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Vision Systems. al
Estimates of camera stat
tate x elk and Pan can
be used to predict the feature position in image space
and the search limited to a window around this
position. The prediction of the feature position in the
image space can be done projecting object entities into
image space using collinearity equations or even the
measurement model defined in this paper. Prediction of
any image feature position is bounded only by the
quality of the state estimates. This way the window
must be defined taking into account the covariance
matrix of the predicted state estimate and the feature
dimensions.
A recursive procedure in which sequential
estimates are used to reduce the feature search space
is depicted in Figure 5.3.1.
[predicted estimate |
V
——>| SEARCH FOR THE i-th LINE
window definition;
Hough space computation;
line location;
[i=i+1] T
| filtered estimate computation
based on the i-th line;
J
| final filtered estimate |
vb
Figure 5.3.1 Recursive search procedure.
Other advantages of using predicted estimates for
image features search are:
the estimated feature length can be used to locate
the most probable cluster in Hough space.
fewer candidate clusters will be present in the
Hough space.
6. RESULTS
6.1 Introduction
In the previous sections mathematical expressions
relating straight features in object and image space
and its treatment using Kalman filtering were
presented. In this section results obtained from
simulated data are presented and discussed.
Camera inner parameters (focal length, principal
point, optical distortion) were supposed known and it
was also assumed no movement of robot or object during
image acquisition. The following parameters for the
simulated camera were used: 15mm focal length, 10x10
mm’ imaging area and 10x10 um pixel size.
Once the exterior camera parameters (position and
orientation) are established the image coordinates of
object points (corners) were | computed using
collinearity equations. Random errors were introduced
in these points which represent endpoints of a straight
line; image line equations were finally computed from
these pair of points.
Three sets of data became available:
- object straight lines parametric equations, assumed
to be known from the object model;
- exterior camera parameters (camera vector state) and
the associated error matrix;
- image lines equations and their covariance matrix.
The covariance matrix of image lines were computed
using covariance propagation.
6.2 Single Frame Calibration
It was supposed we had a single camera, static in
space, observing a cube of 70mm. The base frame is
coincident with the station frame and the object frame
is 200mm far from the origin of the base frame. For the
camera vector state of Table 6.2.1 the resulting
simulated image is presented in Figure 6.2.1.
Table 6.2.1 True Camera State and Predicted Values
Camera Predicted State| Predicted
State State Error | Variance
2
K 0.0 0.02 0.02 (0.02)
9 rad| 0.0 -0.02 -0.02 (0.02)
w 0.959931 0.939931 0.02 (0.02)
Xc 230 225 5 (5.)
Yc mm| -200 -204 4 (3.3
Zc 200 205 -5 (5.*
Figure 6.2.1 Simulated image of a cube.
The wireframe cube shown in Figure 6.2.1 can be
described by twelve lines in image space, the
correspondent object lines of which in base coordinates
are known. Using the recursive approach stated in
previous sections estimates for the camera vector are
obtained. In Figure 6.2.2. graphics are presented
showing the true errors and estimated standard
deviations for rotation and translation variables. The
true error is defined as the difference between the
estimated and the true parameter value and the standard
deviation is defined as the square root of the
estimated variance.
ROTATIONS
True Errors (rai Lines
0.019 +
0,00 | i
a / Bg s
me lg EE ETES nS a
o : "d = rer put
t ‘
$7,
-0.00 bh, ^
T Lu
-0.018 | /
Estinatad Standard Deviations
9.015 |-*
po^.
o0 Li: XM
X *
s A.
di
. M
ii
EXTA OE. tte.
0 i 1 E
TRANSLATIONS
True Errors (re Lines
40 | >
zc
2.0 | X M me mra mama
^ ^ Mn
L
9 S chum
A£0Ll mU eet
-a.0 | „X Ye
Estinated $tandard Deviations
ues
4.0 | ae
Ma
v
"v
“>
2.0 | He
nari. s
SH — =
0 L L L I
Figure 6.2.2 Error analysis in single frame calibration
From the analysis of the graphics in Figure 6.2.2
we can conclude:
the filter has a strong convergence over the twelve
lines. In fact, when the ninth feature was
