In this project, we concentrate on a very specific part of the reverse engineering process, the automation of the data acquisition stage. The problem is as follows: given a measuring instrument, e.g. a laser rangefinder, determine a trajectory in 3-D that will result in an optimal sampling of the object being scanned. What makes this particular problem interesting is that the object is not known a priori, so the system must simultaneously optimize measurement parameters (e.g. maintain a prescribed sampling density) while discovering the object's surfaces.
Borrowing from differential geometry and topology, we have developed a solution to this problem that has thus far shown excellent promise in laboratory experiments. Briefly, one can define a space of local covers in terms of an atlas of charts derived from sensor measurements. The sensor itself is parameterized, e.g. position and orientation, so that different instances give rise to different local covers. Globally we seek a sensor trajectory that generates a complete surface covering subject to prescribed sampling requirements, local sensor optimization (e.g. constraints on field of view), and kinematic limits on sensor positioning. Even with these constraints the solution space is still intractable. However, by exploiting the further constraint that surface shape and sensor trajectory are locally coupled, we show that it is possible to automatically generate a suitable trajectory.
F. Callari, G. Soucy, F.P. Ferrie (McGill), D. Baird, D. Lamb (Hymarc Ltd.)