International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004 
error means higher probability of two blocks are similar. The 
details of MSE are shown as follows. 
Let B, is the candidate block with position (p.q) in next image 
and T, is the target block with position (r,s) in current image. 
The Mean Square Error of two blocks is given as: 
MSE(B, T.) LY S (B5 - r5] e 
A ot MRM To] Ko ie e 
Where: M,N are the dimensions of the block. 
i,j represent the position of pixels in blocks. 
5. OBJECT POSITIONING 
As mentioned before, the orientations of the camera can be 
obtained from the hardware system, furthermore, the 
shape-based matching and feature point tracking can be used to 
compute the image coordinates of the object. Consequently, for 
each image that has orientation data, will give rise to set three 
equations. These will be derived from the following 
relationships between the recording position and the object’s 
location in local geodetic system (E, N, H). 
— — — 
To PS Uo 
where 
T_ = Target position vector. [T x Ty Ty] 
P! - The ith frame position vector p P : P t ] 
s! - Scaling factor of ith frame 
— 
U ' - The unit vector pointing from the camera to the 
target of ith frame [U r U iP U > ]. 
It can be shown as U "= R^ .Obs : /|Obs 43 
where R a = 
c(#’)c(K') 
s(9^) —s(o' )e() c(o )c(o^) 
R en is a rotation matrix and use the shorthand c for cos and s 
for sin. 
If there are N images that have orientation data, it will exist 3*N 
equations and N+3 unknowns. The unknowns include the 
object’s three dimension coordinates and N scaling factors. The 
least squares adjustment is suitable to solve the following linear 
equations. 
s(o )s(d )c(«') -c(o sx) - c(e )s(o )c( K')+ s(o sx) 
—c(d')s(x') - s(o)s(o)s() - c(o)e(x!) (mw )s(@ s(x’) + s(o )c(x') 
1900-10} 0 A 9 7. P) 
Q 159p c9 AN Hig 73 P 
0.0 LU. 0 A © T5 pl 
1 0 0 0 -u: A7 9 [ves sl wom^l p? inr 
0 10 9 "-UtrAIN S S, p 
MMM M M M M M M 
gue qm 0° A =U s. p 
6. EXPERIMENT RESULTS AND CONCLUSIONS 
The experiment of this study was designed to trace and position 
a motionless ship near the coast. The video images were 
recorded at a frame rate of 10 fps and with image size of about 
320 pixels by 240 pixels. The ground survey was also used to 
obtain the coordinates of the ship that will be used as the 
accuracy check. A part of the tracking results are shown in 
Fig.4 (a), Fig. 4(b) and Fig. 4 (c). The red contour on the image 
represents the result of tracking, and the green cross is the result 
of feature point tracking. The results indicate that even though 
the shape of the object changes entirely, the proposed algorithm 
not only can trace the contour of ship, but also can trace the 
feature point on the ship. The ground coordinates of feature 
point on ship are also calculated by the collinearity equations. 
A position comparison is made between the feature point on the 
ship from the video images and the ship itself from the ground 
survey. The comparison indicates that a position discrepancy of 
about 35 meters can be found. The position discrepancy 
basically can be attributed to the limited precision of the 
orientation recording devices. However, if the position of ship 
includes the range of the whole ship body (the ship has the 
length of at lest 100 meter), the position discrepancy can be 
considered acceptable. 
    
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