2 February 2006 Elastic surface registration by parameterization optimization in spectral space
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Abstract
This paper proposes a novel method to register 3D surfaces. Given two surface meshes, we formulate the registration as a problem of optimizing the parameterization of one mesh for the other. The optimal parameterization of the mesh is achieved in two steps. First, we find an initial solution close to the optimal solution. Second, we elastically modify the parameterization to minimize the cost function. The modification of the parameterization is expressed as a linear combination of a relatively small number of low-frequency eigenvectors of an appropriate mesh Laplacian. The minimization of the cost function uses a standard nonlinear optimization procedure that determines the coefficients of the linear combination. Constraints are added so that the parameterization validity is preserved during the optimization. The proposed method extends parametric registration of 2D images to the domain of 3D surfaces. This method is generic and capable of elastically registering surfaces with arbitrary geometry. It is also very efficient and can be fully automatic. We believe that this paper for the first time introduces eigenvectors of mesh Laplacians into the problem of surface registration. We have conducted experiments using real meshes that represent human cortical surfaces and the results are promising.
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Fijoy Vadakkumpadan, Fijoy Vadakkumpadan, Yunxia Tong, Yunxia Tong, Yinlong Sun, Yinlong Sun, } "Elastic surface registration by parameterization optimization in spectral space", Proc. SPIE 6065, Computational Imaging IV, 606513 (2 February 2006); doi: 10.1117/12.643212; https://doi.org/10.1117/12.643212
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