A Probabilistic Approach to Geometric Hashing using Line Features

CHAPTER 3. NOISE IN THE HOUGH TRANSFORM 25
3.2 Various Hough Transform Improvements
Since the above straightforward implementation of the Hough transform needs improvement
in highly degraded environments ë22ë, we have investigated the factors aæecting the
performance of the technique and implemented and experimented on a series of variations
of the Hough transform.
Factors that adversely aæect the performance èreliability and accuracyè of the Hough
transform include:
æ Short lines inherently result in low peaks in Hough space Hèç; rè, which prevents the
detection of short lines relative to long lines.
æ When r = x cos ç + y sin ç is rounded to pick a particular bucket in Hèç; rè for a
speciæc ç, fractional r information is lost and all subsequent computations are done
on the rounded r values.
æ ç is also sampled. If a line has an orientation ç 0 , not exactly equal to any sampled
ç, the points on the line, when mapped to Hough space, will not have identical r
values. Instead, their r values will spread out near the real r value.
æ Using the coordinate èç; rè of the peak in Hough space as the line parameter limits
the precision of the parameters detected, since Hough space is quantized.
To strengthen the low peaks in Hough space which result from short lines present in
a source image ècompared to the inherently high peaks which result from long linesè, we
apply background subtraction by removing the contribution made to Hough space by edgels
along a long line after this long line has been detected. This method is attributed to Risse
ë48ë. To implement the idea, a global maximum in Hough space, say bucket èç; rè, is
located; then its corresponding line in the image is identiæed and all accumulator buckets
which were incremented during processing edgels lying along this line are decremented.
This algorithm diæers from the algorithm described in the previous section in that instead
of detecting local maxima in the accumulator array as candidate lines in the image, it
detects lines one after one iteratively as follows:
while still more lines to be detected do
è^ç; ^rè := globalMaxèaccumulator Aè;