It is shown that an index space can be a powerful tool for reducing the image-model match search by a factor of k/sup G-3/, but only when accompanied by some mechanism, such as grouping, that prevents the system from having to consider all matches between image groups of size G and model groups of size G. It is also shown that if image groups are to index a single point at recognition time, then the index space must contain pointers to each model group over a 2-D sheet, and should therefore be 2G-4 dimensional. A simple indexing system has been implemented to demonstrate these concepts, and a series of experiments have been conducted to investigate the tradeoffs between space and time. They indicate that the speedups are achievable, but require a large amount of space.>

Model-based visual recognition systems often match groups of image features to groups of model features to form initial hypotheses, which are then verified. In order to accelerate recognition considerably, the model groups can be arranged in an index space (hashed) offline such that feasible matches are found by indexing into this space. For the case of 2D images and 3D models consisting of point features, bounds on the space required for indexing and on the speedup that such indexing can achieve are demonstrated. It is proved that, even in the absence of image error, each model must be represented by a 2D surface in the index space. This places an unexpected lower bound on the space required to implement indexing and proves that no quantity is invariant for all projections of a model into the image. Theoretical bounds on the speedup achieved by indexing in the presence of image error are also determined, and an implementation of indexing for measuring this speedup empirically is presented. It is found that indexing can produce only a minimal speedup on its own. However, when accompanied by a grouping operation, indexing can provide significant speedups that grow exponentially with the number of features in the groups.>