Abstract

In this paper, we present a new technique for constructing mathematical representations of solids from cross-sectional data sets. A collection of 2D cross-sections is generated from the sliced data by merging circular primitives using Implicit Solid Modelling (ISM) techniques which approximate Boolean unions. The spatial locations and radii of the circles for each slice are determined through a nonlinear optimization process. The cost function employed in these optimizations is a measure of discrepancies in the distance from points to the boundary of the reconstructed cross-section. The starting configuration of the optimization, (i.e. initial size and location of the primitives) is determined from a 2D Delaunay triangulation of each slice of the data set. A morphing technique utilizing blending functions is applied to merge the implicit functions describing each slice into a 3D solid. The effectiveness of the algorithm is demonstrated through the reconstruction of several sample data sets, including a femur and a vertebra.

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