1 Introduction

There has been a recent flurry of effort on reconstructing 3D geometric models of objects from single [ 2 , 5 , 6 ] or multiple [ 3 , 10 , 9 , 11 ] range images, in part motivated by improved range sensors, and in part by demand for geometric models in the CAD and Virtual Reality (VR) application areas. Mainly, these reconstructions are of objects with smooth, free-form surfaces. Oddly enough, in this case, curved surface objects are easier to work with, as: 1) the variety of surface geometry provides many more features for multiple dataset registration, and 2) the tolerances needed for most curved surface applications are not high. Or, conversely, one could say that objects with developable surfaces are harder to reconstruct accurately, because: 1) the developable surfaces ( e.g. including standard engineering surfaces produced by simple machining -- planes, cylinders and cones) allow translations of the surfaces from different observations relative to each other that still satisfy distance constraints ( i.e. two views of a planar surface that slide in the same infinite plane relative to each other), and 2) developable surfaces tend to have shape tolerances that are much higher than that achievable by standard range sensors because these surfaces are commonly used to mate parts together, whereas smooth freeform or spline surfaces tend to have shape tolerances comparable to typical range sensor data.

Further, even if all of the data were from a single view, thus avoiding multiple dataset registration errors, reconstruction must still cope with errors from mis-calibration across the full sensor field of view.

This paper describes a technique of global shape improvement based on feature position and shape constraints. The constraints might be either interactively supplied by a user, or inferred by a knowledge-based system reasoning from general engineering principles.

The types of constraints exploited here are of these families:

1. a set of features have a fixed orientation relationship ( e.g. a set of surfaces or edges that meet at a specified angle or are parallel) and
2. a set of features have a fixed separation ( e.g. the distance between a pair of parallel lines or planes).

The key to the approach is to parameterize the features in a way that allows constraints to be expressed as a function of the shape parameters, and to then apply an optimization procedure that searches for parameter vectors that satisfy the constraints while simultaneously optimizing the surface fit to the range data.