An Optimal Experimental Design Approach for Light Configurations in Photometric Stereo

Abstract: This paper presents a technique for finding the surface normal of an object from a set of images obtained under different lighting positions. The method presented is based on the principles of Photometric Stereo (PS) combined with Optimum Experimental Design (OED) and Parameter Estimation (PE). Unclear by the approach of photometric stereo, and many models based thereon, is how to position the light sources. So far, this is done by using heuristic approaches this leads to suboptimal and non-data driven positioning of the light sources. But what if the optimal positions of the light sources are calculated for photometric stereo? To this end, in this contribution, the effect of positioning the light sources on the quality of the normal vector for PS is evaluated. Furthermore, a new approach in this direction is derived and formulated. For the calculation of the surface normal of a Lambertian surface, the approach based on calibrated photometric stereo; for the estimation the optimal position of the light sources the approach is premised on parameter estimation and optimum experimental design. The approach is tested using synthetic and real-data. Based on results it can be seen that the surface normal estimated with the new method is more detailed than with conventional methods.