of data across subjects.
surface registration, shape-based diffeomorphism, parameterization, conformal, landmark features
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@inproceedings{ronald2010optimized,
  title={Optimized Conformal Surface Registration with Shape-based Landmark Matching},
  author={Ronald Lok Ming Lui, Sheshadri Thiruvenkadam, Yalin Wang, Paul M. Thompson, and Tony F. Chan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160906123311032293650},
  booktitle={SIAM Journal of Imaging Sciences},
  volume={3},
  number={1},
  pages={52-78},
  year={2010},
}
Ronald Lok Ming Lui, Sheshadri Thiruvenkadam, Yalin Wang, Paul M. Thompson, and Tony F. Chan. Optimized Conformal Surface Registration with Shape-based Landmark Matching. 2010. Vol. 3. In SIAM Journal of Imaging Sciences. pp.52-78. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160906123311032293650.
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