Object reconstruction from layered data using implicit solid modeling

Abstract

Abstract This paper presents an automated technique for constructing 3-D implicit solids from moderately to very dense cross-sectional (layered) data sets. A collection of 2-D cross sections is generated from the layered data by merging circular primitives using implicit solid modeling (ISM) techniques. The geometry of the circles comprising each layer is determined through a nonlinear optimization process using a cost function that measures discrepancies in the distance from data points to the boundary of the reconstructed cross section. The starting configuration of the optimization (that is, the initial size and location of the primitives) is developed from information provided by a 2-D Delaunay triangulation of each layer of the data set. After optimization, the individual 2-D cross sections are joined into a 3-D solid by performing a blend, or “morph,” between the separate layers. By utilizing weighted information from multiple layers, local curvature information is included in the blend object, resulting in a smooth transition between cross sections. The effectiveness of the algorithm is demonstrated through the reconstruction of several representative examples.