We describe a robust method for the recovery of the depth map (or height map) from a gradient map (or normal map) of a scene, 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, and also for sharp discontinuities in the scene’s depth, e.g. along object silhouette edges. By using a multi-scale approach, our integration algorithm achieves linear time and memory costs. A key feature of our method is the allowance for a given weight map that flags unreliable or missing gradient samples. We also describe several integration methods from the literature that are commonly used for this task. Based on theoretical analysis and tests with various synthetic and measured gradient maps, we argue that our algorithm is as accurate as the best existing methods, handling incomplete data and discontinuities, and is more efficient in time and memory usage, especially for large gradient maps.

In this paper, we describe a data structure and an algorithm to accelerate the table lookup step in example-based multiimage photometric stereo. In that step, one must find a pixel of a reference object, of known shape and color, whose appearance under m different illumination fields is similar to that of a given scene pixel. This search reduces to finding the closest match to a given m-vector in a table with a thousand or more m-vectors. Our method is faster than previously known solutions for this problem but, unlike some of them, is exact, i.e., always yields the best matching entry in the table, and does not assume point-like sources. Our solution exploits the fact that the table is in fact a fairly flat 2-D manifold in m-dimensional space so that the search can be efficiently solved with a uniform 2-D grid structure.

We describe a robust method to recover the depth coordinate from a normal or slope map of a scene, obtained e.g. through photometric stereo or interferometry. The key feature of our method is the fast solution of the Poisson-like integration equations by a multi-scale iterative technique. The method accepts a weight map that can be used to exclude regions where the slope information is missing or untrusted, and to allow the integration of height maps with linear discontinuities (such as along object silhouettes) which are not recorded in the slope maps. Except for pathological cases, the memory and time costs of our method are typically proportional to the number of pixels N. Tests show that our method is as accurate as the best weighted slope integrators, but substantially more efficient in time and space.

We describe an efficient procedure for reassembling unknown two-dimensional objects that have been broken or torn into a large number of irregular fragments, a problem that often arises in archaeology, art restoration, forensics, and other disciplines. The procedure compares the curvature-encoded fragment outlines, at progressively increasing scales of resolution, using an incremental dynamic programming sequence-matching algorithm. The total cost gets reduced by a factor proportional to the mean number of samples per segment, which makes the method viable for problems of practical size (thousands of fragments). The performance of our method is illustrated with an artificial but realistic example.