The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
316 
• Relative RMSE 
RRMSE = 
(3) 
Note that, as the RRMSE enhances the importance of er 
rors on small values, it is important to consider the partic 
ular case of values below the sensor noise. Small values of 
I(x, y, A) can be considered as random and are ignored for 
the computation of the RRMSE. 
• Spectral Fidelity [Eskicioglu and Fisher, 1995] 
F\ = min |F . (4) 
with 
F{U,V) = 1 — 
CliU-V) 
Cl{U) • 
Q(x,y) [Wang and Bovik, 2002] 
Q(x, y ) = min {Q (/(•, -, A),/(-, -, A)) |. 
Q(U,V)=; 
( a U + cr v)(h L lJ F P’v) 
where auv is the covariance between U and V. 
(5) 
(6) 
(7) 
All these criteria measure a distance between an original image 
and a degraded version of this image. 
Representing a combination of five values is a challenge and work 
ing on a five-dimensional plot would not enable efficient assess 
ment. A good way to represent these values is to use a star dia 
gram (Fig 2) which gives a more intuitive vision than a classical 
x-y representation in this case. The five axes of the diagram cor 
respond to the five quality criteria. Scale for all the figures in this 
paper are the same. For MAD, MAE and RRMSE, origin cor 
responds to 0 (no degradation). The extremity of the axes corre 
sponds to value 5000 for MAD, 40 for MAE and 0.1 for RRMSE. 
For F\ and Q( x , y ), origin corresponds to 1 (no degradation), ex 
tremity being 0.9 for F\ and 0.6 for Q( XtV ). These values were 
found to provide a good differentiation between different degra 
dations. These specific values are important for visualization and 
comparison, they are not important by themselves, it is just neces 
sary to use the same scales on the different figures. The shape of 
the diagram is characteristic of the degradation as seen in figures 
2, 3 and 4. 
Parameters for the degradation are presented in [Christophe et al., 
2005]. Basically, this is the variance for the white noise, the filter 
size for the smoothing, the scale factor for the Gibbs filter, and 
the compression rate for JPEG 2000. 
2.2 Shape characterizes the degradation 
This representation is robust relatively to the amplitude of the 
degradation. The shape is similar for a given degradation; the 
degradation pattern is inflated when the degradation level increases 
(Figs. 2-4). For example in Fig. 2, the innermost shape (green) 
corresponds to a white noise with a low variance. When the noise 
variance increases, the quality decreases and the quality diagram 
dilates. 
MAE 
Figure 2: Quality for different values of additive white noise on 
moffett4 image. 
MAE 
Figure 3: Quality for different values of spatial smoothing on 
mojfett4 image. 
MAE 
Figure 4: Quality for different values of spectral smoothing on 
moffett4 image.