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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008 
Since the target points lie at the boundary of two differently- 
coloured materials, the biases cause inflation of the range 
residuals, as will be demonstrated. Other researchers have, 
however, used similar black-and-white checkerboard patterns 
for their LRC calibration (Lindner and Kolb, 2006; Santrac et 
al., 2006). 
3.3 Data Capture 
For the calibration a network of 30 convergent images, 15 with 
tc=0° and 15 with k=90°, was captured, as pictured in Figure 2. 
The images were captured about 1.0 m above the ground along 
two lines such that the convergence angle between them was 
approximately 80°. The minimum and maximum observed 
ranges were 1.1 m and 6.6 m, respectively. This range of 
distances is slightly smaller than that of Lindner and Kolb 
(2006) who performed their calibration between ranges of 0.75 
m to 7.5 m. 
Thirty-three spatial distances between various object points 
measured with a 1 m long, 0.5 mm graduated steel ruler were 
included in the network. The same target field was used for the 
accuracy assessment, but a set of 6 independent images were 
captured at different locations. Forty-nine object points 
distributed throughout the target field were surveyed with a 
total station to provide the basis for the accuracy assessment. 
A A 4 * « * A 4 
Object points 
Exposure stations 
Once the parameters were estimated for each edge, the two lines 
were intersected to obtain the x, y co-ordinates of the target 
comer, as shown in Figure 3. The range at that location was 
then bi-linearly interpolated from those of the four 
neighbouring pixels. 
intensity image 1 
9 10 11 
X (m) 
12 
20 40 60 80 100 120 140 160 
col/x (pix) 
Figure 3. Target measurement by best fit line intersection. 
4. SELF-CALIBRATION RESULTS AND ANALYSES 
4.1 Self-Calibration Adjustment Cases 
Four self-calibration adjustment cases were performed. These 
are summarised in Table 1. Case 1, for which no IO parameters 
were estimated, served as the basis for quantifying the 
improvements gained in the other three cases. Nominal values 
were used for the principal point, principal distance (8 mm) and 
rangefinder offset (300 mm). (The adjustment would not 
converge without the large nominal rangefinder offset.) In case 
2 only these four “basic” IO parameters were estimated. In case 
3 a complete physical model comprising only significant APs 
was estimated. Case 4 comprised the APs in case 3 plus two 
empirical terms identified through analyses of systematic 
patterns the estimated residuals. The degrees-of-ffeedom for 
free-network adjustment of case 4 was 6407. 
Figure 2. Calibration network. 
3.4 Target Measurement 
Measurement of the target comers, which constitute the object 
points, was performed as follows. First, edge detection was 
performed throughout the entire image using orthogonal first- 
derivative-of-Gaussian filters. For a given comer, the best-fit 
lines of the two intersecting edges were determined. This was 
done by fitting the following model to the edge magnitude 
image data 
f (x, y) = Ae _B “ 2 + C + Gx + Hy 
(12) 
where A is the amplitude of the Gaussian edge profile, C is the 
radiometric offset, G and H are the radiometric gradients, B is 
the damping coefficient and the line parameters D and 0 are 
embedded in the function u: 
u = xcos0 + ysin0-D 
(13) 
Case 
IO parameters estimated 
1 
None 
2 
“Basic” IO parameters: x D , y D , c, do 
3 
“Physical” IO parameters: x p , y p , c, kj, do, d 4 , d 5 , c^, 
d7, Ci, e 2 
4 
Physical and empirical parameters: x p , y p , c, k l5 do, 
d 4 , d 5 , d 6 , d 7 , ei, e 2 , e 4 , en 
Table 1. Summary of the self-calibration cases 
4.2 Model Efficacy 
The improvements gained in each case can be assessed in terms 
of the RMS of residuals from all 7161 observations remaining 
after outlier removal by Baarda’s data snooping. These figures 
are presented in Table 2 and show only minor improvement 
when the nominal IO parameters are estimated (case 2). Case 3 
shows considerable improvement due to the large magnitude of 
the cyclic error components (maximum magnitude: 43 mm) and 
the clock-skew errors (maximum magnitude: 95 mm 
(range)/mm (image distance)). The latter correction equates to 
ll