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<p><b>Abstract</b>—We present a method of indexing three-dimensional objects from single two-dimensional images. Unlike most other methods to solve this problem, ours does not rely on invariant features. This allows a richer set of shape information to be used in the recognition process. We also suggest the <tmath>$k$</tmath>d-tree as an alternative indexing data structure to the standard hash table. This makes hypothesis recovery more efficient in high-dimensional spaces, which are necessary to achieve specificity in large model databases. Search efficiency is maintained in these regimes by the use of Best-Bin First search, a modified <tmath>$k$</tmath>d-tree search algorithm which locates approximate nearest-neighbors. Neighbors recovered from the index are used to generate probability estimates, local within the feature space, which are then used to rank hypotheses for verification. On average, the ranking process greatly reduces the number of verifications required. Our approach is general in that it can be applied to any real-valued feature vector. In addition, it is straightforward to add to our index information from real images regarding the true probability distributions of the feature groupings used for indexing. In this paper, we provide experiments with both synthetic and real images, as well as details of the practical implementation of our system, which has been applied in the domain of telerobotics.</p>
Model-based object recognition; indexing; kd-tree algorithm; nearest-neighbors algorithm.

D. G. Lowe and J. S. Beis, "Indexing without Invariants in 3D Object Recognition," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 21, no. , pp. 1000-1015, 1999.
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