Natural representations for straight lines and the Hough transformon discrete arrays
Svalbe, I.D.
Dept. of Appl. Phys., Chisholm Inst. of Technol., Melbourne, Vic.;
This paper appears in: Pattern Analysis and Machine Intelligence, IEEE Transactions on
Publication Date: Sep 1989
Volume: 11,
Issue: 9
On page(s): 941-950
ISSN: 0162-8828
References Cited: 23
CODEN: ITPIDJ
INSPEC Accession Number: 3509340
Digital Object Identifier: 10.1109/34.35497
Current Version Published: 2002-08-06
Abstract
The grid of discrete sampled data points in a digital image
supports a limited set of lines at angles and displacements `natural' to
that grid. The effect of this implicit line quantization on the
parametrization of the Hough transform is presented. The function
describing the discrete Hough transforms line-detection sensitivity is
derived. Expressions for the orientation, frequency, and popularity of
lines in the natural set are given. The results obtained are of
importance to data arrays of small size. The distribution of lines in
the natural set is also important as it determines the precision and
reliability with which straight lines can be measured on a discrete
imaging array. From the natural line set concept, a general (a,
d) slope/offset straight-line parametrization is developed for
which the Hough transform is compact and fast to compute, and which is
as easy to interpret as the class (p,θ) parametrization
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