Space Efficient 3D Model Indexing

Abstract
We show that the set of 2D images produced by the point features of a rigid 3D model can be represented with two lines in two high-dimensional spaces. These lines are the lowest-dimensional representation possible. We use this result to build a system for representing in a hash table at compile time, all the images that groups of model features can produce. Then at run time a group of image features can access the table and find all model groups that could match it. This table is efficient in terms of space, and is built and accessed through analytic methods that account for the effect of sensing error. In real images, it reduces the set of potential matches by a factor of several thousand. We also use this representation of a model's images to analyze two other approaches to recognition: invariants, and non-accidental properties. These are properties of images that some models always produce, and all other models either never produce (invariants) or almost never produce (non-accidental properties). In several domains we determine when invariants exist. In general we show that there is an infinite set of non-accidental properties that are qualitatively similar.... Object recognition, Non-accidental properties, Indexing, Hashing, Invariants, Space efficiency.

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