Shape Reconstruction From Brightness Functions

摘要

In this paper we address the problem of reconstructing the shape of a convex object from measurements of the areas of its shadows in several directions. This type of very weak measurement is sometime referred to as the brightness function of the object, and may be observed in an imaging scenario by recording the total number of pixels where the object's image appears. Related measurements, collected as a function of viewing angle, are also referred to as "lightcurves" in the astrophysics community, and are employed in estimating the shape of at.mosphereless rotating bodies (e.g. asteroids). We address the problem of shape reconstruction from brightness functions by constructing a least-squares optimization framework for approximating the underlying shapes with polygons in two dimensions, or polyhedra in three dimensions, from noisy, and possibly sparse measurements of the brightness values.