In previous research our group, in conjunction with Prof. Iwahori of the Nagoya Technical Institute, had developed a method for obtaining the shape and absolute depth to a surface having an arbitrary reflectance map. This algorithm utilized the 3-D controlled motion of a point light source near to the object. This algorithm, however, required the computation of the gradient of the image intensity with respect to the light source position. As such, the solution provided by the algorithm will be extremely sensitive to noise in the image measurements and errors in the positioning of the light source. In our current work, we have found that the Clark-Iwahori differential algorithm can be transformed, via application of the divergence theorem, into an algorithm that requires only knowledge of the integral of image intensity over various surfaces and volumes in the light source position space. No derivatives need be computed. This integral algorithm promises to be much more robust in the face of image noise and position errors. We have implemented this new algorithm using the facilities of the CIM Artificial Perception Lab. For the purposes of this experiment we constructed a prototype of a planar distributed illumination source, shown below.
The prototype of the planar extended light source used in the active
differential shape from shading experiment.