Segmentation d'images couleur par un opérateur gradient vectoriel ...

QUANTIFICATION ET MORPHOLOGIE DE PHASES DE CLINKER PAR ANALYSE D'IMAGE.
level in the local structure). The following different feature families for the classification of alite
and belite crystals are considered:
• Histogram features which describe the grey-level distribution in the analysing
window.
• Features calculated on the neighbourhood matrix [Haralick et al., 1973] which
measure in a limited neighbourhood the coarseness or busyness of a micro-texture.
• Features calculated on the run lengths matrix [Galloway, 1975] which measure the
length, the number and the distribution of the grey-level runs in the analysing window
and allow detection of the degree of homogeneity or heterogeneity.
• Cooccurrence features [Haralick et al., 1973], which describe the repetition of greylevel
changes, measured for pairs of points in a typical distance and direction. Microtextures
and the Macro-textures can be detected preserving the directionality of each
texture.
• Frequency features (repetition rate of a micro-texture) can be calculated by a
frequency transformation (Fourier- or Cosine-transform [Liu et al., 1990]) of the
image window. These features evaluate the distribution of the frequencies and the
directionality of the texture.
The six families group a huge number of characteristic features or parameters. Some of
the parameters are correlated, others are redundant in the different groups and may be excluded.
The parameter signature obtained in this way will be used for the classification of each window.
Discriminating analysis [Rao, 1952]
A combination of the features can be found by the Multivariable Discriminating Factorial
Analysis (MDFA). It creates a synthetic index, which allows the best separation of the two
textures (alite and belite). This index is a linear combination of the texture features and takes into
account the whole information. The best results are obtained for a combination of six features. A
larger number does not increase the classification result but only introduces noise to the analysis.
The feature selection depends on the size of the window. The most discriminate feature is the
entropy of the test-window.
The MDFA is a statistical analysis and needs a huge learning database. As database, 30
images with about 3000 test-windows for the two kinds of crystals were chosen. Figure 44 shows
the histogram of the synthetic texture index computed by the MDFA on the learning base. The
distribution shows that the texture index is sufficiently different for the two textures alite and
belite, enabling the classification of the majority of the observation-windows. Note that there is
an uncertain zone in which the decision is not possible. This zone represents less than 30% of
the total population.
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