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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004
compare, depending on each study images, the characteristics
and potentialities of the two geometric correction methods.
Particular attention is paid to the following items:
- increasing the number of parameters that define each method
(number of polynomial coefficients for the RFM, number of
nodes of the hidden layer for the NN) the GCPs errors should
decrease (see figure 4);
- increasing the same parameters, the maximum or the minimum
difference among the errors on the GCPs and CPs represents an
index of the smaller or higher generalization capability of the
model (defined as its ability to return correct outputs from
different input based on the transformation parameters between
image and object coordinates (see figure 4);
- considering a model with good generalization capability, the
residuals on the CPs should be higher than those on the GCPs
(see figure 4);
- the mean residuals along & and n directions should be null: if
not, it’s possible to hypothesize the presence of a systematic
error in the data and/or in the used correction algorithm;
The results from the quantitative study, based on the previous
criterions, must be confirmed by a qualitative analysis, that
should verify that:
- the orthocorrected image should not present anomalous
behaviours as discontinuity or asymptote;
- residuals should be maintained constant on the entire image,
also in the areas where the GCPs are not present; this can be
done through transparency overlapping, the correspondence of
the corrected MIVIS image with the reference map.
RMS
CPs
modello non generalizzante_
CPs
- T^ modello generalizzante.
—
numero parametri
Figure 4 - Relationship between RMS on GCPs and RMS on
CPs when evaluating the generalization capacity of the applied
model.
. . 2 . ~
At last, a statistic ^ test has been carried out on the GCPs
residuals for some of the tests elaborated with RFM and NN
methods. This has permitted to verify their adaptation to the
expected normal distribution. The test consists in calculating the
2 A .
X^ parameter for the residuals and comparing the obtained
value with the theoretical one derived from the defined tables
according to the correct degree of freedom and to the chosen
~ ‘ 2 ;
level of confidence. If the obtained y^ is smaller than the
theoretical one the test is positive, therefore the residuals
distribution can be considered to be a normal one. If not it is
possible to hypothesize the presence of some systematic
phenomena.
875
3.5 Series 1 results analysis
Series 1 tests best results, for the RFM method, have been
obtained using a number of coefficients equal to 20. It is
therefore. possible to think of maintaining such configuration to
appraise the characteristics of the model when varying the
number N of GCPs as shown in table 3.
REM 20 coeff. 10 CPs
GCPs RMS, RMS, RMS
(cell n.)
number (cell n.) (cell n.)
GCPs| CPs | GCPs| CPs | GCPs | CPs
39 1,85 518 | 3,41 4,14 | 3,88 | 6,63
50 1,07 | 4,19 1,70 | 289 | 2,06 | 5.09
61 2,17 | 4,09 1,91 289 | 2:39 1 5,01
72 556 | 396 | 200-| 250 591 468
mean Res, mean Res,
(cell n.) (cell n.)
GCPs | CPs | GCPs | CPs | GCPs | CPs
39 -0,02 | 0,49 | -0,02 | -0,05 | 3,28 | 6,16
50 -0,01 | -0,69 | -0,02 | -0,05 | 1,74 | 4,18
61 0,01 1,59 | -0.01 | 0,07 | 2,44 | 4,42
72 -0,61 1.19 ] -0,01 | 0.15 13,13 [405
mean Res
GCPs (cell n.)
number
Table 3 — RMS errors and mean residuals for Serie 2 tests.
Best results are in correspondence of N=61, but it is possible to
conclude that RFM method does not seem to be particularly
sensitive to the variation of GPC number.
However the good numerical results are not confirmed by the
qualitative analysis of the corrected images as shown below.
| 39GCPs 50GCPs |
| 61 GCPs 72 GCPs
|
|
i
|
|
e
Figure 5 - Geometric correction tests results on MIVIS 1
image by RFM with 20 coefficients when increasing the
number of GCPs.
As far as tests performed with the NN approach (table 4) are
concerned it is possible to notice that:
I. the RMS error of the GCPs and CPs decreases as the number
of nodes increases, both in direction & and 1 reaching a stable
value in correspondence of 7 nodes;
2. the RMS of the CPs remain similar as the ones on the GCPs;
3. the worst behaviour is not obvious along & for the RFM
method;
4. the mean residuals along & and n direction are null for the
GCPs, while for the CPs, even though not reaching elevated
values, they are slightly away from zero.
