A comparative study on multispectral agricultural images
classification using Bayesian and neural networks
approaches
B.Solaiman*,M.C.Mouchot*,R.Brown** & B.Brisco**
* Ecole Nationale Supérieure des Télécommunications de Bretagne
BP832,29285 Brest cede
x, FRANCE
(Tel: 33.98.00.13.08, Fax: 33.98.00.10.98)
** Canada Center for Remote Sensing, Application Division
588 Booth Street, 3d Fl, Ottawa, Ontario, CANADA,K1A 0Y7
(Tel:1.613.997.1262, Fax:1.613.947.1385)
Abstract
In this comparative study, the B
ayesian and a neural network (the HLVQ) approaches are used to
classify multispectral LANDSAT images. The studied area contains several agricultural classes (wheat,
flax,....). Some classes are found to be non homogeneous and thus are divided in this study
into several
subclasses. The Gaussian assumption needed by the Bayesian classifier is thus justified by this division. The
main result obtained in this study is that the Bayesian classifier and the neural network considered here provide
equivalent solutio
ns for the classification of agricultural multispectral images.
1

Introduction
In order to produce a high accuracy map of the earth's surface, the classification process, in remote
sensing, assigns each pixel (using the corresponding feature vector)
to its appropriate category of the real

world. Such maps have much potential for applications concerned with topographic mapping, agricultural
production monitoring, and environmental protection.
Several classification methods have already been proposed
. The Bayesian classifier (Maximum
Likelihood Classifier, MLC) based on Gaussian probability distribution functions for the probability estimation
in the discriminate function, is considered to be the best.
1,2
The application of neural networks into t
he classification of multispectral sensed images is
increasingly being used. This is due to the following characteristics :
1)Their ability of learning provides an interesting alternative to MLC,
2)They make no assumptions about the probabilistic model t
o be made,
3)They are capable of forming highly non

linear decision boundaries in the feature space and therefore, they
have the potential of outperforming a parametric Bayes classifier when feature statistics deviate significantly
from the assumed Gaussi
an statistics.
Recently, a comparative study for the classification of multispectral agricultural data using small size
data basis has been conducted
3
. Several conventional and neural network classifiers were tested.
Obtained results are resumed as f
ollows :
1) In terms of recognition rates, neural network classification methods based on clustering
approaches and taking into account the notion of topological neighbourhood (in determining cluster centres) are
very well suited for the classification
of multispectral agricultural data.
2) The Bayesian classifier and the Hybrid Learning Vector Quantization (HLVQ)
4
neural
network have very similar results in terms of recognition rates and generalization capacities when using small
size data basis.
In this paper, the comparative study between the Bayesian classifier based on Gaussian probability
density functions and the HLVQ neural network is detailed. The classification is conducted on a LANDSAT
Thematic Mapper (TM) sub

scene (512x512 pixels) acqui
red over the Canadian province of Saskatchewan.
Only the first 5 TM bands were used in the processing. These cover most of the visible and the near
infra

red spectrum and tend to provide a good discrimination of the different types of land use.
2

L
earning data base
In this section, the establishment of the data base used in the learning process is discussed. In fact, the
test area land contains mainly agricultural fields. From the ground truth analysis, 8 classes are defined: water,
humid area, wh
eat, flax, peas, barley, canary grass and summer fallow.
According to the spectral signatures analysis and the ground truth information, in order to obtain the
learning data base, several classes are found to be non homogeneous. Mainly, the wheat class i
s found to be
easily divided into 5 subclasses, the flax and peas classes are found to be easily divided into 2 subclasses each.
This is essentially due to two reasons. First, at the period of the year when these images were obtained
(June), the wheat, fl
ax and peas classes can be observed in different development phases. Secondly, June 1988
was a drout period, so a lot of agricultural fields were not well developed.
This observation is confirmed by establishing the histograms in the five spectral bands
for each class.
In figure.1, histograms of the five spectral bands of classes : wheat and flax are shown (Figure1.a, and 1.b.).
Figure.1.a, Histograms of the 5 spectral bands of the class wheat
Figure.1.b, Histograms of the 5 spectral bands of the class flax
Another important remark concerning these histograms is that the Gaussian assumption for the classes
: wheat, flax and peas is not justified.
Therefore, the classificat
ion problem to be considered in this study concerns 14 classes and not the
original 8 classes. The learning data base is composed of 1400 labelled input vectors. Each input vector
contains the five spectral intensities (grey levels in the spectral bands)
, and a labelling index indicating the
class membership of the vector.
The validation of the learning data base is tested as follows. Firstly, the spectral signature dynamic
range (determined by the minimum and the maximum spectral intensities values) of
each class is determined.
Secondly, spectral input vectors, of the studied area, having a spectral reflectance curve that does not match
with any of the 14 spectral signature dynamic ranges are rejected.
In figure.2, pixels for which the spectral reflect
ance curve matches at least one spectral signature
dynamic range are shown in white. Otherwise, the pixel is shown in black.
Figure.2. Validity image of the learning data base
This validity approach has sh
own that 61.4% of the pixels contained in the studied area match in one
of the 14 spectral signature dynamic ranges determined by the small size learning data base (only 1400
samples).
3

Classifiers description
The classification strategy used in thi
s study can be resumed as follows: Firstly, each classifier is
trained in order to discriminate the 14 classes: classes water, humid area, barley, canary grass, summer fallow,
5 classes representing the wheat class, 2 classes representing the flax class a
nd 2 classes representing the peas
class.
Recall that in this context of 14 classes, the Gaussian assumption is justified and therefore the
Bayesian classifier can be applied. Secondly, the classification results obtained in terms of reconstructed
images
are processed in order to group classification decisions of different sub classes into their mother classes.
This classification strategy is shown on Figure.3.
Figure.3. The classification strategy.
The two class
ifiers considered are the Bayesian classifier, using the Gaussian assumption for each of
the 14 classes, and the HLVQ neural network classification method for which no statistical assumption is made
about the probability density function distributions for
different classes.
3

1

The HLVQ neural classification method
The HLVQ neural network aims to obtain an array of cells, S, realising a topology

preserving
mapping. At the same time, those labelled cell positions must be well distributed in
N
g楶楮g good
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5
ov敲 愠
background
of the unsupervised self

organizing feature map algorithm. This means that the supervised
learning par
adigm plays the role of
"attention focusing"
applied over the unsupervised background
learning.In fact, after each input vector presentation (X), both best matching and next best matching cells are
determined.
First, the position (W
C
) of all cells in the
neighbourhood of the best matching cell are adjusted
using the unsupervised learning algorithm (1):
The decreasing step function used is given by :
(t) =
.
(t), where
is an attenuation factor
assuming small values (
[0.05,0.2]).Th楳 慬aor楴im 捡n b攠summ敲楺敤 慳o汬lws :
Step

0

Given the labelled data set { (X1,d1), ...., (Xk,dk)}, where Xk
N
, (h敲攠丽5) 慮d dk 楳 瑨攠
捯rr敳eond楮
g d敳楲ed ou瑰u琠 v散瑯r r数r敳敮瑩tg 瑨攠 捬慳c 瑯 wh楣i 瑨攠 楮pu琠 v散瑯r 填 b敬engs. Th攠
d業敮s楯ns of 瑨攠慲r慹 匬S瑨攠m慸業um numb敲 of 汥慲n楮g 楴敲慴楯ns, 瑨攠d散r敡s楮g s瑥t fun捴楯n
(t) and the
attenuation factor
are fixed.
Step

1

All cells of the map are labelled. Labelling affects to each cell C
匬S瑨攠捬慳c for wh楣i 瑨攠捥汬lw慳a
瑨攠b敳琠e慴捨楮g mor攠瑨慮 o瑨敲 捬慳c敳e
Step

2

For iteration=1,2,..
., Max_Iterations ,
A)
Learning Iteration:
for k=1,2,... ,K,
a)
Present the input vector Xk to the input,
b)
Find the best matching C* and the next best matching C" cells,
c)
The background unsupervised learning
:
cells in the neighbourhood o
f the best
matching cell are adjusted according to (1).
d
)Attention focusing
:
1)
If the three conditions of the application of the LVQ2 algorithm hold true, then cells C*
and C" are adjusted according to (2):
2)
If the be
st matching and the next best matching cells answer correctly, then the following
adjustment rule is applied :
This rule constitutes a "punishment" to the next best matching cell.
3)
If both the best matching and the next bes
t matching cells give bad classification results, a
third winning cell C3 from the neighbourhood of the C* or C" corresponding to the class of X is
searched for.
If C3 is found, then the updating rule (1) is applied to adjust the position of this cell.
If no cell corresponding to the class of X is found in the neighbourhood, the algorithm
searches a non labelled cell C3 in the same neighbourhood. If such a cell exists, then the updating
rule (1) is applied to adjust the position of this cell.
next k,
B)
Labelling iteration :
All cells of the map are labelled
,
C)
Adjust the learning rate,
Next iteration.
4

Classification results
In this section, simulation results of the classification operation are given. The topological map used
by
the HLVQ neural network is a 8x8 map. This means that the maximum number of classes prototypes is 64.
Recognition rates using the Bayesian and the HLVQ neural network classifiers are respectively given by 97.2%
and 96.2%. These rates are obtained over the
same learning data base.
Reconstructed images using input vectors of all the pixels of the studied area even rejected ones (those
having a spectral reflectance curve that does not match with any of the 14 spectral signature dynamic ranges),
are given i
n Figure.4.
Bayesian classifier
HLVQ classifier
Figure.4. Reconstructed images using the Bayesian and the HLVQ classifiers
On Figure.5, the differenc
e image between these two classification methods is given. White pixels
indicate input vectors that were classified the same by both classifiers, black pixels to rejected pixels and grey
pixels to input vectors that were classified differently by both clas
sifiers.
Figure.5, Difference image between the Bayesian and the HLVQ classifiers
Several remarks can be made at this stage :
A) The Bayesian and the neural network classifiers, give the same decision over 73% when applied to non
rejected pixels.
B
) Difference in decisions between both classifiers generally happens in a "salt and pepper" distribution.
Homogeneous agricultural fields are generally well classified by both classifiers.
C) TAB

I

shows the ground distribution decisions of both classifie
rs.
TAB

I

HLVQ Water Humid Wheat Flax Canary Summer Peas Barley
Bayesian area grass fallow
Water 0.5 0.08 0.19 0.17 0.01 0.01 0.12
0.11 1.2%
Humid
area 0.05 1.82 2.06 0.23 0.06 0.22 0.24 0.20 4.9%
Wheat 0.15 0.74 22.56 2.08 5.35 4.83 6.01 1.82 43.5%
Flax 0.01
0.07 2.32 5.44 0.16 0.09 1.97 0.22 10.3%
Canary
grass 0.01 0.05 0.74 0.43 5.2 0.45 3.18 0.07 10.1%
Summer
fallow 0.01 0.09 1.58 0.02 1.18
2.26 0.41 0.02 5.6%
Peas 0.07 0.13 1.66 2.58 0.89 0.16 9.32 1.36 16.2%
Barley 0.04 0.1 1.94 0.48 0.12 0.07 2.32 3.14 8.2%
0.9 3.1 33.0 11.4 13.0 8.1 23.6 6.9 100%
TAB

I

covers all pixels in the image (including rejected ones). Keeping in mind that some
agricultural classes, specially the class wheat, had been divided
into several subclasses, where each subclass
satisfies the Gaussian assumption, it is to be noticed that the Bayesian classifier tends to generalize its decision
concerning these classes into others.
For example, the Bayesian classifier decision concern
ing the class wheat is 43.5% of the whole studied
area.
This means that by choosing to validate the Gaussian assumption by deviding the wheat class into 5
subclasses, the intersection between different probability density functions between different cla
sses becomes
very important.
Therefore, errors in terms of classifying other classes into the wheat class would increase.
5

Conclusions
A detailed comparative study between the Bayesian and a neural network (HLVQ) classification of
multispectral
images was conducted. The test area contains mainly agricultural classes.
Several classes are found not to justify the Gaussian assumption in the estimation of the probability
density functions. Therefore, and in order to apply the Bayesian classifier,
these classes were divided into
several subclasses.
Both classifiers were trained using the same learning data base. Obtained results, in terms of
recognition rates, over the learning data base are equivalent.
When studying the generalization capacity
of both classification methods over the whole studied
scene, very similar results are obtained when applied to homogeneous regions. Nevertheless, the Bayesian
classification method seems to generalize much more than necessary when dealing with classes that
have been
divided.
Consequently, when dealing with multispectral image classification of agricultural areas, the Gaussian
assumption must be treated carefully when choosing classes to be discriminated. Also, class division into
several subclasses is of
great importance from a statistical point of view. Nevertheless, this division increases
the risk of errors in generalization.
Finally, neural networks making no assumptions on the probability density functions are well adapted
for the classification o
f agricultural areas where high variance values are encountered.
6

References
[1]
R.A.Schowengerdt," Techniques for Image Processing and Classification in Remote Sensing",Academic
Press, 1983.
[2]
K.S.Fu and T.S.Yu," Statistical Pattern Classificatio
n using Contextual Information", Research Studies
Press,1980,
[3]
B.Solaiman and M.C.Mouchot, "A Comparative Study of Conventional and Neural Network Classification
of Multispectral Data", IGARSS94, 8

12 Aug 1994, Pasadena, USA.
[4]
B.Solaiman, M.C.Mouchot
and E.Maillard," A hybrid algorithm, HLVQ, combining unsupervised and
supervised learning approaches",IEEE/ICNN94, 27Jun

1 Jul 1994, Orlando,USA.
[5]
T.Kohonen," Self

Organization and associative Memory",3d ed, 1989, Berlin :Springer

Verlag.
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