Ontological Intelligent Agent for Impulse Noise Removal
Chang-Shing Lee1,*, Mei-Hui Wang2, and Chin-Yuan Hsu31 Department of Computer Science and Information Engineering, National University of Tainan,
Tainan 700, Taiwan leecs@mail.nutn.edu.tw
2 Department of Computer Science and Information Engineering, National University of Tainan,
Tainan 700, Taiwan
mh.alice.wang@gmail.com
3 Advance e-Commerce Institute, Institute for Information Industry
Tainan 700, Taiwan hsucy@iii.org.tw
Received 27 February 2007; Revised 26 March 2007; Accepted 30 March 2007
Abstract. This paper presents an ontological intelligent agent to remove impulse noise from highly corrupted images. It contains an image noise ontology to represent the image noise knowledge for the agent, a fuzzy inference mechanism for noise detection and removal, and an intelligent learning process for automatically generating the fuzzy numbers of the agent. The working environment for the intelligent agent is defined and the image noise ontology referred by the fuzzy inference mechanism is utilized to perform the task of noise removal. Then, using orthogonal array and factor analysis, a genetic algorithm is applied to the intelligent learning process. Finally, the fuzzy numbers of the image noise ontology are adjusted via the intelligent learning process to increase the performance of the intelligent agent. Experimental results show that the proposed approach can achieve better results than the state-of-the-art filters based on the criteria of Mean-Absolute-Error and Mean-Square-Error. Besides, on the subjective evaluation of those filtered images, the proposed approach can also generate a higher quality of global restorations.
Keywords: Ontology, Intelligent Agent, Fuzzy Inference, Genetic Learning, Image Processing
1 Introduction
The ontology is a computational model of some portions of the world. It is a collection of key concepts and their inter-relationships collectively providing an abstract view of an application domain [1]. In addition, ontology is no longer a mere research topic, but its relevance has been recognized in several practical fields. Recently, the research on the ontology has been spread widely to be critical components in the knowledge management, Semantic Web, business-to-business applications, and several other application areas [2]. For example, in [1] and [3], Lee et al. proposed a fuzzy ontology application to news summarization and a genetic fuzzy agent using the ontology model for meeting scheduling system, respectively. Alani et al. [4] proposed an automatic ontology-based knowledge extraction from Web documents and used it to generate personalized biographies. Burstein [5] presented a dynamic invocation of semantic web services using unfamiliar ontologies. Hameed et al. [6] presented an approach to acquire knowledge and construct multiple experts’ ontologies in a uniform way. Navigli et al. [7] presented an OntoLearn system for automated ontology learning to extract relevant domain terms from a corpus of text, relate them to appropriate concepts in a general-purpose ontology, and detect taxonomic and other semantic relations among the concepts.
An agent is a physical or virtual entity that is capable of acting in an environment and communicating directly with other agents. The concept of the action is based on the fact that the agents carry out actions, which are going to modify the agents’ environment, and the future decision making [1][8]. There are many various definitions for an agent. For example, an agent possesses skills and can offer service, it iscapable of perceiving its environment, it is driven by a set of tendencies, and so on [8].Furthermore, an intelligent agent is more powerful than an agent because of the reasoning and learning capabilities [9]. Delen and Pratt designed and developed an intelligent
machine learning mechanism for web mining [11]. Lee et al. proposed a genetic fuzzy agent for meeting scheduling system [3]. Wang applied the concept of agent-based control for networked systems in control theory to traffic and transportation management [12]. Yan et al. proposed a perceptron-based medical decision support system for the diagnosis of heart diseases [13]. Grossklags and Schmidt studied how software agents affect the market behavior of human traders [14].
An image may be corrupted during the process of image transmission, so that a number of approaches have been developed for removing impulse noise from corrupted image. For example, the median filter [15] performs well for low corrupted image, but it does not work efficiently when noise rate is above 50%. Eng et al. [16] presented a novel switching-based median filter to remove impulse noise and preserve signal details. Abreu et al. [17] proposed an efficient nonlinear algorithm, called signal-dependent rank ordered mean (SD-ROM) filter, to suppress impulse noise from highly corrupted images while preserving details and features. Russo [18] presented the hybrid neuro-fuzzy filters for highly corrupted impulse noise removal. Wang et al. [19] presented a histogram-based fuzzy filter (HFF) to the restoration of noise-corrupted images, which is particularly effective at removing highly impulsive noise while preserving image details. Lukac [20] proposed an adaptive vector median filter for impulse noise suppression and outliers rejection in multi-channel images. Pok et al. [21] proposed a decision-based, signal-adaptive median filtering algorithm for removal of impulse noise. Chang et al. [22] proposed a classifier-augmented median filter for impulse noise removal from images. Liu [23] proposed a fuzzy neural network filter for impulse noise removal from images. Lin et al. [24] proposed a multi-channel filtering by gradient information for impulse noise removal from images. Ng and Ma [25] proposed a switching median filter (SMF) to effectively remove noise from the extremely corrupted image. Lee et al. proposed a genetic-based fuzzy image filter (GFIF) [27], a multi-dimension genetic fuzzy filter (MGFF) [28], and an ontology-based genetic fuzzy filter (OGFF) [26] to remove impulse noise from highly corrupted images and preserve the quality of fine details and textures. W. Luo [29] proposed an efficient impulse detection algorithm (EIDA) to remove impulse noise.
In this paper, we propose an ontological intelligent agent (OIA) based on the GFIF and OGFF filters to remove impulse noise from highly corrupted images. The proposed agent consists of an image noise ontology to represent the image noise knowledge for the intelligent agent, a fuzzy inference mechanism for noise detection and removal, and an intelligent learning process to automatically generate the fuzzy numbers stored in the ontology for the agent. Through the constructed noise ontology and the technique of noise detection, the OIA can automatically generate the optimal parameters for the fuzzy inference mechanism and use the orthogonal array to help the learning process of the OGFF. From the experimental results, the proposed ontological intelligent agent not only performs better than our previously proposed works [27][28] and other works [18][25][29], but also largely outmatches the state-of-the-art methods in the literature. The reminder of this paper is organized as follows. In Section 2, we describe the intelligent agent based on the image noise ontology, including the ontology structure, the image noise ontology construction for ontological intelligent agent, and the ontological intelligent agent. Section 3 describes the intelligent genetic learning process for the ontological intelligent agent. The experimental results are shown in Section 4. Finally, conclusions are drawn in Section 5.
2 The Intelligent Agent based on Image Noise Ontology
This paper proposes an ontological intelligent agent for image processing. First, the structure and construction of the image noise ontology for the intelligent agent are briefly described in Section 2.1 and 2.2, respectively. Then, we present the intelligent agent in Section 2.3.
2.1 Ontology Structure
Fig. 1 shows the domain ontology structure adopted in this paper, including the domain layer, the category layer, the sub-category layer, and the class layer. The domain ontology contains three types of relationships, namely the “generalization,” the “aggregation,” and the “association.” The “generalization” relation denotes a semantic relationship between the domain name and the categories in the category layer. The “aggregation” relation denotes a semantic relation among the category layer, the sub-category layer, and the class layer. The relationship between two concepts in the class layer is the “association.” The domain layer represents the domain name of an ontology, and comprises various categories defined by domain experts. The category layer defines several categories, namely “category 1, category 2, …, category k.” Each concept in the class layer, contains a concept name C , an attribute set i { }
i i
i1 Cq
C , ,A
A L and an operation set { }
i i i1 Cq C , ,O O L for an application domain [1].
… … Domain Layer Category Layer Domain Class Layer C3 A C31,AC32 ,…,AC3q3 OC3 1 ,OC31 ,…,OC3q3 C2 AC21,AC2 2 ,…,AC2q2 O C2 1 ,OC2 1 ,…,OC2q2 … Generalization Aggregation C : Concept A : Attribute O : Operation Cm ACm1,ACm2,…,ACmqm OCm1 ,OCm1,…,OCmqm C1 AC11,AC1 2 ,…,AC1q1 OC1 1 ,OC11,…,OC1q1 C4 AC41,AC42,…,AC4q4 OC41,OC41,…,OC4q4 C5 AC51,AC52,…,AC5q5 OC51,OC51,…,OC5q5
Category 1 Category 2 Category 3 Category k
SubCategory 1 SubCategory 2 SubCategory 3 SubCategory k SubCategory Layer
Association
Fig. 1. Structure of domain ontology
2.2 Image Noise Ontology Construction for Ontological Intelligent Agent
In this section, we developed the image noise ontology for the OIA, based on the Knowledge-Engineering methodology [30]. The steps of the developing the image noise ontology are listed as below.
Step.1 Determine the domain and scope of the ontology. Step.2 Consider reusing existing ontologies.
Step.3 Enumerate important terms in the ontology. Step.4 Define the classes and the class hierarchy. Step.5 Define the properties of classes-slots. Step.6 Define the facets of the slots. Step.7 Create instances.
Fig. 2 shows the image noise ontology for the OIA. This image noise ontology has five layers, called the domain layer, category layer, sub-category layer, fuzzy variable layer and linguistic term layer. The domain name is the “image noise ontology.” The category layer has several categories such as the “Additive Impulse Noise”, “Uniform Mixed Noise”, and so on. The next layer, sub-category layer, also has some sub-categories such as “Salt & Peppers Noise”, “Additive Long-tailed Noise”, “Additive Middle-tailed Noise”, and so on. In the Fuzzy Variable Layer and Linguistic Term Layer, each concept contains a concept name, an attribute set and an operation set for an application domain. For example, a Fuzzy Luminance concept has concept name, “Fuzzy Luminance,” and its attributes are “Linguistic Term 1,” “Linguistic Term 2,” …, and “Linguistic Term n.”
In this paper, we adopted the trapezoidal function to be the membership function. The trapezoidal membership function fA(x:a,b,c,d) of fuzzy set A is represented as A = [a, b, c, d] and shown in (1). Fig. 3 illustrates an example for the luminance fuzzy variable with five linguistic terms. The membership degree is usually a value in the range [0, 1], where “1” denotes a full membership, and “0” denotes no membership. There are five fuzzy numbers “VDK,” “DK,” “MD,” “BR,” and “VBR” to denote the linguistic terms “Very Dark,” “Dark,” “Medium,” “Bright,” and “Very Bright,” respectively, for the gray level image.
≥ < ≤ − − < ≤ < ≤ − − < = d x 0 d x c c d x d c x b 1 b x a a b a x a x 0 d c b a x fA , ), /( ) ( , ), /( ) ( , ) , , , : ( (1)
Image Noise Ontology
Additive Impulse Noise Uniform mixed Noise
Salt & Pepper Noise
Additive Middle- tailed
Noise
Fuzzy Variable Layer
Linguistic Term Layer
Fuzzy Luminance Linguistic Term 1: string Linguistic Term 2: string
…
Linguistic Term n: string
…
…
Additive Long -tailed Noise Additive Short -tailed Noise Uniformly Random Noise Noise type name:string ratio:string Image Name:string imageFormat:string imageType:string Filter Name:stirng fuzzySet:string fuzzyRule:string fuzzyHedge:string Parameter Domain Layer Category Layer Sub-Category Layer Fuzzy Difference Linguistic Term 1: string…
Linguistic Term n: string
Fuzzy Mean Linguistic Term 1: string
…
Linguistic Term n: string Fuzzy Rule
Rule 1: string … Rule n: string
Fuzzy Hedge Linguistic Hedge 1: string
…
Linguistic Hedge n: string
Very Dark α : string β : string γ : string δ : string Dark α : string β : string γ : string δ : string Median α : string β : string γ : string δ : string Bright α : string β : string γ : string δ : string Very Bright α : string β : string γ : string δ : string α : string β : string γ : string δ : string α : string β : string γ : string δ : string Mean Very Dark hedge: string Dark hedge: string Median hedge: string Bright hedge: string Very Bright hedge: string R1: string … Rn: string Small Large
Very Dark α : string β : string γ : string δ : string R1: string … Rn : string Dark R1: string … Rn : string Median R1: string … Rn : string Bright R1: string … Rn : string Very Bright
membership degree gray level 1 VDK DK MD BR VBR 0 255
Fig. 3. The luminance fuzzy variable with five linguistic terms
2.3 Ontological Intelligent Agent
This section describes the ontological intelligent agent (OIA) for image processing. First, we define the working environment for the intelligent agent as follows. The signal space ζ of the OIA is a set of digital signals together with five operators, namely the arithmetic sum, the arithmetic difference, the bounded sum, the bounded difference and the scalar multiplication[31]. The gray level of each signal is represented by an n-bits value so it is ranged in [0 ,2n−1]. The bounded sum associates two signals x ,y∈ζ with a signal x⊕ y∈ζ where the operator ⊕ is the bounded sum of two signals x and y. The bounded difference associates two signals x ,y∈ζ with a signal xΘy∈ζ , where the operator Θ is the bounded difference between two signals x and y. The scalar multiplication associates a signal x∈ζ and a scalar λ∈[ 10 , ] with a signal λx∈ζ calculated by the arithmetic multiplication of signal x and scalar value λ.
[Definition 1] Fuzzy Signal Space for OIA
A fuzzy signal space is a signal space whose partitions are determined by fuzzy numbers stored in the ontology. The partitions of the fuzzy signal space, including fuzzy normal subspace, fuzzy negative subspace, fuzzy positive subspace and fuzzy undecided subspace, are determined using the following four fuzzy numbers:
1. The fuzzy number OIA_normal of fuzzy normal subspace is defined as follows: OIA_normal = [αnor ,βnor ,γnor ,δnor]
2. The fuzzy number OIA_negative of fuzzy negative subspace is defined as follows: OIA_negative =[αneg ,βneg ,γneg ,δneg]
3. The fuzzy number OIA_positive of fuzzy positive subspace is defined as follows: OIA_positive = [αpos ,βpos ,γpos ,δpos]
4. The fuzzy number OIA_undecided of fuzzy undecided subspace is defined as follows: OIA_undecided = [αund ,βund ,γund ,δund]
Fig. 4 shows the structure of the OIA. First, a noise-free image is input to learn the best parameters of the image noise ontology during the intelligent learning process. Meanwhile, this intelligent learning process also retrieves the information stored in the image noise ontology to perform the learning process, and then restores the learning parameters back to the image noise ontology. The structure of the fuzzy inference mechanism consists of three layers, including the fuzzy linguistic layer, the fuzzy term layer, and the rule layer [27]. There are three kinds of nodes in this inference mechansim, including the fuzzy linguistic nodes in the fuzzy linguistic layer, the fuzzy term nodes in the fuzzy term layer, and the rule nodes in the rule layer. A fuzzy linguistic node represents a fuzzy variable. A fuzzy term node represents the mapping degree of the fuzzy variable. A rule node represents a rule and decides the final firing strength of that rule during inferring. The fuzzy linguistic nodes just directly transmit input values to the next layer. Each fuzzy variable of the fuzzy linguistic layer appearing in the premise part is represented with a condition node. Each of the outputs of the condition node is connected to the rule nodes in the rule layer to constitute a condition specified in some rules. The fuzzy term layer performs the first inference step to compute matching degrees. The links in the rule layer are used to perform precondition matching of fuzzy logical rules. The fuzzy inference rules are listed in Table 1. The fuzzy mean process performs the fuzzy mean of input variables F_mean. There are five computation functions including f (⋅), f−(⋅),
x1 x5 x 9 RVDK RMD RVBR … … … … Layer1 Fuzzy Linguistic Layer Layer2 Fuzzy Term Layer Layer3 Rule Layer fcomp( ‧) … … f-(‧) flarge fsmall fx 1(.) fx2(.) f+(‧) y
Image Noise Ontology
Additive Impulse Noise Uniform mixed Noise
Salt & Pepper Noise
Additive Middle- tailed
Noise
Fuzzy Variable Layer
Linguistic Term Layer
Fuzzy Luminance Linguistic Term 1: string Linguistic Term 2: string
…
Linguistic Term n: string
Selection Evaluation Module Begin Initiation Current Population New Population replace elitism Y Output Image
and the parameters Crossover Mutation X (Noise Image) … … Additive Long -tailed Noise Additive Short -tailed Noise Uniformly Random Noise Noise type name:string ratio:string Image Name:string imageFormat:string imageType:string Filter Name:stirng fuzzySet:string fuzzyRule:string fuzzyHedge:string Parameter Domain Layer Category Layer Sub-Category Layer Fuzzy Difference Linguistic Term 1: string
…
Linguistic Term n: string
Fuzzy Mean Linguistic Term 1: string
…
Linguistic Term n: string Fuzzy Rule
Rule 1: string … Rule n: string
Fuzzy Hedge Linguistic Hedge 1: string
…
Linguistic Hedge n: string
Very Dark α : string β : string γ : string δ : string Dark α : string β : string γ : string δ : string Median α : string β : string γ : string δ : string Bright α : string β : string γ : string δ : string Very Bright α : string β : string γ : string δ : string α : string β : string γ : string δ : string α : string β : string γ : string δ : string Mean Very Dark hedge: string Dark hedge: string Median hedge: string Bright hedge: string Very Bright hedge: string R1: string … Rn: string S (Noise-free Image)
Fuzzy Inference Mechanism
Small Large
Very Dark α : string
β : string γ : string δ : string R1: string … Rn : string Dark R1: string … Rn : string Median R1: string … Rn : string Bright R1: string … Rn : string Very Bright
Intelligent Learning Process
fF_mean(.)
Fig. 4. Structure of Ontological Intelligent Agent
Table 1. Fuzzy inference ruels
Rule VDK: IF (x is VDK with weight 1 w ) AND (11 x is VDK with weight 2 w21) AND … AND (x is VDK 9
with weight w ) THEN 91 3 1
µ is VDK
Rule DK: IF (x is DK with weight 1 w ) AND (12 x is DK with weight 2 w22) AND … AND (x is DK with 9
weight w92) THEN µ23 is DK
Rule MD: IF (x is MD with weight 1 w ) AND (13 x is MD with weight 2 w23) AND … AND (x is MD with 9
weight w93) THEN µ33 is MD
Rule BR: IF (x is BR with weight 1 w14) AND (x is BR with weight 2 w24) AND … AND (x is BR with 9
weight w94) THEN µ43 is BR
Rule VBR: IF (x is VBR with weight 1 w15) AND (x is VBR with weight 2 w25) AND … AND (x is VBR 9
with weight w95) THEN 3 5
The final output y of fuzzy decision process is the computing result of f+(⋅). The membership functions,
large
f and fsmall, define the detailed preserving process of the mechanism. In fact, the function f−(⋅) can be interpreted as a measure function of the correction process. If this measure is large, a full correction is allowed. If this measure is small, on the contrary, the correction is further reduced in order to better preserve the quality of fine details and textures. Next, the Protege 2000 [32], developed by Stanford University to build the Web Ontology Language (OWL), is used to build the noise ontology.
3 Intelligent Genetic Learning Process for OIA
This section introduces the intelligent genetic learning process for the OIA. The learning approach proposed by Ho et al. [33] is used to learn the parameters of fuzzy numbers and fuzzy rules. Fig. 5 shows the main parameters of the image fuzzy numbers [26]. The four components of the fuzzy numbers to be encoded are the membership functions of the fuzzy variables (CS anda1 CSa2), the fuzzy rules (CS ) and the linguistic modifiers (b1 CSb2) of the linguistic terms: (1) the CS denotes the parameters of fuzzy numbers and is represented by 20 genes; (2) a1 the CSa2denotes the parameters of fuzzy numbers F_mean; (3) the CSb1denotes a group of 9-gene which directly encodes the binary weights {w } where i = 1, …, 9 and j = 1, …, 5; (4) the ij CSb2 denotes the linguistic modifiers of the linguistic terms and is represented by 5 genes. For example, the set of binary weight {{0, 1, 0, 0, 1, 0, 1, 0, 0}, …, {0, 0, 1, 0, 0, 0, 0, 1, 0}, …, {1, 0, 0, 1, 0, 1, 0, 0, 1}} identifies the pattern defined by the set of indexes {{2, 5, 7}, …, {3, 8}, …, {1, 4, 6, 9}}, and the corresponding fuzzy rules are denoted as follows.
Rule VDK:
IF ((x is VDK) AND (2 x is VDK) AND (5 x is VDK)) THEN 7 µ13 is VDK
M
Rule MD:
IF ((x is MD ) AND (3 x is MD)) THEN 8 µ33 is MD
M
Rule VBR:
IF ((x is VBR ) AND (1 x is VBR ) AND (4 x is VBR ) AND (6 x is VBR)) THEN 9 µ53 is VBR
Two of the most well-known modifiers are the erosion linguistic modifier “very” (Ω=2) and dilation linguistic modifier “more-or-less” ( Ω = 0.5). The functions of these two modifiers are presented using
2 )) ( ( ) (x x very µ
µ = and µmore−or−less(x)=(µ(x))0.5, respectively. The initial population for the gene pool is composed of four groups with the same number CS +a1 CSa2 part and CS +b1 CSb2 part. The first group contains the original CS +a1 CSa2 part and original CS +b1 CSb2 part with the binary weight (w = 1, i = 1,…,9, and j = ij 1,…, 5) and the unit modifier (Ω=1). The second group includes the original CS +a1 CSa2 part and randomized
1 b
CS +CSb2 part. The third group has randomized CS +a1 CSa2 part and original CS +b1 CSb2 part. The fourth group consists of randomized CS +a1 CSa2 part and randomized CS +b1 CSb2part. Table 2 illustrates an example of the orthogonal arrays. Generally, level 0 and level 1 of a factor represent the selected genes from parents 0 and parents 1, respectively. After proper tabulation of experimental results, the summarized data are analyzed to determine the relative effects of various factors.
…
w
15…
w
11…
w
91…
w
95
(a) CS
a1(c) CS
b1(d) CS
b2(b) CS
a2 VDKα
β
VDKγ
VDKδ
VDKα
VBRβ
VBRγ
VBRδ
VBRλ
1λ
2λ
3 VDKΩ
Ω
VBRFig. 5. (a) Encoding of the parameters of fuzzy numbers, (b) Encoding of the parameters of fuzzy number F_mean and fuzzy numbers for luminance difference, (c) Encoding of fuzzy rules, and (d) Encoding of the linguistic modifiers of the linguistic
terms.
Table 2. Orthogonal Array [26]
Experiment Number 1 2 3 4 5 6 7 8 Factor 1 2 3 4 5 6 7 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 0 1 1 0 1 1 1 1 0 0 1 0 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 1 0 1 0 0 1 Evaluation Value y1 y2 y3 y4 y5 y6 y7 y8
The crossover structure is briefly described as follows. The parameters of CSa1 are divided into five groups,
VDK, DK, MD, BR, and VBR. If the input factors are the parameters of the fuzzy numbers, then the output of the main factor is CS . The parameters of a1 CS are also divided into five groups, VDK, DK, MD, BR, and VBR. If b1 the input factors are the parameters of the rule sets, then the output of the main factor is CS . Otherwise, if the b1 input factors are the parameters of the hedge sets, then the output of the main factor for this layer is CSb2.
The genetic learning process initiates the population by the encoding schema and restrictions, and then records the initiation population as the current population. The chromosome in the current population is evaluated by the fitness function. If the evaluation module does not satisfy the fitness function, then the intelligent learning process will execute the selection process. In addition, the elitism is also used in the learning process. In the beginning of the selection, the best two chromosomes in the current population are selected to new population without crossover and mutation. After the elitism, we produce the other population by mean of reproduction, crossover and mutation operators. The individuals having the best fitness have more chances to be reproduced. The one-point crossover method is adopted and the crossover one-point is randomly placed. The mutation process is applied to each offspring after the crossover. We use the Mean-Absolute-Error (MAE) to measure the fitness of each individual between the processed image and the original noise-free image. The MAE is calculated by (2), where
M
N× denotes the number of the processed pixels, y(n,m)denotes the pixel of the processed image, and )
, (n m
s denotes the pixel of the original noise-free image. The learning process is stopped when an assigned number of generations have been evolved or when a satisfactory value of fitness has been obtained. The Mean-Square-Error (MSE) is another criteria to evaluate the performance of the proposed approach, which is calculated by (3), where N×M , y(n,m), and s(n,m) denote the same meanings as (2).
M N m n s m n y MAE N 1 n M 1 m × ∑ ∑ − = = = ( , ) ( , ) (2)
(
)
M N m n s m n y MSE N 1 n M 1 m 2 × ∑ ∑ − = = = ( , ) ( , ) (3)4 Experimental Results
The ontological intelligent agent (OIA) for impulse noise removal described in this paper was implemented with the Visual Basic (Version 6.0) programming language. The experimental environment was constructed to test the performance of the proposed approach. Fig. 6 shows the user interface of the OIA, which is highlighted the functions with opening the desired image, making noise rate, selecting the filter method, and showing the values based on the criteria of peak signal to noise ratio (PSNR), MSE, MAE, and the time complexity after implementation. Fig. 7 shows the screenshot of the OIA when the agent is learning and tuning the best membership functions of the different fuzzy variables for the gray image “Barbara.” Fig. 8 shows the similar screenshot of the OIA with Fig. 7 but it is for the color image “Lena.” The experiments involved in comparing with our previous works [26][27][28] and other famous works [18][25][29] based on the criteria of MAE, MSE, and the time complexity. The experimental images are corrupted with 50%, 60%, 70%, and 80% additive identical independent distribution (i.i.d.) impulse noise, and the impulses take on positive and negative values with an equal. To decide the parameter sets of the experiments, both gray and color 256×256 images “Lena” are utilized as the sample gray and color images, respectively. A small population of 20 individuals is chosen and the parameters of the genetic learning are set as follows: crossover probability equals 0.9, mutation rate equals 0.3, and 50 generations.
In our experiments, four images, including two gray images and two color images, are adapted to implement the performance of the proposed approach. Fig. 9(a)-(d) show the original test images for the gray image “Barbara,” the gray image “Bridge,” the color image “Butterfly,” and the color image “Lena,” respectively. Fig. 10(a), 14(a), 18(a), and 22(a) show the corresponding noisy image of Fig. 9(a)-(d) with 50% noise rate. The first experiment is to compare the results of denoising the corrupted gray image “Barbara” by using different types of the filters. Fig. 10(b)-(f) show the implemented results by using the EIDA filter, the Russo filter, the SMF filter, the GFIF filter, and the OIA, respectively, when the noisy image is corrupted with 50% noise rate. Fig. 10 indicates that the performance of the OIA is better than other filters. The second experiment is to evaluate the performance of different types of the filters using the MAE criteria. Fig. 11 shows the results of MAE bar chart of each filter for the noisy gray image “Barbara” corrupted with 50%, 60%, 70%, and 80% noise rate. The third experiment is to observe the OIA’s performance from the MSE criteria. Fig. 12 shows the results of MSE bar chart of each filter for the noisy gray image “Barbara” corrupted with 50%, 60%, 70%, and 80% noise rate. The results depicted in Fig. 11 and Fig. 12 demonstrate that the MAE and MSE values of the OIA are the smallest than other filters under the identical corrupted noise rate condition. The fourth experiment is to carry out the efficiency for different types of the filters through the time complexity. Fig. 13 shows the time complexity for the gray image “Barbara.” Compared with other filters on the executing time, the results depicted in Fig. 13 demonstrate that the cost of implementing an OIA is not the most efficient but it is the most effective when the impulsive noise corruption noise rate is above 50%. Therefore, it is necessary to make a balance between efficiency and effectiveness of an image processing. The difference between the OIA and the OGFF is in the method of acquiring the parameters of the genetic learning process. The OIA automatically generates the optimal parameters for the fuzzy inference mechanism and uses the orthogonal array to help the learning process of the OGFF, but the OGFF manually does this. In addition, the difference between the OIA and the GFIF is briefly summarized as follows: (1) The OIA utilized the image noise ontology to represent the image noise knowledge for the agent, (2) the noise detection technique is able to choose the best fitted filter parameters, and (3) the evolution computation of the GFIF is able to be modified by using the orthogonal array to acquire the best filter parameters. Therefore, the performance of the OIA is better than the GFIF filter.
Finally, we also do the same experiments for the gray image “Bridge,” the color image “Butterfly,” and the color image “Lena,” which are shown as Fig. 9(b)-(d), respectively. The results of denoising corrupted image using different filters for Fig. 9(b)-(d) are shown in Fig. 14, Fig. 18, and Fig. 22, respectively. The results of MAE bar chart of each filter for Fig. 9(b)-(d) are shown in Fig. 15, Fig. 19, and Fig. 23, respectively. The results of MSE bar chart of each filter for Fig. 9(b)-(d) are shown in Fig. 16, Fig. 20 and Fig. 24, respectively. The results of time complexity bar chart of each filter for Fig. 9(b)-(d) are shown in Fig. 17, Fig. 21, and Fig. 25, respectively.
Open File (*.jpg)
Make Noise and Select Filters
Noise Ratio
PSNR Value MSE Value MAE Value Time Value
Fig. 6. User Interface of the OIA Open file
(*.raw)
Make Noise
Tuning Process
Open file
(*.raw) Make Noise
Tuning Process
(a) (b)
(c) (d)
Fig. 9. Original test images for the (a) gray image “Barbara,” (b) gray image “Bridge,” (c) color image “Butterfly,” and (d) color image “Lena”
(a) (b)
(c) (d)
(e) (f)
Fig. 10. (a) Noisy gray image “Barbara” corrupted with 50% noise rate, and the results of denoising corrupted image using the (b) EIDA filter, (c) Russo filter, (d) SMF filter, (e) GFIF filter, and (f) OIA
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OIA
Fig. 11. Results of MAE bar chart of each filter for the noisy gray image “Barbara” corrupted with 50%, 60%, 70%, and 80% noise rate
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10000
12000
50%
60%
70%
80%
Noise Rate
M
S
E
GFIF
EIDA
Russo
SMF
OIA
Fig. 12. Results of MSE bar chart of each filter for the noisy gray image “Barbara” corrupted with 50%, 60%, 70%, and 80% noise rate
2.26925
3.17475
6.615
167.645
6.9775
0
20
40
60
80
100
120
140
160
180
Filters
T
im
e(
s)
GFIF EIDA Russo SMF OIA
(a) (b)
(c) (d)
(e) (f)
Fig. 14. (a) Noisy gray image “Bridge” corrupted with 50% noise rate, and the results of denoising corrupted image using the (b) EIDA filter, (c) Russo filter, (d) SMF filter, (e) GFIF filter, and (f) OIA
8
10
15
26
22
35
54
74
16
26
40
55
25
31
37
44
6
7
8
9
0
10
20
30
40
50
60
70
80
50%
60%
70%
80%
Noise Rate
M
A
E
GFIF
EIDA
Russo
SMF
OIA
Fig. 15. Results of MAE bar chart of each filter for the noisy gray image “Bridge” corrupted with 50%, 60%, 70%, and 80% noise rate
328
539
1122
2640
2322
4301
7253
10450
1263
2325
4027
6063
933
1127
1379
1777
263
291
333
403
0
2000
4000
6000
8000
10000
12000
50%
60%
70%
80%
Noise Rate
M
S
E
2.285
3.106
6.36725
176.365
6.92
0
20
40
60
80
100
120
140
160
180
200
Filters
T
im
e(
s)
GFIF EIDA Russo SMF OIA
(a) (b)
(c) (d)
(e) (f)
Fig. 18. (a) Noisy color image “Butterfly” corrupted with 50% noise rate, and the results of denoising corrupted image using the (b) EIDA filter, (c) Russo filter, (d) SMF filter, (e) MGFF filter, and (f) OIA
6 8 12 21 18 32 50 72 14 24 38 56 19 23 27 34 4 6 7 10 0 10 20 30 40 50 60 70 80 50% 60% 70% 80% Noise Rate M A E
MGFF EIDA Russo SMF OIA
Fig. 19. Results of MAE bar chart of each filter for the noisy color image “Butterfly” corrupted with 50%, 60%, 70%, and 80% noise rate 394 655 1350 3287 2326 4240 7161 10508 1229 2230 3848 6109 1216 1487 1794 2356 159 502 960 1567 0 2000 4000 6000 8000 10000 12000 50% 60% 70% 80% Noise Rate M S E
MGFF EIDA Russo SMF OIA
Fig. 20. Results of MSE bar chart of each filter for the noisy color image “Butterfly” corrupted with 50%, 60%, 70%, and 80% noise rate
12.5755
9.83525
22.01625
215.375
10.2925
0
50
100
150
200
250
Filters
T
im
e(
s)
GFIF EIDA Russo SMF OIA
(a) (b)
(c) (d)
(e) (f)
Fig. 22. (a) Noisy color image “Lena” corrupted with 50% noise rate, and the results of denoising corrupted image using the (b) EIDA filter, (c) Russo filter, (d) SMF filter, (e) MGFF filter, and (f) OIA
3
5
10
23
17
30
48
71
13
23
37
55
12
14
18
22
3
4
6
15
0
10
20
30
40
50
60
70
80
50%
60%
70%
80%
Noise Rate
M
A
E
MGFF
EIDA
Russo
SMF
OIA
Fig. 23. Results of MAE bar chart of each filter for the noisy color image “Lena” corrupted with 50%, 60%, 70%, and 80% noise rate
152
470
1627
4936
2265
4492
7565
11609
1252
2473
4431
7090
335
418
541
734
148
162
506
1667
0
2000
4000
6000
8000
10000
12000
14000
50%
60%
70%
80%
Noise Rate
M
S
E
MGFF
EIDA
Russo
SMF
OIA
12.88275 9.77675
20.61275
213.835
10.1975
0
50
100
150
200
250
Filters
T
im
e(
s)
GFIF EIDA Russo SMF OIA
Fig. 25. Results of time complexity bar chart of each filter for the noisy color image “Lena”
5 Conclusions
In this paper, an ontological intelligent agent (OIA) is proposed to remove impulse noise from highly corrupted images. The fuzzy signal space for the working environment of the intelligent agent is defined and presented in the paper. The OIA consists of an image noisy ontology, a fuzzy inference mechanism, and an intelligent learning process. The fuzzy inference mechanism executes the fuzzy inference not only to remove impulse noise but also to keep the image structure. The image noise ontology stored the fuzzy numbers of the OIA for impulse noise removal is also presented in this paper. An intelligent learning process is used to adjust the fuzzy numbers of the image noise ontology. The proposed approach can achieve more effective results than other approaches such as the EIDA filter, the Russo filter, the SMF filter, the GFIF filter, and the MGFF filter. However, there are still some problems need further study in the future. For example, improving the learning process to reduce the time complexity of the OIA is one of our future works.
Acknowledgement
The authors may express their acknowledgement to the anonymous reviewers for their comments that improved the quality of this paper, and to the financial support of the project numbers: NSC 95-2221-E-024 -009-MY2 and NSC 95-2221-E-024-010.
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