Multi-scale Integration of Slope Data on an Irregular Mesh

We describe a fast and robust gradient integration method that computes scene depths (or heights) from surface gradient (or surface normal) data such as would be obtained by photometric stereo or interferometry. Our method allows for uncertain or missing samples, which are often present in experimentally measured gradient maps; for sharp discontinuities in the scene's depth, e.g. along object silhouette edges; and for irregularly spaced sampling points. To accommodate these features of the problem, we use an original and flexible representation of slope data, the weight-delta mesh. Like other state of the art solutions, our algorithm reduces the problem to a system of linear equations that is solved by Gauss-Seidel iteration with multi-scale acceleration. Its novel key step is a mesh decimation procedure that preserves the connectivity of the initial mesh. Tests with various synthetic and measured gradient data show that our algorithm is as accurate and efficient as the best available integrators for uniformly sampled data. Moreover our algorithm remains accurate and efficient even for large sets of weakly-connected instances of the problem, which cannot be efficiently handled by any existing algorithm.