Computing length-preserved free boundary for quasi-developable mesh segmentation
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From Voxels to Knowledge: A Practical Guide to the Segmentation of Complex Electron Microscopy 3D-Data
Published on: August 13, 2014
1Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, PR China. cwang@mae.cuhk.edu.hk
Abstract:
Stretch-free surface flattening has been requested by a variety of applications. At present, the most difficult problem is how to segment a given model into nearly developable atlases so that a nearly stretch-free flattening can be computed. The criterion for segmentation is needed to evaluate the possibility of flattening a given surface patch, which should be fast computed. In this paper, we present a method to compute the length-preserved free boundary (LPFB) of a mesh patch which speeds up the mesh parameterization. The distortion on parameterization can then be employed as the criterion in a trial-and-error algorithm for segmenting a given model into nearly developable atlases. The computation of LPFB is formulated as a numerical optimization problem in the angle space, where we are trying to optimize the angle excesses on the boundary while preserving the constraints derived from the closed-path theorem and the length preservation.
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