Feature-Adaptive Frequency Domain Method to Representing 3D Medical Images

This paper proposes a novel variational dimension frequency domain method for feature-adaptive mesh Representation. The eigen functions given by the eigen decomposition of the Laplace-Beltrami operator are used to define Fourier like function basis to project the actual geometry of the mesh into the spectral space because of their geometry aware and orthogonal. But, low-pass filters based on Fourier-like methods cannot preserve the geometry feature very well. This paper propose an anisotrpic viewpoint to shove the problems. We extend 2D Fourier to 3D geometry model using eigen decomposition with respect to a geometry aware Laplace-Beltrami operator of mesh, extracting the 3D Fourier represent or, and use the analogous Fourier-like representers to represent mesh geometry. We give every vertices a geometry feature descriptor, defining feature-adaptive function bases with local supports, executing anisotropic spectral encoding to reconstruct geometry. As a result, the frequency localization of geometry feature is improved, and geometry shape will be preserved better. Moreover, the algorithm can get rid of various of noise in arbitrary mesh surfaces, and prevent the model from shrinking absolutely.