The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008
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ing only the five values of the criteria and a link for one image
between the five values and the impact for a given application.
It is possible to define a validation protocol for the previous rep
resentation at different levels (each being more difficult). We as
sume that we know the quality criteria values corresponding to
several degradations for few levels (e.g. Fig. 2-4). We also know
the impact on one application (SAM classification in our case) of
these degradations on the results. We can now try to predict the
impact for
• a known degradation but with a different level on the same
image (first situation);
• an unknown degradation on the same image (second situa
tion);
• an unknown degradation on a different image (third situa
tion).
It has to be highlighted that the choice of the SAM classification
is not determinant and is chosen only for demonstration purpose.
Any other hyperspectral application giving a quantifiable result
could have been used.
In the following part, results obtained on mojfett3 image are used.
Only one image is used as a reference as it is not easy to obtain
applications results for different images (it is precisely the reason
why quality criteria are important). In the situation where another
image is required, mojfett4 is used.
When we are confronted to an unknown situation, we will try to
find the nearest known diagram. To be able to find the nearest
diagram, we need to define a distance. A Euclidean distance, in
this five-dimensional space, is the most intuitive solution.
We are still confronted to the problem of the scale between cri
teria: the MAD variation domain, which can easily reach 2000,
has nothing in common with the variation domain of F\, which
is kept between 0.9 and 1. There is no ideal solution to this prob
lem so we decide to normalize arbitrarily the values using the
same scales as on the previous diagrams. We denote as 7 this
normalized value.
Thus, the distance between two diagrams is defined as:
^ ~ ^MAD + ^MAE + ^RRMS + + ^Q( x , y ) • (®)
The lower the distance, the more similar the two degradations.
We now need to check if this distance performs well in the three
situations described above.
3.2 Changing the degradation level (1st situation)
In the case where a white noise with a variance of 150 is applied
to the image, let us compute the distance (8) to known degrada
tions on the same image. Results are presented in table 1. Small
est distances are highlighted in bold and correspond to those with
the white noise with a variance of 200 and the white noise with a
variance of 100 (Tab. 1). In this situation, we can accurately pre
dict the impact of the degradation on the application. We can infer
a number of misclassified pixels between 163 and 255, which is
correct: the real value is 222 (of the 65536 pixels in total).
Table 1: Distances for a white noise of variance 150.
Degradation type
Deg. param.
Distance
# of misclass.
White noise
50
0.169285
112
White noise
too
0.0735083
163
White noise
200
0.0619829
255
White noise
1000
0.634494
634
Spectral smoothing
3
1.57091
262
Spectral smoothing
5
0.917740
166
Spectral smoothing
7
0.627584
123
Spatial smoothing
13
1.40636
4248
Spatial smoothing
15
1.11240
3778
Mixed smoothing
11
1.90406
4881
Gibbs
50
0.195913
698
Gibbs
100
0.258957
425
JPEG 2000
0.5
0.857591
450
JPEG 2000
1.0
0.503311
142
The same accuracy is also observed when using this distance for
other degradations. For example, in the case of spectral smooth
ing (Tab. 2) with an attenuation parameter of 4, the smallest dis
tances correspond to the spectral smoothing with the parameters
3 and 5, which gives a number of misclassified pixels between
166 and 262 (the real value is 207).
Table 2: Distances for a spectral smoothing with an attenuation
parameter of 4.
Degradation
Deg.
Distance
# of misclass.
type
param.
pixels (SAM)
White noise
50
1.31986
112
White noise
100
1.40968
163
White noise
200
1.60283
255
White noise
1000
2.83994
634
Spectral smoothing
3
0.365524
262
Spectral smoothing
5
0.271982
166
Spectral smoothing
7
0.567515
123
Spatial smoothing
13
1.55253
4248
Spatial smoothing
15
1.35135
3778
Mixed smoothing
11
1.76783
4881
Gibbs
50
1.18216
698
Gibbs
100
1.22852
425
JPEG 2000
0.5
1.01159
450
JPEG 2000
1.0
0.931696
142
3.3 Unknown degradation (2nd situation)
In this second situation, let us consider some unknown degrada
tion on moffett3 image. The above examples (Tab. 1) show that,
when dealing with the same image, the smallest distance is able
to identify the degradation nature. To reinforce this, we remove
the JPEG 2000 degradation from the known situations to be able
to consider it as an unknown situation and find the nearest degra
dation to infer the number of misclassified pixels.
Distances are presented in table 3. The degradation caused by
JPEG 2000 compression at 1 bit per pixel per band (bpppb) is
identified as a mixture of a white noise with a variance of 100 and
a spectral smoothing with an attenuation of 7. This identification
corresponds to the intuitive one, looking at the diagram shape and
considering the well-known effects of JPEG 2000. The predicted
numbers of misclassified pixels are 163 and 123. The real value is
142. However, given the available possible prediction in the table,
we can notice that the diagram distance managed to select some
the closest values to the right answer to give a rough prediction.
3.4 Different images (3rd situation)
In this case, we use results obtained on mojfett3 to infer the likely
degradation on moffett4. In the case of a white noise with a vari
ance of 100, the distance between diagrams properly identifies
the degradation as a white noise (Tab. 4). The distance interprets
a white noise with a variance of 100 on mojfett4 as having the
same effect than a white noise of variance 100 on moffett3. The
predicted value of misclassified pixels is 163 whereas the real
number is 91.
