A Mathematically Justified Algorithm for Shape from Texture

In this paper we propose a new continuous Shape from Texture (SfT) model for piecewise planar surfaces. It is based on the assumptions of texture homogeneity and perspective camera projection. We show that in this setting an unidirectional texture analysis suffices for performing SfT. With carefully chosen approximations and a separable representation, novel closed-form formulas for the surface orientation in terms of texture gradients are derived. On top of this model, we propose a SfT algorithm based on spatial derivatives of the dominant local spatial frequency in the source image. The method is motivated geometrically and it is justified rigorously by error estimates. The reliability of the algorithm is evaluated by synthetic and real world experiments