Geometry Construction from Caustic Images

In this work we investigate an inverse geometry problem. Given a light source, a diffuse plane and a caustic image, how must a geometric object look like (transmissive or reflective) in oder to project the desired caustic onto the diffuse plane when lit by the light source? In order to construct the geometry we apply an analysis-by-synthesis approach, exploiting the GPU to accelerate caustic rendering based on the current geometry estimate. The optimization is driven by simultaneous perturbation stochastic approximation (SPSA). We confirm that this algorithm converges to the global minimum with high probability even in this ill-posed setting. We demonstrate results for precise geometry reconstruction given a caustic image and for reflector design producing an intended light distribution.