Blind de-rendering, or how to turn a wall into a mirror

This work considers the problem of recovering both the BRDF of a surface and the light distribution incident to that surface from the outbound light distribution. This problem is referred to as blind de-rendering. The proposed geometrical configuration, which consists in a small light source reflected on a flat wall, allows for simplifying assumptions that lead to the reformulation of de-rendering as well-known inverse problems. One of those inverse problems is the deconvolution problem. Assumptions leading to the formulation of the rendering equation as a convolution are detailed. Numerical experiments demonstrate the effectiveness of deconvolution algorithms in the non-blind case. The limitations of single and multi-channel blind deconvolution algorithms are then discussed. Rendering can also be expressed as a linear system. An algorithm for blind de-rendering is developed based on this observation, and its performance is assessed. Diversity related to the source and to the BRDF is exploited, and useful matrix manipulations tied to the aforementioned geometrical configurations are detailed.