Efficient indexing techniques for model based sensing

Indexing is a model-based recognition technique, in which unknown objects are identiied using lookup tables. Indexing coordinates are extracted from sensed features, and the indexing coordinates specify a table entry containing the object's identity. Usually, only a small fraction of the possible indexing coordinates correspond to modeled objects, and hash tables are often used to save space. In this paper, we present a new indexing data structure called a tree grid which has two advantages over hash tables: (i) The tree grid preserves spatial ordering, so that nearby indexing entries can be retrieved eeciently (ii) The tree grid compacts the storage size of the table by a factor of as much as two orders of magnitude. k coordinates index an ordering of the interpretations, and 1 coordinate determines the consistent interpretations for objects with k degrees of freedom. We also show that for almost all model sets, 2k + 1 indexing coordinates are suucient to discriminate between two generic models, implying that 2k + 1 indexing coordinates specify a unique interpretation. We have implemented an indexing algorithm for recognizing 3D objects from pairs of image rays using the tree grid technique, and the results are reported.