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Computational Mathematics and Mathematical
Geophysics SB RAS
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The
algorithm is implemented in
software environment of system of object-oriented programming Visual
C++ versions 5.0 company Microsoft with library of classes MFC
developed for OS Windows. In software development a multiple documents
mode was used.
Considered remote sensing date has large volume, high
density and
significant correlation for different types of land cover. The
histogram approximates the probability density of this data.
The fast
nonparametric Narendra technique separates multidimensional vector
space of the features into the unimodal clusters. Modal vectors
correspond to local maxima of histogram, clusters boundaries correspond
to valleys that are areas of law density of vector space. Description of
Narendra
technique
[1] and demonstration version of its using for clustering satellite
image are brought on site
http://loi.sscc.en/lab/Weblab/LeraKlas/DEMRU/DemonEn.htm.
The Narendra
algorithm quantizes discrete vector space preliminary for reduction of
data volume and number of clusters. The automatic choice of number of
quantization levels which corresponds to best cluster
separability was proposed in [2].
The quality measure for each
individual unimodal cluster and the quality measure of the overall
distribution is calculated as an average of over all K
clusters was defined in [2] also. Measure of cluster separability
allows cluster validity for unimodal clusters disposed closely.
The nature of
investigated types of land cover is that spectral
features are combined into clusters closely verging in repressing
majority data.
But data can be heterogeneous and some areas of feature
space may be of different cluster structure and separability. New
hierarchical
algorithm proposed makes the automatic choice of different
numbers of quantization levels for various
areas of a given vector space depending on cluster separability in
them. It uses the minimization of
the average separability for
all obtained clusters. Hierarchical technique first finds
number of quantization levels at which unimodal
clusters are separated best. Then, it finds new own number of
quantization levels,
greater than beside parent, within each cluster obtained, and own best cluster
distribution, and so on.
Due separability measure of one cluster does not depend on other, the measure of separability for K sub-clusters is determined as the average separability of these sub-clusters for the hierarchical algorithm too. The goal of the proposed hierarchical algorithm is a choice of such general distribution, that the separability of the aggregate of all obtained sub-clusters is the best, when the measure of separability of all sub-clusters has reached the minimum.
For comparison, to reach the same detail of classification for melted part (n = 48), the basic algorithm (without hierarchy) have got the number of clusters K=55 and value measure of separability 0,43
Example 2
For the first stage of the hierarchy
the minimum of the cluster separability measure equal 0, 14 for
n
= 16, the number of clusters
K =7.
In Fig. 6a the
map of these clusters is shown.
The objects,
referring to water surfaces, meadows and songs are in the different
clusters. Nearly all forest objects have fallen into one big cluster 1.
In Fig.
6b the
map for the second stage of the hierarchy is shown. The number of
sub-clusters is 16.
As a result of clustering is received 55 clusters, 24 of
them pertain
to the forest. The
cluster
separability
measure
equal 0.28.
Maximum number of quantization levels is 64. Analysis
of results has shown the maps of automatic recognition correspond to
one
obtained with
use of the forest assessment.
When clusterization was carried without hierarchical
method, then minimum of the measure reached 0.38 under
n=61.
Number of clusters was 365 herewith moreover majority of them were bad
separated fine false clusters, appearing on borders of textures on
image.
References
1. Narendra
P.M. and Goldberg M. A non-parametric clustering scheme for LANDSAT.
// Pattern Recognition. 1977.
9. P. 207.
2.Сидорова В.С. Оценка качества классификации многоспектральных изображений гистограммным методом.//Автометрия. 2007.Том 43, №1, С. 37– 43.
3.
V.S. Sidorova. Unsupervised Classification of
Forest’s Image by Texture Model Features. // Pattern Recognition and Image
Analysis. 2009.Vol. 19, No.4. pp. 698 – 703
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