D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 546 – 553, 2006. © Springer-Verlag Berlin Heidelberg 2006

Rule-Based Expert System for Selecting Scene Matching Area

Guozhong Zhang and Lincheng Shen

College of Mechatronics Engineering and Automation, National University of Defense Technology, China

zgz_2001@sina.com

Abstract. The selection of Scene Matching Area is a key technology in mission planning of unmanned aircraft navigated by scene matching. Since many current methods didn’t consider the stability of scene area, constraint conditions of mission planning and expert knowledge, they have little credibility and cannot resist disturbance efficiently. In order to solve this problem, a rule-based expert system for scene navigability analysis with high efficiency and intelligence is presented. The principal decision rules of the system are extracted based on rough set theory. The method of certainty factor model is used to reason in the rule-based expert system. Experimental results demonstrate that the proposed system is effective and more suitable for scene navigability analysis.

1 Introduction

Scene matching system provides position-correction information for Inertia Navigation System of unmanned aircraft, which adopts Digit Scene Matching Area Correlator (DSMAC) techniques. The principle of scene matching system is summarized as follows. The geography position of reference map in scheduled aircraft’s flight course is known. If one can get the relative location of sensor map in the reference map based on the results of certain algorithm, then the actual localization of aircraft can be determined. The precision of scene matching based navigation is independent of the aircraft’s flight distance in theory. Compared with traditional navigation approaches, scene matching based navigation gives much higher accuracy and has higher autonomy.

Scene navigability analysis, is evaluating the matching and fix properties of scene area for scene matching system beforehand. According to what the matching system’s requirement for matching fix property, one can determine whether the scene area is Scene Matching Area (SMA) or not. How to select the SMA is a key technology in DSMAC system, and there is no mature scheme to resolve it at present.

As an ideal method for selecting the SMA, the unique features, stability features, expert knowledge, information of terrain classification and constraint conditions of the aircraft should all be considered. Therefore a rule-based expert system for scene navigability analysis ought to be set up.

Rule-Based Expert System for Selecting Scene Matching Area 547

2 Proposed Expert System

The basic structure of a rule-based expert system for selecting the SMA is shown in Fig. 1.

The reference map usually refers to remote sensing image. The typical set of reference maps must be built firstly when we set up rule-based scene navigability expert system. We choose 576 samples of reference map representing different regions. These samples include residential area, farmland, canal, lake, highway, airport, grassland, desert and so on. The corresponding terrains of these reference maps are plain, hill and mountainous region. The width and length of reference map are both 1200 meters.

Secondly, the reference maps should be interpreted and analyzed quantitatively, thus the database of condition attributes and decision attribute can be set up. For statistical attribute alone cannot describe the unique features of reference map, texture feature, fractal feature, entropy, non-similarity between sensor map and reference sub-map, undulating degree of terrain which corresponds to reference map should all be considered when setting up the database of condition attributes.

It is difficult to build the mathematic model of scene for navigability analysis because the relationship between scene’s space position and matching suitability is complex. Unfaithful model always leads to false evaluation of SMA’s performance. In addition, the features computed from raw scene are sometimes incomplete and inconsistent. So it is necessary to choose a powerful tool to discover knowledge of scene navigability without building any model for scene signal. Rough set is a valid mathematical theory to deal with imprecise, uncertain, and vague information [1-2]. It has been applied in such fields as machine learning, data mining, intelligent data analyzing and controls algorithm acquiring, etc. Thus, we construct decision rules from sets of condition attributes and decision attribute based on rough set theory. These rules expressed in form of production rule are main body of the scene navigability knowledge base.

The experts who work on the field of scene matching accumulate some valuable experience and common sense, which belongs to qualitative knowledge. Such knowledge cannot be gained when analyzing the raw image automatically. It is

Fig. 1. Basic structure of a rule-based scene navigability expert system

548 G. Zhang and L. Shen

necessary to integrate expert knowledge into scene navigability knowledge base. The constraint conditions of the aircraft are also important. It amounts to an increase in the credibility of rule-based expert system when considering actual constraint conditions. The corresponding terrain contour data are needed so that we can make simple classifications of terrain. The information of terrain classification, which is a kind of descriptive geoscience knowledge, reflects spatial geography phenomenon and characteristic of distribution directly.

Logical reasoning system is the embodiment of the application for knowledge acquisition, and it applies scene navigability knowledge to the selection of SMA.

3 Knowledge of the Expert System

Rough set theory has been introduced as a tool to deal with incomplete, uncertain information. It is no need to build any model for scene signal when we make knowledge acquisition for selecting SMA. Minimal expression of knowledge can be gained through a procedure of reduction of a decision table, which is based on attributes data. As for the selection of condition attributes, there are 8 features to be considered, statistical feature, fractal feature, texture feature, etc. As for that of decision attribute, the acquisition probability is chosen and it is computed on the assumption that scene signal is non-stationary process. How to evaluate acquisition probability is explained in [3]. In the analysis of scene navigability, abbreviations are used to represent attributes and are shown in Table 1. The features and acquisition probability of reference map are integrated as decision table S of navigability information system. Then firstly, it will deal with missing attribute values and discretize real data of decision table S. Secondly decision rules are mined out using some reduction algorithm [4].

Table 1. Description of attributes

Attributes Description

Var Variance of image

Entropy Entropy of image.

MD Margin density of image

RMQ Quantity of image’s repeat mode

ANQ Measurement of image’s anti-noise

RSNR Relative Signal-to-Noise of image

LHR Ratio of low-frequency energy to high-frequency energy after the wavelet decomposition of raw image

H Fractal feature of image

Navigability The acquisition probability of image

A small handful of rules for scene navigability are listed in Table 2. Each rule has associated with some numerical measures, such as accuracy and coverage, which are explained in detail in [2]. They are sorted according to accuracy. These rules read “if

Rule-Based Expert System for Selecting Scene Matching Area 549

then ” is denoted by . The pattern is called the rule’s antecedent, while the pattern is called the rule’s consequent. Intuitively, a “strong” rule is both accurate and has a high coverage. Rules with high coverage form succinct characterizations of the outcome classes, and are good for descriptive purposes. The accuracy of a rule reflects how “trustworthy” its consequent is.

Table 2. Some descision rules of scene navigability extracted based on rough set theory

Rule � Accuracy Coverage

RSNR([- , 2.41)) AND H([0.191, )) => Navigability(Bad) 0.985507 0.43038

Entropy([6.27, )) AND H([- , 0.191)) => Navigability(Good)

0.983051 0.446154

Entropy([6.27, )) AND RMQ([- , 0.116)) => Navigability(Good)

0.976744 0.323077

Var([- , 26.63)) AND H([0.191, )) => Navigability(Bad) 0.971429 0.43038

MD([0.366, )) AND H([- , 0.191)) => Navigability(Good)

0.96875 0.476923

Var([26.63, 30.96)) AND MD([0.366, )) AND H([- , 0.191)) => Navigability(Good)

0.962963 0.2

MD([0.314, 0.366)) AND ANQ([0.27, 0.36)) AND H([0.191, )) => Navigability(Bad) 0.958333 0.14557

Entropy([5.88, 6.27)) AND MD([0.366, )) AND H([- , 0.191)) => Navigability(Good)

0.952381 0.153846

…… … …

There are 734 decision rules mined out by the method of rough set theory. Accuracy and coverage of each rule has been computed. It is inadequate to analyze the matching suitability of reference map based on these rules, and corresponding expert system lacks intelligence. Heuristic knowledge of scene-matching expert, constraint conditions of the aircraft, knowledge of terrain classification should be appended to the knowledge base to increase the effectivity of expert system. For the sake of uniform expression, this knowledge is also expressed as “production rule”.

If the scenery of certain reference map varies according to seasons or there are many man-made alterations in this reference map, the expert considers that it cannot be selected as SMA even though its estimated matching suitability is good. If there is a great undulation in the terrain area or residential area included in the reference map, it cannot be selected as SMA either. The heuristic knowledge is listed as rules in Table 3. Among these rules, “Stability” represents the stability feature of scene. “TerrainSigma” represents undulating degree of the corresponding terrain.

550 G. Zhang and L. Shen

Table 3. Some Added Rules for Knowledge Base

Rule � Accuracy

Navigability(Good) AND Stability(Bad) => SMA(No) 1

Navigability(Good) AND TerrainSigma(Big) => SMA(No) 1

Navigability(Good) AND Stability(Good) => SMA(Yes) 1

Navigability(Good) AND TerrainSigma(Short) => SMA(Yes) 1

Navigability(Bad) => SMA(No) 1

�� �

4 Reasoning Method

Researchers in artificial intelligence have developed some reasoning procedures for manipulating uncertain information, such as Bayesian probability theory, Dempster Shafer (DS) theory, fuzzy logic and certainty factor model [5-6]. Certainty factor model was invented for use in the medical expert system MYCIN, which was intended both as an engineering solution and as a model of human judgement under uncertainty.

In the rule-based expert system of scene navigability analysis, the method of certainty factor model is used to reason. As has been mentioned before, we model all knowledge of this field in a set of production rules of the form E H. Such production rule has the following meaning: if evidence E has been observed, then the hypothesis H is true. An expert associates with the hypothesis H of each production rule E H a (real) number, quantifying the degree to which the actual observation of evidence E confirms the hypothesis H. All assertions being considered by this system have associated with them two numbers: measure of belief (MB) and measure of disbelief (MD) of a hypothesis H given evidence E.

−−

== otherwise

HP

HPHPEHPHPif

EHMB ,)(1

)()}(),|(max{1)(,1

)|( . (1)

−−

== otherwise

HP

HPHPEHPHPif

EHMD ,)(

)()}(),|(min{0)(,1

)|( . (2)

Certainty factors range from –1 to +1, which is given as

)|()|()|( EHMDEHMBEHCF −= . (3)

When using the production rules, however, the evidence E used may be an intermediate hypothesis that has been confirmed to some degree )|( SECF not

necessarily equalling +1; S denotes present observation. That is, it may be the case that the truth of the evidence E is not known with certainty. After application of the rule E H described above, the actual certainty factor for H is computed by means of

Rule-Based Expert System for Selecting Scene Matching Area 551

))|(,0max()|()|( SECFEHCFSHCF ×= . (4)

This computation rule is called the combination function for uncertain evidence. When 0)|( <SECF , it means that the rule’s antecedent is false, then the rule E H

will not be used. When 0)|( >SECF , it means that the rule’s antecedent is true to

some degree, then the certainty factor for H is defined by

)|()|()|( SECFEHCFSHCF ×= . (5)

Before the combination function for uncertain evidence can be applied, a certainty factor for the entire combination of evidence E has to be known. This certainty facor is computed from the separate certainty factors for each of the atomic pieces of evidences E comprises, using

)}|(,),|(),|(min{)|( 2121 SECFSECFSECFSEEECF nn =∧∧∧ . (6)

where nEEE ∧∧∧ 21 denotes the conjunction of n evidences, and

)}|(,),|(),|(max{)|( 2121 SECFSECFSECFSEEECF nn =∨∨∨ . (7)

where nEEE ∨∨∨ 21 denotes the disjunction of n evidences. These functions are

called the combination functions for composite hypotheses. When different successful production rules E BiB H (e.g. i=2), conclude on the same

hypothesis H, a certainty factor )|( 21 EEHCF ∧ is derived from the application of

each of these rules. The net certainty factor for H is computed using

{ }−+

<<⋅++

≥≥⋅−+

=∧

otherwiseEHCFEHCF

EHCFEHCFEHCFEHCFif

EHCFEHCFEHCFEHCFEHCFEHCFif

EHCFEHCFEHCFEHCF

EEHCF

,)|(,)|(min1

)|()|(0)|(,0)|(

),|()|()|()|(0)|(,0)|(

),|()|()|()|(

)|(

21

21

21

2121

21

2121

21 . (8)

This computation rule is called the combination function for co-concluding production rules.

5 Case Study

After introducing certainty factor model, we provide a small case study to exemplify how this model can be applied to analyze the scene navigability of a reference map.

A reference map XB1B to be classified is shown in Fig. 2, and its condition attributes and decision attribute are described in Table 4. The corresponding terrain is plain, and has little undulation. It means that the TerrainSigma attribute is Small. The satisfied rules are R1: A X, R2: B X, R3: X�F Y, which are described as follows:

R1: MD([0.366, )) AND RSNR([3.17, )) => Navigability(Good);

R2: Var([26.63, 30.96)) AND RMQ([- , 0.116)) => Navigability(Good); R3: Navigability(Good) AND TerrainSigma(Small) => SMA(Yes)

552 G. Zhang and L. Shen

Fig. 2. Reference map xB1 Bto be classified

Table 4. XB1B’s Attributes Described in Decision Table

Var Entropy MD RMQ ANQ RSNR LHR H Navigability

29.81 6.11 0.370 0.098 0.39 3.82 8.68 0.176 Good

Where R1 and R2 are extracted based on rough set theory, and R3 is the field knowledge of expert for scene matching. The accuracy of R1 is 0.88, and that of R2 is 0.96, and that of R3 is 1. Obviously, for this problem, the certainty factors for evidences A, B, and F are 1, namely, 1)|()|()|( === SFCFSBCFSACF . And from

evaluation of samples’ navigability, we get 45.0)( =XP .

In the expert system, let )()|( HEaccuracyEHP →= , and then we obtain

88.0)|( =AXP � 96.0)|( =BXP � 1)|( =∧ FXYP . Applying (1) to (3) to obtain

certainty factors for A and B and X�F yields

78.045.01

45.0}45.0,88.0max{)|( =

−−

=AXMB . (9)

78.0)|( =AXCF , 93.0)|( =BXCF , 1)|( =∧ FXYCF . (10)

By the combination for co-concluding production rules R1 and R2, we obtain

98.0)|( =∧ BAXCF . (11)

Making the conjunction of evidence A and B, that is

1}1,1min{)|( ==∧ SBACF . (12)

In terms of propagating principle of certainty factors, we obtain

98.0))|(,0max(98.0)|( =∧×= SBACFSXCF . (13)

Rule-Based Expert System for Selecting Scene Matching Area 553

Making the conjunction of evidences X and F, that is

98.0}1,98.0min{)|( ==∧ SFXCF . (14)

In terms of propagating principle of certainty factors, we finally obtain

98.0))|(,0max()|()|( =∧×∧= SFXCFFXYCFSYCF . (15)

It means that the certainty factor of reference map X B1 B to be SMA at present observation is 0.98.

6 Conclusions

In this paper, we present an overview of our research. Rough set theory is introduced as a useful and successful solution of data mining in scene navigability analysis. The method of certainty factor model is used to reason in the rule-based production system. We develop a novel system for selecting SMA, and collected some real scene data for testing. The future work is to enrich the knowledge base to improve the adaptability of the expert system.

References

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3. Zhang G. Z., Shen L. C., Chang W. S.: An Acquisition Probability Estimation Model of Density Correlation Scene Matching System. International Conference on Image and Graphics, Proceedings of SPIE , China, 4875 (2002) 546-551

4. Jan, G., Bazan, Andrzej, S., Piotr, S.: Dynamic Reducts as a Tool for Extracting Laws from Decision Tables. In Proc. International Symposium on Methodologies for Intelligent Systems, Lecture Notes in Artificial Intelligence, Springer-Verlag, Berlin Heidelberg , 869 (1994) 346-355

5. Heckman, D. E.: Probabilistic Iinterpretations for MYCIN’s Certainty Factors. In, Kanal L. N., Lemmer J. F. (eds.), Uncertainty in Artificial Intelligence North Holland, Holland (1986) 167-196

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