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1993) and Macaire et al. (Macaire et al., 2006).
With natural color images, the classification
generally leads to an over-segmented image with
small regions scattered through the image. This may
be explained by the lack of correspondence between
some peaks in the color space and significant
regions in the image, or by the merging of too small
peaks with higher ones colorimetrically close but
corresponding to inhomogenous spatial regions. To
cope with these problems, original approaches
taking into account both spatial connectivity and
color information have been proposed by (Macaire
et al., 2006) (Foucher et al., 2001) (Trémeau, 1993)
(Busin et al., 2005) (Noordam and Broek, 2000)
(Comaniciu and Meer, 2002). They have developed
original supervised or not algorithms or fixed
important axioms.
These approaches are facing the double difficulty
of treating a huge quantity of information and
dealing with a high algorithmic complexity.
In this paper we present a new contribution to
unsupervised spatio-colorimetric classification. For
several years, our laboratory has been involved in
developing classification algorithm based on
multidimensional histograms (Clément and
Vigouroux, 2003), (Ouattara and Clément, 2008).
Thanks to the compact histogram (Clément and
Vigouroux, 2001) and an original compact spatial
neighborhood probability matrix, a new
unsupervised vectorial segmentation method taking
into account the full 3D histogram and the spatial
organization of pixels has been developed. This
method is based on a hierarchical analysis of the
histogram. In a standard colorimetric approach,
colorimetic t-uples are attributed to classes
minimizing a colorimetric distance like Euclidean or
Mahalanobis. We insert here a spatio-colorimetric
distance taking into account the information of
pixels neighborhood colors. This distance is defined
as a weighed mixture between a colorimetric
distance and the spatial distance calculated from the
spatial neighborhood probability matrix. The
vectorial classification method is based on the
spatio-colorimetric distance and achieves a
hierarchical analysis of the color histogram using a
3D-connected components labeling.
In a first part, the principle of the compact
histogram is explained and the spatial neighborhood
probability matrix is detailed.
Secondly, the hierarchical unsupervised
classification method is presented and the spatio-
colorimetric distance is defined.
In a third part, the classification method has been
applied to synthetic color images with different
spatio-colorimetric results according the weight
given to spatial and color information. Real images
of plants have been tested, in order to separate
plantlets and loam.
Finally, we discuss previously obtained results,
and propose further development taking into account
the spatial information, during the classification
process, both in the decision and in the learning
steps.
2 COMPACT HISTOGRAM
Segmentation methods based on the analysis of color
histograms are facing the difficulty of treating a
huge quantity of information. For a color image of
resolution NM with each component coded on 8
bits, a standard 3D histogram is an array of 2
24
cells,
the number in each cell being coded on at least
log
2
(MN) bits in order to store the greatest number
of pixels. In the case where M=N=256, the standard
3D histogram requires 128 Mo.
A few years ago, we proposed a new way of
coding the nD histograms, leading to the so-called
compact histogram (Clément and Vigouroux, 2001).
Considering that most cells of the standard
histogram are empty, the compact histogram retains
only the C occupied cells. It consists of two arrays
(figure 1): an array of size C×3 to store the colors,
sorted out in lexicographical order, and an array of
size C×1 for the corresponding populations of
pixels. Since C is lower than MN, the compact
histogram occupies less memory space, although it
contains the full color information present in the
image. For a 256256 image with color components
coded on 8 bits, the memory space required is less
than 500 ko.
Figure 1: Example of 3D compact histogram for a RGB
color image (8 bits per component).
3 SNPM
Taking into account previous researches in spatio-
colorimetric classification such as (Trémeau, 1993)
and (Macaire et al., 2006), it is interesting to have a
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