Computational Geometry: Theory and Applications
Geometric modeling in shape space
ACM SIGGRAPH 2007 papers
ACM SIGGRAPH 2008 papers
IEEE Transactions on Visualization and Computer Graphics
Computing Teichmüller Shape Space
IEEE Transactions on Visualization and Computer Graphics
Non-rigid surface registration using spherical thin-plate splines
MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention - Volume Part I
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A novel approach based on the shape space concept is proposed to classify quasi-conformal deformations of 3D models. A new metric on the quotient space of meshes is introduced to capture changes of the curvature at each vertex of a simplicial complex during deformation. Then, the deformation curve is obtained by calculating the geodesic curve connecting two shapes in the shape space manifold. In order to compare the deformations, the deformation curves are first transferred to the same part of shape space. And then, the Multi-Dimensional Scaling method is employed to eliminate the redundant dimensions facilitating easy comparison of the deformations. To evaluate our method, some synthetic datasets and 23 datasets of gated images of the left heart ventricle during one heartbeat have been examined. Our experiments show that the algorithm can effectively classify normal and abnormal left heart ventricle deformations in shape space.