Three-Dimensional Medical Image Modeling of Scattered Data by Using Asymptotic Decider Criterion
Kun Hee Lee, Ohbong Gwun · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2002
3-D image modeling of volumetric scattered data is highly demanded for automated visual inspection and non-destructive testing. Scattered data is defined as a collection of data that have little specified connectivity between data points. For example, supersonic data are much different from cuberille MRI (magnetic resonance imaging) or CT (computed topography) data. One possible way of interpolating volumetric scattered data is with a piecewise linear interpolation. The quality of a piecewise linear interpolation over tetrahedral depends on the specific tetrahedrization of the data points. Therefore, one main task is to provide the best 3-D domain consisting tetrahedral. In this paper, we proposed the idea to solve the case of ambiguity in the process of tetrahedral domain formation. Asymptotic decider criterion is used instead of sphere criterion. The construction of the tetrahedral domain is based on whether or not connecting vertices are joined by a component of the tetrahedral domain. To apply asymptotic decider criterion to tetrahedrization, we need to find the forth point of quadrilateral. Side-vertex method is used for approximate the forth point. A method based on asymptotic decider criterion for computing iso-surfaces of trivariate scattered data interpolation is discussed. Asymptotic decider criterion, considers not only functional value, but also positional data. The results of prevaricated scattered data interpolation is visualized through an iso-surface rendering. The visualization algorithm of this study was implemented on an O2 workstation of Silicon Graphics Systems.