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Due to their improved capability to handle realistic illumination scenarios, nonLambertian reflectance models are becoming increasingly more popular in the Shape from Shading (SfS) community. One of these advanced models is the Oren-Nayar model which is particularly suited to handle rough surfaces. However, not only the proper selection of the model is important, also the validation of stable and efficient algorithms plays a fundamental role when it comes to the practical applicability. While there are many works dealing with such algorithms in the case of Lambertian SfS, no such analysis has been performed so far for the Oren-Nayar model. In our paper we address this problem and present an in-depth study for such an advanced SfS model. To this end, we investigate under which conditions, i.e. model parameters, the Fast Marching (FM) method can be applied – a method that is known to be one of the most efficient algorithms for solving the underlying partial differential equations of Hamilton-Jacobi type. In this context, we do not only perform a general investigation of the model using Osher’s criterion for verifying the suitability of the FM method. We also conduct a parameter dependent analysis that shows, that FM can safely be used for the model for a wide range of settings relevant for practical applications. Thus, for the first time, it becomes possible to theoretically justify the use of the FM method as solver for the Oren-Nayar model which has been applied so far on a purely empirical basis only. Numerical experiments demonstrate the validity of our theoretical analysis. They show a stable behaviour of the FM method for the predicted range of model parameters.

Shape from Shading for Rough Surfaces: Analysis of the Oren-Nayar Model