(a)
(b)
Figure 10: The result after bilateral filtering with SEF and
α = 0.25 is in (a) (PSNR=19.6dB). Outliers sill remains due
to the fact that the corresponding ρ function is non convex.
However, a better result is obtained in (b) using GNC strat-
egy (PSNR=28.1dB).
M-estimators that achieve the maximum breakdown
point of approximately 50%, and that the robustness
associated with SEF increases towards the maximum
as α decreases towards 0.
In the second part of this paper, we illustrated how
useful these results are in the context of image analy-
sis: SEF and GTF approximate models seems to cor-
rectly fit observed noise pdfs in diverse applications
and contexts. Moreover, many image analysis prob-
lems can be seen as parametric estimation or cluster-
ing. In the applications we shown (curve fitting and
edge-preserving image smoothing), we observed the
advantage of varying the noise model, progressively
introducing robustness, with the so-called GNC strat-
egy. We therefore believe that the SEF and GTF fam-
ilies can also be used with advantages in many other
image analysis algorithms.
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