A Probabilistic Approach to Geometric Hashing using Line Features

CHAPTER 3. NOISE IN THE HOUGH TRANSFORM 27
èaè go back to the image èedge mapè and scan edgels èx; yè's on the line
with a 1-D sliding window of appropriate size èdepending on the image
resolutionè.
èbè if the number of edgels in the window is less than, say 1=3, of the
window size, take èx; yè to be a noise edgel which happens to lie on
the line èç i ;r i è.
ècè re-accumulate the evidence support for the line without counting the
noise edgels.
3. sort these lines by their new evidence support and select the top n from
among them.
The reason we simply select the top n from among 2n lines detected by our previous
algorithm is that our previous algorithm already has good performance, and we just want
to further remove spurious lines.
Figure 3.1 shows an example, comparing the result of the standard Hough technique
and our improved Hough technique. Figure 3.1èaè shows a synthesized image without noise.
It contains roughly 40 segments. Figure 3.1èbè shows the result of the standard Hough
analysis. 50 lines are detected. 17 true lines are missing. Also many of the true lines are
detected multiple times. Figure 3.1ècè shows the result by applying our improved Hough
technique without enhancement of using proximity grouping. Also, 50 lines are detected.
There is no missing true lines. Yet, since more lines are detected than are actually present
in the source image, a few true lines are detected multiple times. Figure 3.1èdè shows the
result by applying our improved Hough technique with proximity grouping enhancement.
Figure 3.2èaè shows the same image as in Figure 3.1èaè, yet with serious noise. Figure
3.2èbè to Figure 3.2èdè are the correspondences of Figure 3.1èbè to Figure 3.1èdè . The
performance improvement over the standard Hough technique is much obvious.
3.3 Implementation and Measured Performance
In our implementation, we use æç = 1 è1 degreeè and ær = 1 è1 pixelè as the quantization
values for ç and r in Hough space. This appears quite suæcient for our subsequent applications.
Intuitively, smaller values of æç might give better precision but can result in the
spreading of peaks èrecall that image is digitized so that the edgels of a line will not lie