The International Archives of the Phatogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B3b. Beijing 2008 
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similarity, proximity and extent between segments(Ralescu and 
Shanahan 1995). In order to decrease the uncertainty of 
grouping, the proposed algorithm considers related information 
of the pixels between the line segments which deserve to be 
grouped. Reasonable grouping which is accordance with the 
feature of linear perception can gained and most false edges can 
also be removed. The procedures of grouping and linking are as 
following: 
(1) Grouping the line segments according to their spatial 
relationship. Divide the segments to 180/a groups according to 
their 9 value and with the interval of a degree (a is an integer 
can be 180 divisibility). Then, divide each group again 
according to their p value. From the formula 
p = xcos9 + ysmO , we can get that if 9 value has a slim 
difference of A9, the difference of p value is 
A/? = |x cos # + y sin <9 - x cos(# + A 6) - y sin(# + A 9)\ (0 
By the influence of the value of x and y, the difference of p 
increases many times as the difference of ^(Huang 2006). So, 
before dividing according to p value, the segments must be 
rotated to get a uniform 9 value. The proposed algorithm 
employs the average 9 value with the weight of their length: 
0 = 
YJS, 
2> 
(2) 
Where li = length of segment i 
Oi = 0 value of segment i 
After the twice grouping, the segments with similar 9 and p 
value are gathered into the same group, it means that the 
segments in a group are collinear. Then, check the proximity for 
the segments in each group, delete the segments without 
proximity. 
(2) Pick out reasonable group by considering related 
information of pixels between segments. Firstly, construct a 
buffer area between the segments, apply nonmaxima 
suppression to the pixels in the buffer area, and store the 
maxima pixels. Secondly, search the maxima pixel form one 
endpoint to the other, typical search result is shown in the 
Figure 4. The fitting factor and continuous factor of the maxima 
pixels decide the reasonability of the group. Formula to 
calculate the probability of a reasonable group is 
(3) 
l — b l 
where P = reasonable probability 
/ = length of the buffer area 
b = count of discontinuous pixels 
Adi = difference of distances from 
pixel i and pixel i-1 to the line segment 
w u w 2 = weight of fitting factor and 
continuous factor 
So, j ^(^') indicate the fitting factor, and ^indicates 
l-b l 
the continuous factor, both of the two values range form 0 to 1. 
Experiments show the influences of the two factors are 
probably equal, so w\ = w 2 => 0.5 is employed as experiential 
value, the P value for the three situations of (1)(2)(3) in Figure 
4 are 0.891, 0.723 and 0.750, we can get the conclusion that the 
situation of 
(1) is the most reasonable grouping and the conclusion accords 
with the rule of objectivity. 
(3) Finally, link the reasonable grouping and mark them as 
credible edges. 
(c) 
Figure 4. Sketch map of pixels with maxima in buffer 
3.4 Extending Edges 
Sometimes, weak edges can not be detected because of gradient 
magnitude not reaching the loose threshold. Extending the 
edges, we can get such edges which can not be detected before. 
Searching maxima pixels from edge extension is similar to 
searching in the grouping and linking edges procedure: set up 
the buffer with certain width on the edge extension line, apply 
nonmaxima inhibition to the pixels in the buffer area, and go 
along with the extension to search the maxima pixels from each 
endpoint in turn, then calculate the probability for extension to 
certain length according to formula (3). Keep on searching 
when the probability is above certain threshold, then mark 
extension as credible edges; stop searching when the probability 
is below certain threshold or arriving at the boundary of the 
image. 
Concluded the credible edges marked all above procedure, the 
edge detection results can be gained using proposed algorithm. 
The enhancing effects on typical weak edges of each procedure 
are shown in Figure 5. 
(d) (e) 
Figure 5. Processing on weak edges, (a) An image with 
some weak edges, (b) Preliminary edge 
detection result (c) Line fitting result, (d)