Plane-wave SfS reconstruction of water surface characteristics from Lambertian reflectance data

The classical shape from shading (SfS) problem of computer vision is concerned with the reconstruction of a 3D object surface from its photographic image. Essential non-uniqueness and intrinsic nonlinearity make the problem challenging. This work considers the case where the object is a water surface so that the statistical approximation by superposition of plane waves is natural. An efficient greedy algorithm involving recursive refinement of wave fronts, subject to a wave-front frequency constraint is developed. The approach is evaluated using simulated reflectance data based on a set of wind-generated wave-field images obtained from detailed wave-tank measurements. The traditional setup for the SfS problem (orthographic cameras, light sources at infinity and the Lambertian surfaces) is used. Generalization to include a specular (Phong) reflectance component is also discussed. Results indicate that key statistical characteristics of the wave field related to its stage of development (evolution) are properly recovered by the approach. Thus there may be future potential for novel photographic-based remote sensing of physical drivers (e.g. wind velocity) of local water surface patterns.