Paper summary of:
Hu, J., Hamidian, H., Zhong, Z., & Hua, J. (2017). Visualizing Shape Deformations with Variation of Geometric Spectrum. IEEE transactions on visualization and computer graphics, 23(1), 721-730.
This is a continuation of the MICCAI 2016 paper summarized here.
See paper for short summary of other shape analysis methods.
Shape spectrum is inspired by the Fourier transform in signal processing. basically the same thing but in 3d. See paper for a short review on the publications on the laplace beltrami spectrum.
"In this paper, we focus on spectrum alignment of general shapes using the eigenvalue variation in order to quantify the non-isometric deformations between surface shapes. In our approach, shapes are au-tomatically aligned by calculating the metric scaling on both shapes. Our method defines the surface shape deformation by the variation of Laplace-Beltrami spectrum of the shapes and quantifies the multi-scale deformations through the use of different sets of eigenvalues. Compared to the traditional approaches, it can detect and localize small non-isometric deformations in addition to global difference of the shapes, without using any defined landmarks on the manifolds. This is because the spectrum only depends on the intrinsic geometry of the shape and is invariant to spatial translation, rotation, scaling and isometric deformation. This method is computationally affordable and suitable to map surface shapes for non-isometric deformation analysis."
Good review of ICP method and spectral methods.
Main contributions of the paper:
Methods, Theorems etc.
see paper, too hard to summarize adequately
They did 3 main 'experiments'. One is the same as the one reported in the 2016 paper so I will not summarize it again.
To test the sensitivity of the model they used the Bunny model with 3000 vertices and made a bump on the back of the bunny. They tested the method with 30, 50, and 80 eigenvalues and 10 iterations. The more eigenvalues the better the results. Figure 2 shows the results.
They also tested 80 eigenvalues with 1, 5, and 10 iterations. Figure 3 shows the results.
Alzheimer Study and Diagnosis
They looked at 10 healthy and 10 AD patients with longitudinal data. Globally: The AD hippocampi both right and left are shrunk after one year. The average shrinkage for AD subjects is more than healthy subjects. There is more shrinkage in the left than the right.
the middle region (CA1) is affected more serverely in both left and right. see the figure.
Comparisons to Spatial Registration Methods
They compare their method to ICP and voxel based methods and find that their method comes out on top and does not need correspondence. See the paper for figures and details.
I will be using this blog space as a repository of notes on various articles and lectures related to my research. Click on the categories below to organize the posts by topic.