Neural network to reconstruct specular surface shape from its three shading images

This paper proposes a new method to reconstruct the shape of the specular surface by learning the mapping between three image irradiances observed under the illumination from three lighting directions and the corresponding surface gradient. The method uses Phong reflectance function (1975) which can describe the specular reflectance including Lambertian reflectance, and its neural network is constructed to determine the values of reflectance parameters and the objective surface gradient distribution under the condition that the values of reflectance parameters included in this function are unknown. The method reconstruct the surface gradient distribution after determining the values of reflectance parameters of a test object using two step neural network which consist of one to extract two gradient parameters from three image irradiances and its opposite one. The effectiveness of this proposed neural network was confirmed by computer simulations.