Conformal Metric Optimization on Surface (CMOS) for Deformation and Mapping in Laplace-Beltrami Embedding Space

Lab of Neuro Imaging, UCLA School of Medicine, Los Angeles, CA, USA.
Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention 01/2011; 14(Pt 2):327-34. DOI: 10.1007/978-3-642-23629-7_40
Source: PubMed


In this paper we develop a novel technique for surface deformation and mapping in the high-dimensional Laplace-Beltrami embedding space. The key idea of our work is to realize surface deformation in the embedding space via optimization of a conformal metric on the surface. Numerical techniques are developed for computing derivatives of the eigenvalues and eigenfunctions with respect to the conformal metric, which is then applied to compute surface maps in the embedding space by minimizing an energy function. In our experiments, we demonstrate the robustness of our method by applying it to map hippocampal atrophy of multiple sclerosis patients with depression on a data set of 109 subjects. Statistically significant results have been obtained that show excellent correlation with clinical variables. A comparison with the popular SPHARM tool has also been performed to demonstrate that our method achieves more significant results.

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Available from: Rongjie Lai, Dec 19, 2013
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    • "For numerical implementation, we first built the signed distance function [30], [31] of the white matter surface in 3D space and then computed the CT as the value on the signed distance function at those locations. The cortical surfaces and the corresponding CT maps were registered to the International Consortium for Brain Mapping (ICBM) brain surface [32] and then vertex-wise correspondences were established between all cortical surface models using a Conformal Metric Optimization method [33]. An experienced human brain researcher rated each brain surface reconstruction by visually inspecting the surfaces using LONI ShapeViewer ( "
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    • "For anatomical shapes without perfect symmetry, we find this assumption always holds in our experience. For synthetic shapes with perfect symmetry, we can perturb the metric [37], [43] and make sure this assumption is valid. To accurately represent the partition of the surface by neighboring saddle points on the Reeb graph, which could have very subtle differences in the function values, we will augment the original mesh by splitting its triangles along the level contours during the Reeb graph construction process. "
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    10/2012; 32(3). DOI:10.1109/TMI.2012.2224879
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    • "In addition, a new surface quadrangulation can be also obtained using the Morse-Smale complex of certain LB eigenfunction [13]. Moreover, LB eigenfunctions can be viewed as either global or local embedding to analyze surface geometric structures [30] [7] [28] [17] [18]. Furthermore, the LB operator is also closely related to harmonic maps between two surfaces. "
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