【免费】论文研究-利用卫星图像的合理和悖论推理理论对植被，水生和矿物表面进行建模和表征：科特迪瓦V包卢省Toumodi-Yamoussoukro-Tiébissou区的案例资源-CSDN文库

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Open Journal of Applied Sciences, 2017, 7, 520-536

http://www.scirp.org/journal/ojapps

ISSN Online: 2165-3925

ISSN Print: 2165-3917

DOI:

10.4236/ojapps.2017.710038 Oct. 26, 2017 520 Open Journal of Applied Sciences

Modeling and Characterization of Vegetation,

Aquatic and Mineral Surfaces Using the Theory

of Plausible and Paradoxical Reasoning from

Satellite Images: Case of the

Toumodi-Yamoussoukro-Tiébissou Zone in V

Baoulé (Côte d’Ivoire)

Jean-Claude Okaingni

1,2

, Sié Ouattara

1,2

, Adles Kouassi

1,2,3

, Wognin J. Vangah

1,2

Aubin K. Koffi

1,2

, Alain Clement

Laboratory of Signals and Electrical Systems (L2SE), Institut National Polytechnique Houphouët Boigny,

Yamoussoukro, Cote D’Ivoire

Institut National Polytechnique Houphouët Boigny (INPHB), Yamoussoukro, Cote D’Ivoire

Ecole Supérieure des Technologies de l’Information et de la Communication (ESATIC), Abidjan, Cote D’Ivoire

Institut Universitaire de Technologie d’Angers (IUT), Angers, France

Abstract

In this paper, the theory of plausible and paradoxical reasoning of Dezert

Smarandache (DSmT) is used to take into account the paradoxical character

through the intersections of vegetation, aquatic and mineral surfaces. In order

to do this, we developed a classification model of pixels by aggregating inform

tion using the DSmT theory based on the PCR5 rule using the

NDVI

MNDWI

and

NDBaI

spectral indices obtained from the ASTER satellite im

ages. On the

qualitative level, the model produced three simple classes for cer

tain knowledge

(E, V, M) and eight composite classes including two union

classes characterizing

partial ignorance ({E,V}, {M,V}) and six classes of intersection of which three

classes of simple intersection (E∩V, M∩V, E∩M) and three classes of comp

site intersection (E∩{M,V}, M∩{E,V}, V∩{E,M}), which represent paradoxes.

This

model was validated with an average rate of 93.34% for the well-classified pi

els and a compliance rate of the entities in the field of 96.37%.

Thus, the model 1

retained provides 84.98% for the simple classes against

15.02% for the composite

classes.

Keywords

Theory of Plausible and Paradoxical Reasoning, PCR5 Rule, ASTER Satellite

How to cite this paper:

Okaingni, J.-C.,

Ouattara, S

., Kouassi, A., Vangah, W.J.,

Koffi, A

.K. and Clement, A. (2017) Model-

ing and Characterization of Vegetation,

Aquatic and Mineral Surfaces Using the

Theory of Plausible and Paradoxical Re

soning from Satellite Images : Case of the

Toumodi

-Yamoussoukro-Tiébissou Zone

V Baoulé (Côte d’Ivoire)

Open Journal of

Applied Sciences

, 520-536.

https:

//doi.org/10.4236/ojapps.2017.710038

Received:

September 21, 2017

Accepted:

October 23, 2017

Published:

October 26, 2017

7 by authors and

Scientific

Research Publishing Inc.

This work is licensed under the Creative

Commons Attribution International

License (CC BY 4.0).

J.-C. Okaingni et al.

DOI:

10.4236/ojapps.2017.710038 521 Open Journal of Applied Sciences

Images,

NDVI

MNDWI

NDBaI,

Modeling, Classification

1. Introduction

The surface state of the Earth can be represented in remote sensing by three ent-

ities that are vegetation surfaces, aquatic surfaces and mineral surfaces. Any sur-

face area observed, depending on the size of the area, may be a combination of

these three entities.

Thus, it can be observed vegetation surface, aquatic surface, mineral surface,

vegetation and aquatic surface, vegetation and mineral surface, mineral and aq-

uatic surface, vegetation, mineral and aquatic surface.

The use of satellite images, for mapping purposes, has been the subject of sev-

eral studies ([1] [2] [3] [4]). Researchers have used spectral indices to map vege-

tation surfaces, aquatic surfaces, and surfaces of bare soil and mansions.

These indices were used for image classification. Unfortunately, imperfections

(uncertainties, inaccuracies, etc.) on the information produced by the images

associated with said indices are observed ([5] [6]). Taking into account and good

management of these imperfections are done by the theory of belief functions.

The Dempster-Shafer theory has been used successfully to handle cases of un-

certainty, vagueness and ignorance in the classification of pixels to classes of ve-

getation surface, aquatic surface and mineral surface [4].

In this article, the theory of plausible and paradoxical reasoning of Dezert-

Smarandache (DSmT) is used to take into account the paradoxical character through

the intersections of the elements vegetation surface, aquatic surface and mineral

surface.

The general objective of the study is to develop a model of pixel classification

by aggregating information using the DSmT theory, spectral indices

NDVI

(Nor-

malized Difference Vegetation Index),

MNDWI

(Modification of Normalized Dif-

ference Water Index) and

NDBaI

(Normalized Difference Bare Index) and ASTER

satellite images. It acts specifically first, to model the frameworks of discernment

and reasoning and belief functions, then define the decision criteria and write

algorithms and programming codes under the MATLAB software; finally realize

and evaluate classified image.

The contribution of this study is to give an approach of unsupervised classifi-

cation of mapping that takes into account the plausible and paradoxical charac-

teristics related to the information of ground that is to say without needing to

know the real spatial state of the ground concerned.

This paper, which proposes to report on the work carried out, presents succes-

sively the theory of plausible and paradoxical reasoning of Dézert-Smarandache,

the material used, the methodological approach that guided the work and the re-

sults obtained.

J.-C. Okaingni et al.

DOI:

10.4236/ojapps.2017.710038 522 Open Journal of Applied Sciences

2. Principle and Formalism of DSmT

Dezert-Smarandache theory (DSmT) is interpreted as a generalization of the

theory of Dempster-Shafer (DST) ([7]). Its basic principle and formalism for ag-

gregating information can be characterized by a four-stage structure of modeling,

estimation, combination and decision.

Modeling consists in choosing the representation of the frameworks of dis-

cernment and reasoning and the models of the mass functions to be used.

The discernment framework

{ }

θθ

Θ= 

of DSmT is an exhaustive set of

different hypotheses, not necessarily exclusive assumptions. The reasoning frame-

work

associated, also called hyper-powerset, is the set of all possible proposi-

tions constructed from the elements of Θ, including the empty set (

), with the

operators

∪ and ∩. It is characterized by the following conditions ([8]):

,, ,

φθ θ

∈

2) If

∈

AA D

then

∩∈

AAD

and

∈

AAD

3) There are no other elements belonging to

, except those obtained using rules

1 or 2.

The construction of the reasoning framework

can be obtained by a matrix

product between the binary matrix of Dedekind and the coding vector of Sma-

randache ([1] [7]). Its cardinal increases according to the cardinal of the discern-

ment framework on which it is based.

In order to fix ideas, it is considered the cardinal of Θ equal to 3. Thus, ac-

cording to Dedekind ([9]), the cardinal of

is equal to 19. Then we get ([1]):

{

}

123

θθθ

Θ=

{

( )

}

1231 22 31 31 2 31 2

2 31 31 2 3 3 1 2 2 1 3

2 1 33 1 21 2 3

13 12 23123

,,,,,,, ,,

,,,,,

,,,

φθθθθ θθ θθ θθ θ θθ θ

θθθθθ θθθ θθθ θθ

θ θθθ θθθ θθ

θθ θθ θθθθθ

= ∪ ∪∪∪∪∩

∩ ∩ ∩∪ ∩∪ ∩∪

∪∩ ∪∩ ∪∩

∩∪∩∪∩ ∩∩

In general, we define a generalized mass function

with values in [0,1]

satisfying the following conditions of Equation (1):

( )

() 1

∈











∑

(1)

where

is the empty set. The value

(

) quantifies the belief that the class

sought belongs to the subset

(and to no other subset of

). The subsets

such that

(

) > 0 are called focal elements.

The following special mass functions are defined ([10]):

 a mass function

is said to be normal when

(

) = 0;

 a mass function

is said to be categorical when it has a single focal element

such that

(

) = 1. In the case where

is a set, knowledge is certain but

imprecise.

When

= {



}, knowledge is certain and precise;

J.-C. Okaingni et al.

DOI:

10.4236/ojapps.2017.710038 523 Open Journal of Applied Sciences

 a mass function

is said to be empty (or total ignorance) when the func-

tion

is categorical in Θ:

(Θ) = 1;

 a mass function

is said to be Bayesian if all the focal elements are single-

tons of Θ in

Equation (2):

( )

∈Θ

∑

; (2)

 a mass function

is said to be dogmatic if

(Θ) = 0;

 a mass function

is said to be consonant if all the focal elements are nested;

 a mass function

is said to have a simple support when it has 2 focal ele-

ments, one of which is Θ

(Equation (3)):

( )

(

)

0, \



=−∈



Θ=





= ∀∈





mA A D

mB B D A

(3)

In this case, the function

can also be denoted

where

represents the

weight of the ignorance of the mass function

The estimation consists in determining all the parameters of the mass func-

tions selected at the modeling stage. This is a difficult problem that does not have a

universal solution. The difficulty is further increased if we want to assign masses

to compound hypotheses involving intersections and/or unions ([11]).

The combination is the grouping phase of the information, from the mass func-

tions of the different information sources, using an operator adapted to the for-

malism of the modeling. The DSmT has two types of combination ([12]): the clas-

sic version and the hybrid version. Consider

initial mass functions

, ,,

mm m

representing the respective information of

different sources, which can be com-

bined according to the DSmT.

The classic combination of DSmT is (Equation (4)):

( )

( ) ( )

( )

11 2 2

1, , ,

θθ

∩ ∩∩ =

= ∗ ∗∗

= ∈ ∀∈

∑



AA AC

mC m A m A m A

Ai n D C D

(4)

The hybrid combination of DSmT is used in the presence of integrity con-

straints applied to

. An integrity constraint of a set

is an impossibility of

considering a mass assignment to this set ([12]). The mass of the set

is then

assigned to the empty set

. Thus, the hybrid combination is defined ([13]) by

Equations (5)-(8):

( )

( ) ( ) (

) ( )

123

= ∗ + + ∀∈





mA A HAHAHA AD

(5)

( ) (

) ( )

( )

1 11 2 2

1, ,

= ∈

∩ ∩∩ =

= ∗ ∗∗

∑



Xi n D

X X Xn A

HA mX mX mX

(6)

( ) ( )

( )

2 11 2 2

1, ,

)

= =

= ∈



  

= ∨ ∈∧=Θ









  



= ∗ ∗∗

∑







Xi n

uX A uX A

H A mX mX mX

(7)

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