An Improved Frankot and Chellappa Method for Surface Normal Integration Using Fuzzy Concepts

In this paper, we propose the Fuzzy formulation of the classic Frankot-Chellappa method by which surfaces can be reconstructed using normal vectors. In the Fuzzy formulation, the surface normal vectors may be uncertain or ambiguous. The underlying model yields a Fuzzy Poisson partial differential equation, where it is imperative to give meaningful representations of Fuzzy derivatives. The solution of the resulting Fuzzy model is approached numerically. To this end, a fuzzy formulation for the discrete sine transform method is explored, which results in a fast, accurate and robust method for surface reconstruction. In experiments we consider specifically the robustness with respect to noisy surface normal vectors.