This paper is largely a summary of recent research results at Edinburgh University. There are two other significant streams of research that should be compared to that presented here. The first is research from the University of Utah [48,47], who have also been investigating constrained reconstruction of parts from 3D data sets, particularly parts with pocket profiles. They categorized the types of engineering knowledge as domain specific and pragmatic (roughly corresponding to our use of a restricted set of shapes), and functional constraints (corresponding to our use of interfeature constraints). They exploit this knowledge to select surface types and manufacturing actions. Thus, with some user assistance, planar features that bound pockets are found. The contour that is swept to form the pocket can then be found automatically. Shape and positional constraints are represented and solved in a manner similar to our approach. A particularly notable aspect of their research that we have not addressed is the automatic inference of feature relationships and how these can be used to reduce the degrees of freedom of the reconstruction by equating parameters (which we have exploited [38].
The other significant research stream is that at the University of Cardiff [2,3]. That research has also followed a route similar to that in this paper, exploiting designed-in relationships to improve reconstruction. In their case, a much larger set of relationships were explored, and the constraints arising from the relationships were used to used to reduce the dimensionality of the reconstruction parameter space. A sequential numerical constrainment processes was used, which allowed them to detect (which we also did) and automatically reject (which we did not) inconsistent constraints. A nice alternative to fitting tangential and blend surfaces was to parameterize swept two dimensional features, with the cross-section of the inter-surface join/blend as the two-dimensional feature.
What all three of these projects have in common is an appreciation of the role of intent in the design of artifacts, and how this intent is expressed in relationships that can be exploited in the reverse engineering process. There are differences in the numerical optimization process, but all express both the geometric fitting and the shape constraints in a numerical evaluation function that can be effectively solved to reconstruct the constrained shape.
While this paper is more of a summary paper, in addition to the commonality discussed above, the paper also points to several other pieces of research not in common with the others, namely: beautification by constrained triangulation flattening, application to architecture as well as parts, constrained fitting of spline surfaces, the benefits of Euclidean fitting, the practical impossibility of complete scene scanning, shape and texture hypothesising, triangulation with fold edge preservation, and higher level reverse engineering by using structures parameterized at the object level rather than the feature level.
One of the issues that has arisen in the course of this research is the fragility of the reconstruction process. If reconstruction requires several stages, then: 1) the process can fail at an early stage or 2) the process can succeed, but its outputs will have results that are affected by the data errors. These `perturbed' results then become effectively locked and affect the subsequent processes. We are exploring how to overcome the second effect and how to also reduce the failures from the first stage by looking at a one-step reconstruction process that does dataset registration, assigns point data to features, extracts feature shape parameters and accounts for standard surface shapes and constraints. Obviously this is an ambitious exploration. Optimistically, we think that the evolutionary search methods discussed above coupled with careful choices of representations will enable us to explore and achieve this goal.
We are also continuing the exploration of the knowledge-directed recovery of missing data. Many individual cases can still be investigated, but the interesting ones that we are currently exploring are 1) hypothesizing the back sides of objects based on ideas of symmetry and local space relationships and 2) recovery of unscanned 3D shape from alignment with color photographs of the unscanned areas.
