Reconstruction of three-dimensional surfaces from two-dimensional binary images

Abstract

The authors describe a method for reconstruction of three-dimensional visible and invisible opaque surfaces using moving shadows. An object whose shape is to be determined is placed on a reference surface. A beam of substantially parallel rays of light is projected at the object at a set of different angles relative to the reference surface. Using a camera which is placed above the reference surface, the shadows cast by the object for each angle are transferred to a computer. A three-dimensional binary level shadow diagram (3DBL shadowgram) is formed and analyzed. The shadowgram has some features which make the reconstruction very simple: a section of the 3DBL shadowgram, referred to as a 2DBL shadowgram, can be used to determine the heights of points of the object to be reconstructed. Further analysis of some curves of the shadowgram can be used for the partial reconstruction of invisible surfaces. A set of experimental results to test the effects of the threshold, camera resolution, and the number of pictures demonstrates the robustness and usefulness of the method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>