MSM) as the original image, but, as desired, a more uni-
form graylevel distribution. In fact, this image ideally at-
tains the most uniform distribution of graylevels compat-
ible with the multifractal structure of the original image.
RMI images define smaller (i.e., more compressed) codes
than FRI images; both images are very similar when the
original images are uniformly illuminated.
In Fig. 3, we present the images reconstructed from the
fields ¥ and vg defined by the MSM previously com-
puted (see section 2). This approximates the original im-
age of Fig. | with a Peak Signal to Noise Ratio (PSN R)
of 24.93 dB and PSNR = 21.34 dB respectively.
4 DISCUSSION
From the whole reconstructions displayed in Fig. 3 and the
details displayed in Fig. 4, we see that:
eo for both reconstructions, there is a high degree of smoo-
thing in rather homogeneous areas,
e main edges are preserved, even those ones being rep-
resented by small gray value changes, like inside the
culture fields,
e even if it may happen that edges between small areas
are deleted, like for small culture fields, small homo-
geneous regions are generally conserved.
The similarity between both reconstructions is mainly due
to the fact that on this kind of images (namely, land cover
images with rather linear edges induced by culture fields)
the field v does not strongly deviate from the field 7.
S0, in first approximation, the RMI could be used for pro-
viding the information about the boundaries. However, the
corresponding graylevel distributions (Fig. 4) show that the
FRI provides a good smoothed version of the original im-
age, with suppression of peaks in the distribution; whereas
the RMI provides a completely different chromatic distri-
bution. The RMI represents a different, possible view of
the same scene, with the same objects and the same ge-
ometry as the FRI, but different distributed illumination of
each part. Namely, the differences between the RMI and
the original image are only due to these differences in il-
lumination. In spite of the advantages of a more compact
code as the one associated to the RMI, we finally retain
the FRI as the convenient edge-preserving smoothing ap-
proximation of the original image: it cleans up noise in
the homogeneous areas but preserves important structures
and also preserves the luminance distribution. Besides, the
quality of the approximation of the original image is good
for the FRI, which is an essential requirement for further
processing like feature extraction. Close inspection to the
image also shows that the method is able to enhance subtle
texture regions, like small culture fields. It is clear that the
results are superior to the results of a simple method like
pixel averaging for instance.
Now, one of the major advantages of our method of pre-
segmentation is that it is parameterizable. We should no-
tice that the reconstruction algorithm for computing the
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
1128
FRI defined by the eq. (4) is linear (Turiel and del Pozo,
2002). It means that, if the reconstructing manifold is
the union of two subsets (o; U (», then the FRE, ee 7€-
constructed from this manifold equals the addition of the
FRI, and FRI. reconstructed from each part separately.
Thus, the more singular pixels the reconstructing manifold
gathers, the closer to the original image the FRI is. In par-
ticular, when the MSM consists of all the points in the im-
age, eq. (4) becomes a trivial identity and the reconstruc-
tion is perfect. So, we can approximate the original image
as close as desired. We just need to choose the density of
the manifold used for the reconstruction, i.e. we need to
adjust the range of values accepted for the singularity ex-
ponents of the pixels belonging to the MSM. By this way,
the degree of smoothing of objects in the image can be con-
trolled. On the Fig. 5, we see that the details of the image
are incorporated in the reconstruction when increasing the
authorized number of pixels in the MSM, and this is done
gradually, according to their degree of singularity.
5 CONCLUSION
In this paper, we have proposed to perform a pre-segmenta-
tion of high resolution images prior to any processing. For
this purpose, we adopt an approach related with data com-
pression and based on the multifractal analysis of images.
The main idea is that of a partial reconstruction process
of the images from the extraction of their most important
features.
The multifractal algorithm is performed in two steps, which
consist in: first, extracting the most singular subset of the
image, i.e. the set of pixels where strong transitions of the
original image occur, and, then, performing a reconstruc-
tion by propagating the graylevel values of the spatial gra-
dient of the image from this subset to the other parts. The
multiscale character of the extraction step allows to retain
the relevant edges, no matter at which scale they happen,
and without significant artifacts. The most singular sub-
set is mainly composed of pixels belonging to the bound-
aries of the objects in the image. So that, our algorithm
to reconstruct images is consistent with classical hypothe-
sis stating that edges are the most informative parts of the
image (Marr, 1982). The quality of the reconstruction de-
pends on the validity of the hypothesis defining the recon-
struction kernel and on the accuracy of the edge detection
step. It should be also noticed that this method can be used
as a starting point for a coding scheme, as it retains the
most meaningful features of the image.
The reconstruction strategy results in very nicely smoothed
homogeneous areas while it preserves the main informa-
tion contained in the boundaries of objects. It is good at
enhancing textures, as it smoothens the image, and, thus,
suppresses small elements corresponding to the main het-
erogeneity. The image structures are not geometrically
damaged, what might be fatal for further processings like
classification or segmentation. Indeed, it creates homo-
geneous regions instead of points or pixels as carriers of
features which should be introduced in further processing
stages. Moreover, the reconstruction is parameterizable.
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