An Efficient Linearisation Approach for Variational Perspective Shape from Shading

Recently, variational methods have become increasingly more popular for perspective shape from shading due to their robustness under noise and missing information. So far, however, due to the strong nonlinearity of the data term, existing numerical schemes for minimising the corresponding energy functionals were restricted to simple explicit schemes that require thousands or even millions of iterations to provide accurate results. In this paper we tackle the problem by proposing an efficient linearisation approach for the recent variational model of Ju et al. [14]. By embedding such a linearisation in a coarse-to-fine Gauß-Newton scheme, we show that we can reduce the runtime by more than three orders of magnitude without degrading the quality of results. Hence, it is not only possible to apply variational methods for perspective SfS to significantly larger image sizes. Our approach also allows a practical choice of the regularisation parameter so that noise can be suppressed efficiently at the same time.