International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B-YF. Istanbul 2004 
  
  
3.1 Line Extraction 
Line extraction was performed by Canny operator with 2 
threshold values which called the height and reliability of edge. 
The height of edge is a variation of the gray level around at a 
interest point, and the reliability is an index for representing 
influence of noise. The height # and the reliability = are 
calculated by following equation. 
(1) 
(2) 
  
where, 
h,h 
y 
: variation of gray level for each direction (x.y) 
x,y : image coordinate of interest point 
€, : variance of gray level around at interest point 
These threshold values were set as h = 10 and r = 0.1 in this 
paper. Furthermore, both ends of these extracted edges were 
connected by straight lines. Figure 2 shows the extracted lines 
by the method for the first image (277 lines). 
  
Figure 2. Line extraction 
3.2 Optical Flow Estimation 
In order to perform line matching, both ends for each extracted 
line were tracked by optical flow. Although many optical flow 
estimation methods have been proposed, Lucas-Kanade method 
(Lucas and Kanade, 1981) which is capable of correct and fast 
procedure was adopted in this paper. The optical flow by 
Lucas-Kanade method (, v) is calculated by following equation 
and estimated optical flow is shown in Figure 3. 
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1(p)=1(x. 1), 
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VS ; (3 
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Figure 3. Optical flow estimation 
4. LINE MATCHING BY TRIFOCAL TENSOR 
The unmatched lines by the optical flow estimation were 
corrected by trifocal tensor in this paper. Details of the line 
matching by trifocal tensor are as follows. 
Trifocal tensor is geometric relation of 3 images which 
contained the same objects from different perspectives. The 
trifocal tensor is expressed by 3 square matrixes (3x3), these 3 
matrixes are T;, T; and T5, components of these matrixes are #;, 
/5;j and /3;, and image coordinates of matched points for these 3 
images are (x), yy, 21), (x2, v2, 22) and (x3, 3, z3). Thus, following 
equations are obtained by the geometric relation. 
—25218» + Z,V38 23 + Va238 3 m Y3J3i83; = 0 
£48: 72484573584 tJFX 98570 
—-ZEG T7 XESTXQE,-0 
T 2273811 + Z8 re X2375831 7 X2ME33 = 0 
where, 
gy; Xf t Yi t zf 
163 
These 4 equations are generated by one conjugated point of 
these 3 images. The trifocal tensor has 27(73x3x3) unknown 
parameters which can be calculated by more than the same 
number of equations. Therefore, more than 7 points needed to 
be conjugated between these 3 images for acquisition of the 
trifocal tensor. Consequently, the unmatched points in the third 
image are calculated by the above equation. 
5. RESULTS OF LINE MATCHING 
In order to evaluate performance of the proposal line matching 
method, line matching in general stereo matching methods such 
as LSM (Gruen, 1985), probabilistic relaxation (Rosenfeld, et al, 
1976) and area correlation (Schenk, 2001) was also investigated, 
and performance of the proposal method was compared with 
these general methods. Table 2 shows results of line matching 
by each method. The line matching by proposal method could 
be performed efficiently more than other general methods. 
Consequently, the optical flow estimation and the trifocal tensor 
is useful method for line matching by image sequences. Figure 
4 shows result of line matching by the proposal method. 
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