A graph-spectral method for surface height recovery

Abstract

This paper describes a graph-spectral method for 3D surface integration. The algorithm takes as its input a 2D field of surface normal estimates, delivered, for instance, by a shape-from-shading or shape-from-texture procedure. We commence by using the Mumford-shape energy function to obtain transition weights for pairs of sites in the field of surface normals. The weights depend on the sectional curvature between locations in the field of surface normals. This curvature may be estimated using the change in surface normal direction between locations. We pose the recovery of the integration path as that of finding a path that maximises the total transition weight. To do this we use a graph-spectral seriation technique. By threading the surface normals together along the seriation path, we perform surface integration. The height increments along the path are simply related to the traversed path length and the slope of the local tangent plane. The method is evaluated on needle-maps delivered by a shape-from-shading algorithm applied to real world data and also on synthetic data. The method is compared with the height reconstruction method of Bichsel and Pentland. © Springer-Verlag Berlin Heidelberg 2003.