3D shape reconstruction from 2D cross-sections

Hyungjun Park and Kwangsoo Kim

Abstract

The reconstruction of a three dimensional(3D) shape of an object from a set of two dimensional(2D) cross sections is an important problem in many applications. Although several different reconstruction methods have been proposed, most of them have allowed only simple branching and have had difficulty in handling complex branching structures. In the paper, we describe a method for reconstructing geometric models of an object known by a sequence of 2D cross sections. Both a triangular network and a piecewise triangular G1 surface produced by the method can be used as reconstructed models. We present a new algorithm for handling complex multiple branching structures in many cases. The algorithm decomposes the branching problem into a set of simpler branching problems by using the composite contour and its canyons. To describe the construction of a composite contour and its canyons, a contour connection graph(CCG) and the bridge selection rule are introduced. With the aid of the CCG and the bridge selection rule, the algorithm can construct a composite contour and its canyons with ease. Some experimental results are given to show that our method gives reasonably good solutions for the representation of complex shaped objects.

Keywords: shape reconstruction, cross-sections, triangulation, multiple branching problem, surface fitting, geometric modelling

Full Text Article

Application to medical visualization



(a) Contours extracted from CT(Computerized Tomography) images of a human femur
(b) Triangular mesh obtained via triangulation techniques such as tiling, branching, capping, and merging
(c) Shaded display of the triangular mesh
(d) Shaded display of the triangular mesh with normal smoothing
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