malization was elaborated. The calculations here are
more time consuming, because they call for iterations
due to the indispensable correction equation li-
nearisation. The V correction equation is :
0x 0x Ox
z— — —c+x-
Vx atop tette X
where :
x _ —b + Vb? — 4a(c — z)
o 2a
àx bVb?— 4a(c —z) * b^ — 4a(c — z) € 2a(c —z)
da 2a? V b? — 4a(c — z)
- V! — 4a(c — z) + D
2aV b^ — 4a(c — z)
ox
öb
Oz +1
àb Vbi -— 4a(c — z)
To solve the above equations there is necessary to
predetermine the approximate values of the un-
knowns a, b, c, therefore the use of this method
had to be preceded by the use of the v
minimum method.
4. THE ACCURACY ANALYSIS AND CON-
CLUSIONS.
The two shots (long distance - image ,2" and close
- up - image ,1") of 9 crosses test were analyzed
applying 3 above described methods. Image ,1"
presented a single crosses 72.7 pixels wide and 108.1
pixel high, with the vertical arms 9.1 pixel thick and
horizontal arms 13.5 pixel thick.
Image ,2" presented a single cross 30.0 pixels wide
and 44.9 pixels high, with the vertical arms only 3.8
pixel thick and horizontal arm 5.6 pixel thick.
Due to the high image contrast and clear background
there were no problems during the analysis. Each
arm of each cross was analyzed separately. Vertical
arms were analyzed along the lines and horizontal
arms along the columns of the digital images. Image
,1" allowed for 100 sections of vertical arm and for
65 sections of horizontal arm, while image „2” al-
lowed only for 35 vertical arm sections and for 25
horizontal arm sections.
The position of the axis of symmetry was derived
for each section of luminosity profile and it was
treated as a single point of the axis of symmetry of
the cross arm on the surface of the CCD image.
All that points issued using one of the 3 analysis
394
methods were approximated by a straight line for
horizontal arm of the cross and by another straight
line for vertical arm of the cross. By the intersection
of that two lines approximating arms of a cross the
image coordinates of the cross center are fixed.
05
10
15
oC
+
ape. + " P
25 + + +
30
35
T
pixel
40
+ +
e? +
LI
T9
29
To
60} 3 + ^
65
70
T
Fig.2. Linear approximation of the points determina-
tion on the digital image surface by subsequent pa-
rabolas axis. The diagram was produced by a computer
program which automatically calculates points on the
axis of the arms of a cross along all the digital image
lines or columns.
On the fig. 2 there is an example presented of the
approximation of arms of the cross nr.1. analyzed
on the image ,1”, resulting from the 3 methods of
digital image interpretation. The dots represent posi-
tions of the luminosity profile symmetry axes.
To value the accuracy of automatic determination
of coordinates of crosses on the CCD image, an
ideal image of the test was calculated. It was cal-
culated by the projective transformation of the ori-
ginal flat test coordinates onto the CCD sensor
