Biharmonic Volumetric Mapping Using Fundamental Solutions

We propose a biharmonic model for cross-object volumetric mapping. This new computational model aims to facilitate the mapping of solid models with complicated geometry or heterogeneous inner structures. In order to solve cross-shape mapping between such models through divide and conquer, solid mode...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on visualization and computer graphics 2013-05, Vol.19 (5), p.787-798
Main Authors: Xu, Huanhuan, Yu, Wuyi, Gu, Shiyuan, Li, Xin
Format: Article
Language:English
Subjects:
Algorithms
biharmonic mapping
Boundaries
Boundary conditions
Computation
Computational modeling
Computer Graphics
Continuity
Decomposition
Effectiveness
Equations
Geometry
Harmonic analysis
Image Enhancement - methods
Image Interpretation, Computer-Assisted - methods
Imaging, Three-Dimensional - methods
Mapping
Mathematical model
Mathematical models
Reproducibility of Results
Sensitivity and Specificity
Shape
Smoothness
Volumetric mapping
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We propose a biharmonic model for cross-object volumetric mapping. This new computational model aims to facilitate the mapping of solid models with complicated geometry or heterogeneous inner structures. In order to solve cross-shape mapping between such models through divide and conquer, solid models can be decomposed into subparts upon which mappings is computed individually. The biharmonic volumetric mapping can be performed in each subregion separately. Unlike the widely used harmonic mapping which only allows C 0 continuity along the segmentation boundary interfaces, this biharmonic model can provide C 1 smoothness. We demonstrate the efficacy of our mapping framework on various geometric models with complex geometry (which are decomposed into subparts with simpler and solvable geometry) or heterogeneous interior structures (whose different material layers can be segmented and processed separately).
ISSN:1077-2626
1941-0506
DOI:10.1109/TVCG.2012.173