The derivation of two-dimensional surface shape from shadows

We study theoretical and implementation issues that arise when solving the shape from shadows problem. In this problem, the shadows created by a light falling on a surface are used to recover the surface itself. The problem is formulated and solved in a Hilbert space setting. We construct the spline algorithm that interpolates the data and show that it is the best possible approximation to the original function. The optimal error algorithm is implemented and a series of tests is shown. We additionally show that the problem can be decomposed into subproblems and each one can be solved independently from the others. This decomposition is suited to parallel computation and can result in considerable reductions in the cost of the solution