Abstract

We present a closed-form, physically-based solution for recovering a three-dimensional (3-D) solid model from collections of 3-D or 2-D features. This method uses the positions of comers, face centers, contours, and edge centers to recover any object that can be generated by smooth deformations of a sphere, e.g., boxes, bowls, bananas, hourglasses, and heads. Given a sufficient number of independent features, the solution is overconstrained and unique, except for rotational symmetries. This method is also effective for recovering 3-D structure from 2-D gray-scale images of line drawings; when only the x and y positions of the features are available, we can generate a good estimate of the unknown z values by finding the 3-D interpretation with the lowest internal energy. A particular advantage of this approach is that the recovered solid model supports extremely efficient shape-comparison and intersection calculations.

© 1990 Optical Society of America