An Algebraic Solution to Surface Recovery from Cross-Sectional Contours

Abstract

A new approach for reconstruction of 3D surfaces from 2D cross-sectional contours is presented. By using the so-called “equal importance criterion,” we reconstruct the surface based on the assumption that every point in the region contributes equally to the surface reconstruction process. In this context, the problem is formulated in terms of a partial differential equation, and we show that the solution for dense contours (contours in close proximity) can be efficiently derived from the distance transform. In the case of sparse contours, we add a regularization term to ensure smoothness in surface recovery. The approach is also generalized to other types of cross-sectional contours, where the spine may not be a straight line. The proposed technique allows for surface recovery at any desired resolution. The main advantages of our method is that inherent problems due to correspondence, tiling, and branching are avoided. In contrast to existing implicit methods, we find an optimal field function and develop an interpolation method that does not generate any artificial surfaces. We will demonstrate that the computed high-resolution surface is well represented for subsequent geometric analysis. We present results on both synthetic and real data.