Shape reconstruction of 3d-objects from noisy slope data

A specific class of 3d-sensors measures the local slope of an object surface instead of the local height or "shape". Examples of those sensor principles are shape from shading, shearing interferometry, differential phase contrast, and deflectometry [1]. Those sensors show very high information efficiency [2] (since the measurement channel does not transmit the stand-off distance). But how can we reconstruct the shape from the slope data (the manufacturers of aspherical eye-glasses demand this, for example)? This is a challenging task if we want to exploit the complete information delivered by the sensor. One has to deal with noisy slope data which even might contain holes. Standard methods mostly cannot cope with these problems. We present a new method based on radial basis functions which yields a global shape reconstruction and can handle scattered data with holes. [1] M. Knauer, J. Kaminski, G. Häusler; Absolute Phasenmessende Deflektometrie, DGaO Proceedings, 2004 [2] C. Wagner, G. Häusler; Information theoretical optimization for optical range sensors, Applied Optics 42, 2003.