Affine Matching with Bounded Sensor Error: A Study of Geometric Hashing and Alignment
Abstract
Affine transformations of the plane have been used in a number of model-based recognition systems to approximate the effects of perspective projection. The mathematics underlying these methods is for exact data, where there is no positional uncertainty in the measurement of feature points. In practice, various heuristics are used to adapt the methods to real data with uncertainty. In this paper, the authors provide a precise analysis of affine point matching under uncertainty. They obtain an expression for the range of affine-invariant values that are consistent with a given set of four points, where each data point lies in a disk of radius E. This analysis reveals that the range of affine-invariant values depends on the actual x-y-positions of the data points. That is, when there is uncertainty in the data, the representation is no longer invariant with respect to the Cartesian coordinate system. This is problematic for the geometric hashing method because it means that the precomputed lookup table used by that method is not correct when there is positional uncertainty in the sensor data. They analyze the effect that this has on the probability that the geometric hashing method will find false positive matches of a model to an image and contrast this with a similar analysis of the alignment method.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1991
- Accession Number
- ADA260154
Entities
People
- Daniel P. Huttenlocher
- David W. Jacobs
- W. E. Grimson
Organizations
- Massachusetts Institute of Technology