• What are the issues in matching/grouping algorithms using more than two 
images? Is simultaneous matching really tractable, or will combinations of 
pairwise matching be the norm? 
This question seems to be somewhat adrift of the core grouping is 
sue, but it is certainly an interesting point to ponder. I can imagine 
matching algorithms analogous, in some aspects, to the bottom- 
up (preattentive) phase of our grouping system. Graphs would be 
constructed in which nodes represent features to be matched and 
arcs represent matching compatibility by some appropriate measure. 
One feature of this measure, naturally, is that the two nodes must 
represent features in two different images. Cliques in this graph 
w r ould then suggest matched features over some set of the images. 
Of course, not all features may be visible or extracted from all im 
ages, so the cliques do not have to contain as many nodes as images; 
the strongest ones will, however. In this scenario, a pairwise mea 
sure of compatibility would be used to build the links in the graph, 
but the decision process, couched in terms of clique extraction and 
analysis, would be carried out using information gleaned over the 
complete image set. Is this, then, truly simultaneous matching? 
Perhaps not strictly, but arguably so. 
To move to true simultaneous matching over more than tw r o images 
(and the need to do so is not clear to me) would require the devel 
opment of N-ary match quality measures. Actually applying such 
N-ary predicates over large numbers of primitives (candidate match 
features) drawn from large (more than two) sets of images would 
induce a considerable combinatorial burden. Only by reducing the 
feature count by increasing their complexity (grouping) could this 
explosion conceivably (and only conceivably) be held in check. Then 
one must accept the computational cost of perceptual organization - 
perhaps a desirable tradeoff given a capability such as ours. And, of 
course, w r e all recognize that more complex features are less ambigu 
ous, but harder to match in complicated scenes wherein portions 
of the feature may be occluded, distorted, or cropped from one or 
more of the other images. So we would tend to argue that true 
simultaneous matching is not likely to become tractable. 
Boyer - 3