Surface Reconstruction from Sparse Fringe Contours

Abstract A new approach for reconstruction of 3D surfacesfrom 2D cross-sectional contours is presented. By using the so-called "Equal Importance Cri-terion, " we reconstruct the surface based on the assumption that every point in the region con-tributes equally to the surface reconstruction process. In this context, the problem is formu-lated in terms of a partial differential equation (PDE), and we show that the solution for densecontours can be efficiently derived from distance transform. In the case of sparse contours, we adda regularization term to insure smoothness in surface recovery. The proposed technique allowsfor surface recovery at any desired resolution. The main advantage of the proposed method isthat inherent problems due to correspondence, tiling, and branching are avoided. Furthermore, the computed high resolution surface is betterrepresented for subsequent geometric analysis. We present results on both synthetic and realdata. 1 Introduction The problem of reconstructing a 3D surface from a set of2D cross sectional contours is an important one in diverse scientific fields. For example, CT and MRI techniques canprovide dense serial section representation of electron density and water molecule concentration at different locationsalong a particular axis. Similarly, in confocal microscopy, cross sections are obtained by focusing the optical systemat specific locations along th