Robust and efficient surface reconstruction from contours

Abstract

We propose a new approach for surface recovery from planar sectional contours. The surface is reconstructed based on the so-called “equal importance criterion,” which suggests that every point in the region contributes equally to the reconstruction process. The problem is then formulated in terms of a partial differential equation, and the solution is efficiently calculated from distance transformation. To make the algorithm valid for different application purposes, both the isosurface and the primitive representations of the object surface are derived. The isosurface is constructed by means of a partial differential equation, which can be solved iteratively. The traditional distance interpolating method, which was used by several researchers for surface reconstruction, is an approximate solution of the equation. The primitive representations are approximated by Voronoi diagram transformation of the surface space. Isosurfaces have the advantage that subsequent geometric analysis of the object can be easily carried out while primitive representation is easy to visualize. The proposed technique allows for surface recovery at any desired resolution, thus avoiding the inherent problems of correspondence, tiling, and branching.