Probabilistic Indexing for Object Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Recent papers [2,3] have shown that indexing is a promising approach To fast model-based object recognition because it allows most of the possible matches between image point groups and model point groups to be quickly eliminated from consideration. Current indexing systems for the problem of recognizing three- dimensional objects from single two-dimensional images require groups of four points to generate a key into the table of model groups and each model group must be represented over a two-dimensional space in a four dimensional table [2]. We present a system that is capable of indexing using groups of three points by taking advantage of the probabilistic peaking effect [1]. Each model group need only be represented at one point in the index table. To be able to index using groups of three points, we must allow false negatives for point group matches. If there are $n$ model points present in the image, there are $O(n^3)$ groups of three correct model points, so we can withstand negatives, by combining information from multiple groups. Since we are able to index on smaller groups of points, indexing can be used with an additional set of algorithms with lower computational complexity. This system can utilize larger point groups to increase accuracy in discriminating between correct and incorrect matches. [1] J. Ben-Arie. The probabilistic peaking effect of viewed angles and distances with application to 3-d object recognition. transactions on Pattern Analysis and Machine Intelligence, 12(8):760-774, August 1990. [2] D. T. Clemens and D. W. Jacobs. Space and time bounds on indexing 3-d models from 2-d images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(10):1007-10-17, October 1991. [3] Y. Lamdan, J. T. Schwartz, and H. J. Wolfson. Object Recognition by affine invariant matching. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 335-344, 1988.