Direct Shape-from-Shading with Adaptive Higher Order Regularisation

Although variational methods are popular techniques in the context of shape-from-shading, they are in general restricted to indirect approaches that only estimate the gradient of the surface depth. Such methods suffer from two drawbacks: (i) They need additional constraints to enforce the integrability of the solution. (ii) They require the application of depth-from-gradient algorithms to obtain the actual surface. In this paper we present three novel approaches that avoid the aforementioned drawbacks by construction: (i) First, we present a method that is based on homogeneous higher order regularisation. Thus it becomes possible to estimate the surface depth directly by solving a single partial differential equation. (ii) Secondly, we develop a refined technique that adapts this higher order regularisation to semantically important structures in the original image. This addresses another drawback of existing variational methods: the blurring of the results due to the regularisation. (iii) Thirdly, we present an even further improved approach, in which the smoothness process is steered directly by the evolving depth map. This in turn allows to tackle the well-known problem of spontaneous concave-convex switches in the solution. In our experimental section both qualitative and quantitative experiments on standard shape-from-shading data sets are performed. A comparison to the popular variational method of Frankot and Chellappa shows the superiority of all three approaches.