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Comparison using a multiresolution quality criterion
It is sometimes useful, as in image restoration where we want
to evaluate the quality of the restoration, to compare images
with an objective criterion.
Very few quantitative parameters can be extracted for that.
The correlation between the original image I(i,j) and
the restored one
gives a
classical criterion. The correlation coefficient is:
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(14.95) |
The correlation is 1 if the images are identical, and less
if some differences exist.
Another way to compare two pictures is to determine the mean-square error:
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(14.96) |
Ems2 can be normalized by:
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(14.97) |
The Signal-to-Noise Ratio (SNR) corresponding to the above error is:
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(14.98) |
These criteria are not sufficient, they give no information on the
resulting resolution. A complete criterion must take into account the
resolution. For each dyadic scale, we can compute the correlation
coefficient and the quadratic error between the wavelet transforms of
the original and the restored images. Hence, we can compare, the
quality of the restoration for each resolution.
Figures 14.21 and 14.22 show the comparison of
three images with a reference image. Data20 is a simulated noisy image,
median and wave are the output images after respectively applying
a median filter, and a thresholding in the wavelet space. These curves
show that the thresholding in the wavelet space is better than the median
at all the scales.
Figure 14.21:
Correlation.
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Figure 14.22:
Signal to noise ratio.
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Next: Deconvolution
Up: The Wavelet Transform
Previous: Hierarchical adaptive filtering
Petra Nass
1999-06-15