Shape from Darkness: Deriving Surface Information from Dynamic Shadows

We present a new method, shape from darkness, for extracting surface shape information based on object self-shadowing under moving light sources. It is motivated by the problem of human perception of fractal textures under perspective. One-dimensional dynamic shadows are analyzed in the continuous case, and their behavior is categorized into three exhaustive shadow classes. The continuous problem is shown to be solved by the integration of ordinary differential equations, using information captured in a new image representation called the suntrace. The discretization of the one-dimensional problem introduces uncertainty in the discrete suntrace; however it is successfully recast as the satisfaction of 8n constraint equations in 2n unknowns. A form of relaxation appears to quickly converge these constraints to accurate surface reconstructions; we give several examples on simulated images. The shape from darkness method has two advantages: it does not require a reflectance map, and it works on non-smooth surfaces. We conclude with a discussion on the method's accuracy and practicality, its relation to human perception, and its future extensions.