A Probabilistic Approach to Geometric Hashing using Line Features

CHAPTER 1. INTRODUCTION 7
1.4.1 Line Extraction
In noisy scenes, the locations of point features can be hard to detect. Line features are
more robust and can be extracted by the Hough transform method with greater accuracy.
Thus we choose lines as the primitive features to be used.
In chapter 3, we ærst brieæy review the Hough transform technique for detecting line
features. Then we point out several factors that adversely aæect the performance of the
method and propose several heuristics to cope with those factors to improve the performance.
A series of experiments relating to this point are presented.
1.4.2 Line Invariants
In chapter 4, we ærst examine the way in which coordinate changes act on various spaces
of potential interest for recognition. This allows us to deæne a method of encoding a line
using a combination of other lines in a way invariant under suitable geometric transformations.
Potentially interesting transformations considered include rigid, similarity, aæne
and projective transformations.
1.4.3 Eæect of Noise on Line Invariants
In chapter 5, we model the statistical behavior of line parameters detected by the Hough
transform in a noisy image using a Gaussian random process with mild assumptions. We
analyze the statistics of the computed invariants and show that these have a Gaussian
distribution in a ærst order approximation.
Analytical formulae for various transformations including rigid, similarity, aæne and
projective transformations are given.
1.4.4 Invariant Matching with Weighted Voting
In chapter 6, we use the result of chapter 5 to formulate a Bayesian maximum likelihood
pattern classiæcation as the basis of weighted voting scheme for matching line features by
Geometric Hashing.
We have implemented a system that makes use of these ideas to perform object recognition,
assuming aæne approximations to more general perspective viewing transformations.