Geography Reference
In-Depth Information
form m-modal histograms in general, we approached a curve of type polynomial regression.
These polynomials have formulated by the equation 12:
=
+
+⋯+
+
(12)
where
is the degree of polynomial.
The continuous function
(the continuous line passing through the vertices of each peak of
the histogram) adjusted using the least squares method, allows to set the degree of the
number of classes centers.
4.3.2. Determination of degree n
The choice of the number of cluster centers in a radar image is difficult. In his thesis,
(Lorette, 1999) uses the entropy criterion for determining the number
of cluster centers for
the analysis of urban areas on satellite images.
As part of this project, we used a map of ancient plant formation of the study site. For this,
we proposed to re-issue the said card with latest radar image from the perspective of
studying the direction of evolution of different forest communities. In general, we decided
to use the same number of class with maps of land of the study sites in our possession.
4.3.3. Principle of threshold detection
Detection modes and valleys take place on the transformed histogram, based on the
concept of change in concavity of the curve of a function. Indeed, a curve changes
concavity through a local minimum (valley) or by a local maximum (mode). The points
where the curve changes concavity points are very sensitive and rich in information. The
detection of these on the histogram of the transformed SAR image is used to inform the
analyzer on the existence of thematic classes. Thematic classes are groups of pixels with
similar characteristics (or almost) with respect to their brightness values in the different
thematic data. The analyst has the role to determine the usefulness of different thematic
classes.
4.3.2.1. Search valleys "inter-modal thresholds"
As part of this work, identification of thresholds is conducted by analyzing the histogram of
gray levels and looking for local minima.
Our detection of these thresholds used Fisher's method which uses the criterion of
minimizing the sum of the inertia of each class. The calculation algorithm is the dynamic
type and evaluating an optimal sequence of partitions according to the scheme described in
(Cocquerez et al., 2001).
4.3.2.2. Search modes
We used to detect patterns by Bhattacharya method (Bhattacharya, 1967) that models the
histogram by a weighted sum of Gaussian and identifies each mode by its mean and
