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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008 
Ç = 
C 3 
—cos t 
a‘ 
c 3 
n = -—sm t 
b l 
(9x) 
where c =a -b , and eliminating t, we get evolute equation (lOx) 
for ellipse. 
( a b) -c ( 10x ) 
If we make regression of our curve, expressed by a formula (7), 
we obtain straight line equation (11) matched to the curve. On 
the basis of two points: curvature center and curve point 
describing plumb line of the test, we can determine straight line 
equation (12). 
y = ax + b 
(il) 
Intersection points of straight line (11) with straight lines 
created according to equation (12) can determine shifts of curve 
points (7) (with distortion) on points laying on the straight line 
without distortion (figure 1). 
where: 
3. EKSPERIMENT 
Experiment wad done using test field, presented in figure 2. 
Figure 2. Calibration test; images: on the left: with Nikon 16 
mm, on the right Nikon 10.5 mm lens 
As the next step, straight line coefficients and statistical 
analyses were calculated. 
a = 
»Z**** y* 
b =-(Ly* ~ a H x k) 
(lia) 
OWi) , *,OWv) 
v = — x + y. 
(X k -x/) 
(12) 
where: 
X,= c, 
Y k =f| 
Distance between curve point and intersection point (11) and 
(12) is a distortion value. Distortion is positive, when curvature 
radius intersect straight line and negative, when radius pass by 
the straight line. 
Lens 10,5 mm 
Lens 16 mm 
Line 
A 
b 
A 
b 
56-65 
-0,01783 
2503,253 
-0,02149 
3093,321 
77-88 
-0,0244 
442,4195 
-0,00466 
372,2463 
89-100 
-0,01073 
872,8104 
-0,00887 
978,3053 
101-112 
0,007564 
1309,888 
-0,00993 
1494,114 
113-124 
0,028315 
1884,573 
-0,01712 
2138,627 
125-136 
0,04134 
2267,059 
-0,02117 
2618,112 
149-160 
0,001459 
1220,161 
-0,01194 
1366,574 
161-172 
0,014498 
1613,97 
-0,01519 
1843,48 
185-196 
0,037156 
2192,086 
-0,01864 
2571,018 
197-208 
0,016929 
1437,506 
-0,00691 
1626,382 
221-232 
0,018275 
1515,701 
-0,00904 
1721,471 
Mean 
value 
0,010234 
1569,039 
-0,01318 
1802,15 
Correlation 
-0,45293 
0,997954 
Table 1. Coefficients of straight line equation (11) for plumb 
line in the image. 
Correlation coefficient for parameters a of a straight line 
equation equals 0.45. It follows from deformation value caused 
by distortion different for both lenses: 10.5 mm and 16 mm. 
Proposed algorithm is perfect for image correction before 
measurements connected with triangulation or surface model. 
Figure 3 shows calibration effects. 
Figure 1. Schema of distortion determination idea. 
i