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2.1 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 an 
interest point, and the reliability is an index for representing 
influence of noise. Therefore, the height / and the reliability r 
are calculated by following equation. 
    
My) ie) (er) en 
h(x, y) 
fie a ES 2 
I (x) ) 20, (x, y) ( ) 
where, 
h,.h, : variation of gray levelfor each direction (x.y) 
x, y : image coordinate of interest point 
c, : 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 first image of the image 
sequences for Koma house, and Figure 3 shows the extracted 
lines by the method for the first image. 
  
Figure 2. Koma house (the first image) 
x 
49 
N 
LI 
TX 
pes 
SE 
- 
t 
a SIRE TTR | RTT et 
aa iru p SEE al 
  
Figure 3. Line extraction 
2.2 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 (x, v) is calculated by following equation 
and estimated optical flow is shown in Figure 4. 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Fart B5. Istanbul 2004 
  
a Hx ol rs 
S a -[J(p)- I(p )] S = [/(p)- l(p ) 
M x — o 3 
AFD 5 NT (3) 
z(t (e 
aM Ox 4 \ Oy d 
where, 
Ip)s Ix, y.t), J(p)s 1(x, y. t ót) 
   
       
  
   
  
   
  
SR t 
S AN ses. 
" sl = r ^. 
RR ARERR aN RN 1-7 
MANNA ERN 91 ng. Y rp 
SN it 1”. 
T 
  
' 
1 
Figure 4. Optical flow estimation 
2.3 Similarity Function 
The line matching between each frame was performed by 
similarity function. The similarity is an index for representing 
how similar are the 2 lines. Figure 5 shows extracted 2 lines L; 
(n-1 frame) and L; (n frame), and L,, shows generated middle 
separating line. Let the average distances between L,, and 2 
lines are D; and Dj, and the projected lengths to the L,, are P, 
and P,,, respectively. Thus, the similarity of 2 lines is calculated 
by following equation. 
  
$= 4 
kD +k P e) 
where, 
D 
D-DrD, p-R(p > P)orP= P (P. » P.) 
: P d 
k,.k, : coefficient parameters (&, — 0.3, „=0.7) 
Ls 
  
  
  
Figure 5. Similarity of 2 lines 
In order to perform line matching efficiently, threshold value of 
the similarity was needed. The threshold value was calculated 
by theory of error diffusion using pointing accuracy of each line 
ends (+1pixel) and accuracy of the optical flow estimation (Ong