Shape from Shadows: A Hilbert Space Setting

We study the problem of recovering a surface from the shadows it casts on itself when lighted by the sun at various times of the day. Shadows can create both linear and nonlinear information. We will show how to incorporate both types of information in the solution. The problem is formulated and solved in a Hilbert space setting and the spline algorithm interpolating the data that result from the shadows is constructed. This algorithm is optimal in terms of the approximation error and has low cost. We furthermore derive optimal information for this problem.

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