Surface Registration with Eigenvalues and Eigenvectors.

08:00 EDT 14th May 2019 | BioPortfolio

Summary of "Surface Registration with Eigenvalues and Eigenvectors."

This paper presents a novel surface registration technique using the spectrum of the shapes, which can facilitate accurate localization and visualization of non-isometric deformations of the surfaces. In order to register two surfaces, we map both eigenvalues and eigenvectors of the Laplace-Beltrami of the shapes through optimizing an energy function. The function is defined by the integration of a smoothness term to align the eigenvalues and a distance term between the eigenvectors at feature points to align the eigenvectors. The feature points are generated using the static points of certain eigenvectors of the surfaces. By using both the eigenvalues and the eigenvectors on these feature points, the computational efficiency is improved considerably without losing the accuracy in comparison to the approaches that use the eigenvectors for all vertices. After the alignment, the eigenvectors can be employed to calculate the point-to-point correspondence of the surfaces. Therefore, the proposed method can accurately define the displacement of the vertices. We evaluate our method by conducting experiments on synthetic and real data using hippocampus, heart, and hand models. We also compare our method with non-rigid ICP and a similar spectrum-based methods. These experiments demonstrate the advantages and accuracy of our method.


Journal Details

This article was published in the following journal.

Name: IEEE transactions on visualization and computer graphics
ISSN: 1941-0506


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