nbul 2004
gravity to
poses the
© points
tor can be
4)
matrix, 9
orithm is
y is poor.
rotational
able for
ntity, and
his linear
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eters, not
;o linear
1atrix R,if
ed skew-
)
a 0. —c 4 1- 9. 0
N=|b Sims -a| I=|0 1 0
e huge 9 Qo 1
br adbuc 2ab - 2c 2ac + 2b |
IDBIBSIZ 2ab + 2¢ icd $55 2bc—2a
ieu dade 2ac —2b 2bc + 2a km Gehe
(16)
according to(13)there is relation formula below:
An = Ba r sol 17)
There into: A = p — P | B d -[P —P
Replace(15)into(17)
Ass ü * St) # Ba (I D Su) (18)
solution equation(18)obtain independent variable (a,5,c).
thereby obtain the rotational matrix R replace R
into(14)translation T can be obtained.
5. EXPERIMENTAL RESULTS
[n present study, we use a binocular stereo computer vision
system, to acquire binocular stereo image sequences pair in turn
constant duration (the true quantity of motion about every
spaced interval of time is Ax = 25/ 2mm, Ay z -25/A2mm)
about the toy car, which is undergoing an approximate even
velocity rectilineal moving in one XY plane in the view scope
of a video camera. The three-dimensional moving parameters of
the moving object sequence images are calculated. The detail
procedures are as below:
(Dthe binocular stereo sequence images pair of moving object
in different time is obtinaed using binocular stereovision
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004
system.
(Using the line (point) features with known geometry relations
established in scene, the stereo vision system is calibrated in
order to obtain the direct linear transformation coefficient L,
according to the 2 Binocular Stereo vision system calibration
model.
@)Sequence, stereo matching is done with the law of relaxation
and relative matching in order to obtain the image coordinates
of moving object corresponeding feature point image
coordinates
(à) The three-dimensional coordinates of moving object
corresponded feature points are calculted according the
coefficient L, :
(S)The parameters R and T of object relative movement are
calculated using Skew-Symmetric Matrix Decomposition
(SSMD).
The results of rotational matrix and translation vector in 10
time intervals are shown in Table 1. The error between
calculated values and true values in x and y directions in 10
time intervals are shown in Table 2. The mean errors of
moving point are shown in Table 3. In Table 3, the mean error
is the error between three-dimensional coordinate P:
(x; Va 2)" of corresponded feature point in the time of
{ + Af which is reconstructed from „procedure D and the
coordinate P (X), ; £y of
corresponding feature point that is calculated from a random
feature point P (x uz) in a moving object in time t
that has moved for Af according to the R and T vector
obtained from the above procedures and using movement
equation (10). Here (; = 1,2,---,n) and n=16.
three-dimensional
computer
Table 1 The results of rotational matrix and translation vector Unit: d * cm
Q œ K DX DY DZ
1 0. 06 70. 56 -0.41 zm 1.78 -0. 06
2 -0. 90 70.81 „ax -2.34 1.27 0.12
3 1.09 -].48 0. 63 72. 10 1.55 0. 34
4 0. 01 70. 01 1. 25 71.38 1. 83 0.22
5 =2.11 1. 26 0. 76 71.92 1. 86 0. 35
6 -0. 40 70. 18 1. 60 “118 1.81 0.28
7 z1.23 0. 06 1. 50 71. 86 1.54 0. 24
8 1.41 1.37 71. 71 =]. 77 ]. 93 70. 12
9 z0. 30 =0. 33 0. 90 z]. 08 1.58 0.01
10 1. 24 0.59 -0. 64 1.91 1. 57 -0. 34
Table 2 The mean errors of moving point Unit: cm
1 2 3 4 2 6 T 8 9 10
di 0.02 -0. 58 r0. 35 0. 38 20. 15 0. 60 -0.09 | 0.0] 0. 08 -0. 14
d, 40: 01 -0. 48 70. 21 0. 06 0. 09 0. 04 "0. 22 0. 17 —0. 18 70. I8
Table3 The mean errors of moving point Unit: © cm
1 2 3 A 5 6 7 8 9 10
m, | 0.57 050 {0.24 1030 {0.63 0.39 0.49 0.23 0.13 0.31
m, | 0.23 a 0.23 0.15 0.27 0.55 0.30 0.36 0.30 | 0.14 | 0.20
m; | 0.31 0.19 0.12 0.21 0.28 0.18 0.21 0.13 0.11 0.13
Âs shown in Table 2, the mean translation errors are 2.4 mm
and 1.7mm, in the directions of X and Y, respectively. Due to
the limitation of experimental conditions, there is no way to
precisely measure the true values
