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Algorithm improves vision system for household robots

13 Jan 2015

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For each pair of successive images, the algorithm generates multiple hypotheses about which objects in one correspond to which objects in the other. The problem is that the number of hypotheses compounds as new perspectives are added. To keep the calculation manageable, the algorithm discards all but its top hypotheses at each step. Even so, sorting through them all, after the last hypothesis has been generated, is a time-consuming task.

Representative sampling

In hopes of arriving at a more efficient algorithm, the MIT researchers adopted a different approach. Their algorithm doesn't discard any of the hypotheses it generates across successive images, but it doesn't attempt to canvass them all, either. Instead, it samples from them at random. Since there's significant overlap between different hypotheses, an adequate number of samples will generally yield consensus on the correspondences between the objects in any two successive images.

To keep the required number of samples low, the researchers adopted a simplified technique for evaluating hypotheses. Suppose that the algorithm has identified three objects from one perspective and four from another. The most mathematically precise way to compare hypotheses would be to consider every possible set of matches between the two groups of objects: the set that matches objects 1, 2 and 3 in the first view to objects 1, 2 and 3 in the second; the set that matches objects 1, 2 and 3 in the first to objects 1, 2 and 4 in the second; the set that matches objects 1, 2 and 3 in the first view to objects 1, 3 and 4 in the second, and so on. In this case, if you include the possibilities that the detector has made an error and that some objects are occluded from some views, that approach would yield 304 different sets of matches.

Instead, the researchers' algorithm considers each object in the first group separately and evaluates its likelihood of mapping onto an object in the second group. So object 1 in the first group could map onto objects 1, 2, 3 or 4 in the second, as could object 2, and so on. Again, with the possibilities of error and occlusion factored in, this approach requires only 20 comparisons.

It does, however, open the door to nonsensical results. The algorithm could conclude that the most likely match for object 3 in the second group is object 3 in the first, and it could also conclude that the most likely match for object 4 in the second group is object 3 in the first. So the researchers' algorithm also looks for such double mappings and re-evaluates them. That takes extra time, but not nearly as much as considering aggregate mappings would. In this case, the algorithm would perform 32 comparisons, more than 20, but significantly less than 304.

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