International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004
P,, P, P,, Pa, are polynomials of maximum 3? degree (78
c c
parameters to be estimated) whose equations are (2) o (3):
PAX. Y, Zy=a, va X +a ral va. X +
fa Xve va Yi Zxa YZ +n, 2
mm M
PUCYZ-Y*SaXYz (3)
i=0 j=0 k=0
0<m <3;0<m, <3; 0<m, <3 € m +m, +M, $3
Equations (1) are known in literature as RFM Upward.
1.1 Neural Network Model
Neural Network (NN) approach for geometric calibration
purposes of remote sensing images can be considered an
innovative and experimental solution. NN are mathematical
models which simulate brain dynamics. Computational scheme
can be thought as a flow of distributed information which are
elaborated within computational node called "neurons" of the
NN. Some of them (input) receive data from the external world ,
some give back information to it (output), some other simply
communicate each other (hidden). Neurons are mathematically
represented by weights, parameters of the model, which have to
be estimated on the basis of the GCP through an iterative
learning process. As far as this work is concerned the developed
orthocorrection procedure is based on an opportunely designed
Multi Layer Perceptron (MLP) NN. This type of NN has been
chosen for its function approximation and estimation features. It
shows its high suitability especially for non linear functions as
considered relations are. Basic idea is to substitute the upward
projecting model relating image (En) and ground (X,Y,Z)
coordinate with a well designed and trained MLP NN. NN
architecture is the one shown in Figure 4. The most appropriate
number of neurons has to be defined time to time according to
the number of GCPs and image type. Only an expert user can
successfully control it. Indications for the best architecture can
be derived from RMSE (Root Mean Square Error) analysis. The
NN approach is quite sensible to the initialization of the weights
of the neurons.
INPUT LAYER HIDDEN LAYER OUTPUT LAYER
bla = =
ZA
Xp * b, 2
| / E yg QN
Á rp "nfi apt à >
«(zy- - i b
* b,
PL Lu QUE
Figure 3 - MLP NN mathematical model with 2
computational layer (hidden e output), for the
orthocorrection problem.
3. METHODOLOGY
The methodology for geometric correction on MIVIS images
have passed through different tests, entirely performed on
MIVIS 1 image. The obtained results were then analyzed from a
quantitative and a qualitative point of view to appraise the
characteristics of the used methods. The method that guarantees
the best performances has been therefore employed for the
MIVIS 2 image. This way it allowed the mosaic of MIVIS 1
and 2 images.
3.1 GCPs and CPs individualization
GCPs and CPs have been collected on the MIVIS images using
both a true colour composite (10-6-1 or 13-7-1) and a single
band where a better contrast was necessary. Reference map has
been the official orthoimages.
Trying to maintain GCPs and CPs well distributed over the
image has been an hard task due to the strength of the original
image distortions and to the extended presence of wooded areas.
Finally, 72 GCPs and 10 CPs have been collected.
3.2 GCPs and CPS elevation extraction
Image coordinates (&,77) and planimetric terrain coordinates
(X,Y) of GCPs and CPs derived from official orthoimages, have
been completed with the elevation data Z extracted from the
available DEM.
Attainable accuracy in such operation strictly depends on DEM
grid dimensions In this case it is certainly too high considering
the mountain test area . In fact, the portion of territory referring
to a single cell 50 m x 50 m wide is characterized by a strongly
varying height which cannot be properly represented by the
univocal value assigned to that cell within the DEM.
To partially solve this problem, the DEM has been resampled to
a geometric resolution of 10 m, but tests have demonstrated that
this operation does not guarantee a better final result. That's
why it has been decided to use for all the performed tests the
original DEM.
3.3 MIVIS 1 image geometric correction
The followings geometric correction tests have been performed
on MIVISI image :
- Series 1: RFM method with 20 coefficients varying the
number of GCPs: 39, 50, 61, 72;
- Series 2: method based on the NN with 72 GCPs and 10 CPs
varying the number of nodes of the hidden layer (from a
minimum of 3 to a maximum of 13):
- Series 3: method based on the NN with 10 nodes varying the
number of GCPs: 39, 50, 61, 72.
In order to simplify the correction procedure, all the tests have
been carried out on three spectral bands out of 102 (bands 10-6-
1 were chosen since they produce a good true colour image),
using the nearest neighbour resampling method in order
minimize image radiometric degradation. Orthoimages
geometric resolution has been set equal to 4m as suggested
considering the flight height.
3.4 Quantitative and qualitative analysis of the results.
The errors achieved, in terms of RMS and residuals on the
GCPs and CPs, for every previous tests allow to proceed to a
quantitative analysis of the results in order to appraise and
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