Algorithms for Reconstructing Shapes from Support-Type Functions

"There are several natural ways to take measurements of an unknown object. One is by means of the support function, which gives for any direction the (signed) distance from some fixed point (usually the origin) to the hyperplane supporting the object orthogonal to that direction. Another is by the distance between the two supporting hyperplanes orthogonal to a given direction. There is also the possibility of measuring the brightness function, which for an n-dimensional object gives the (n-1)-dimensional volumes of its orthogonal projections onto hyperplanes