Multidimensional indexing for recognizing visual shapes

Abstract

This paper introduces an analytical framework for studying some properties of model acquisition and recognition techniques based on indexing. The goal is to demonstrate that several problems previously associated with the approach can be attributed to the low dimensionality of invariants used. These include limited index selectivity. Excessive accumulation of votes in the look-up table buckets, and excessive sensitivity to quantization parameters. Theoretical results demonstrate that using high-dimensional, highly descriptive global invariants produces better results in terms of accuracy, false positive suppression, and computation time. A practical example of high-dimensional global invariants is introduced and used to implement a 2-D shape acquisition/recognition system. The acquisition/recognition system is based on a two-step table look-up mechanism. First, local curve descriptors are obtained by correlating image contour information at short range. Then, seven-dimensional global invariants are computed by correlating triplets of local curve descriptors at longer range. This experimental system is meant to illustrate the behavior of a high-dimensional indexing scheme. Indeed, its performance shows good agreement with the analytical model with respect to database size, fault tolerance, and recognition speed. Model acquisition time is linear to cubic in the number of object features. Object recognition time is constant to linear in the number of models in the database and linear to cubic in the number of features in the image. The system has been tested extensively. With more than 250 arbitrary shapes in the database. Unsupervised shape and subpart acquisition is demonstrated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>