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Applied Soft Computing
j ourna l ho mepage: www.elsev ier .com/ locate /asoc
olor image segmentation using adaptive unsupervised clustering approach
hang Siang Tan, Nor Ashidi Mat Isa ∗, Wei Hong Limmaging and Intelligent Systems Research Team (ISRT), School of Electrical and Electronic Engineering, Engineering Campus, Universiti Sains Malaysia,4300 Nibong Tebal, Penang, Malaysia
r t i c l e i n f o
rticle history:eceived 3 February 2012eceived in revised form 8 November 2012ccepted 19 November 2012
a b s t r a c t
This paper presents the Region Splitting and Merging-Fuzzy C-means Hybrid Algorithm (RFHA), an adap-tive unsupervised clustering approach for color image segmentation, which is important in image analysisand in understanding pattern recognition and computer vision field. Histogram thresholding technique is
vailable online 4 December 2012
eywords:olor image segmentationistogram splitting and merginguzzy C-means
applied in the formation of all possible cells, used to split the image into multiple homogeneous regions.The merging technique is applied to merge perceptually close homogeneous regions and obtain betterinitialization for the Fuzzy C-means clustering approach. Experimental results have demonstrated thatthe proposed scheme could obtain promising segmentation results, with 12% average improvement inclustering quality and 63% reduction in classification error compared with other existing segmentationapproaches.
. Introduction
Data clustering divides objects into clusters, such that similarbjects are grouped together in the same cluster [1]. In scientificiterature, the clustering technique is commonly used to segmentegions of interest [2–4] and detect the borders of objects in anmage [5–8]. Thus, clustering techniques for image segmentationnd edge detection have been used in various applications, includ-ng object recognition [9–12], optical character recognition [13,14],ace recognition [15–17], fingerprint recognition [18,19] and med-cal image processing [20,21].
Fuzzy C-means (FCM) clustering is one of the most popular tech-iques for image segmentation [22]. This technique introduces the
uzzy concept so that an object can belong to more than one classimultaneously. Membership degree is the strength of the associ-tion between an object and a class, with a value in a normalizedashion. As an unsupervised technique, FCM clustering does notequire prior knowledge about the tested data. However, this tech-ique has difficulties obtaining proper initial cluster centers and aufficient number of clusters for initialization [23]. The initializa-ion for the FCM clustering technique plays a vital role in obtainingptimum final cluster centers. Without proper initialization, thisechnique could generate sets of poor final cluster centers that
ould wrongly represent the clusters.
Some initialization methods have been proposed for FCMlustering. Random initialization was proven to be the best
initialization method for the C-means family because it producesgood final cluster centers [24]. However, random initialization doesnot have an adaptive decision mechanism for cluster numbers. Sim-ilar observation could be found in one of the latest works reportedby Ji et al. [25], i.e. the weighted image patch-based FCM (WIPFCM)algorithm. In the WIPFCM algorithm, image patch, instead of imagepixel, is employed as the basic unit to be clustered. A weightingscheme is proposed to adaptively determine the anisotropic weightof each pixel in the patch, as not all of them contribute equally tocalculate the similarity between two patches [25]. Despite of itsability in producing good segmentation results and its robustnesstoward the noise, the prior determination of cluster numbers in theWIPFCM algorithm is set manually by user. The main drawback ofthis strategy is, it generally requires a laborious process of selectingthe number of clusters. Additionally, it is impractical to expect allusers to have sufficient domain knowledges in determining the cor-rect cluster numbers. Wrong determination of cluster numbers bythe user could affect the segmentation results considerably as theinitialization scheme has substantial impact on the FCM’s clusteringperformance.
To mitigate the abovementioned drawbacks, the improved AntSystem (AS) was introduced [26] to automatically obtain initialcluster centers and the number of clusters for the FCM cluster-ing technique. The concept of the Ant Colony algorithm (ACA),with its intelligent searching ability, is applied in AS to obtain bet-ter optimization of clustering results. AS could provide effectiveinitialization for the FCM clustering technique because of its adap-
tive decision mechanism for cluster numbers. Agglomerated JustNoticeable Difference Histogram (AJNDH) [27] is another adap-tive cluster initization scheme that counters the drawback of therandom initialization scheme. Different from the AS initialization
cheme that employs the intelligence searching ability to opti-ize the initial cluster, the AJNDH initialization scheme adopts the
oncept of histogram bins in determining the initial cluster. Theistogram bins of the color images are calculated in such a wayhat each color bin in the histogram represents a visually differentolor. As a result, the number of colors present in the histogramins is significantly less than the number of unique colors in theolor image. The number of histogram bins can be further reducedsing the agglomeration technique by introducing an agglomera-ion threshold to combine the perceptually similar color segmentsnto a larger color segment. The drastic reduction in the numberf unique colors in the color images suggest the feasibility of theJNDH technique in real-time machine analysis applications.
Chen et al. [28] proposed a FCM-based segmentation tech-ique by the fusion on multi-color space components. In theirpproach, the input images are firstly converted into six colorpaces, i.e. grayscale, HSV, YIQ, YCbCr, LAB and LUV color spaces,nd the color space components of gray, V, I, Cr, B, and U fromhe corresponding color spaces are then selected. A peak-findinglgorithm is applied on these components to determine their cor-esponding initial cluster centers and the number of clusters. Thepatial FCM (SFCM) algorithm [29] is then used to generate sixifferent initial segmentation results from these six selected com-onents with different cluster numbers. To calculate the finalluster numbers, the SFCM algorithm is applied again to fusehe previous six segmentation results. Bahght et al. [30] pro-osed a new validity index to access the validity of a cluster.
n their approach, a multi-degree entropy algorithm is proposedo perform partition on the input image into different level ofntensities using the multi-degree immersion process. Mergingechnique is then applied on the aforementioned process’s outputo obtain the final cluster numbers based on the predefined validityunction criteria. Meanwhile, Sowmya and Sheela Rani [31] inves-igated the capability of FCM, possibilistic FCM (PFCM) [32], andompetitive neural network (CNN) [33] in performing the imageegmentation. In their investigation, a self-estimation algorithmroposed in [34] are adopted to automatically determine the clusterumbers.
In this paper, we propose the Region Splitting and Merging-uzzy C-means Hybrid Algorithm (RFHA) that consists of twoain modules: Region Splitting and Merging (RSM) and FCM clus-
ering. A color image with RGB representation is composed ofultiple homogeneous regions having different intensity ranges
or each color channel. The pixels belong to each homogeneousegion, with intensity values within the intensity ranges of thatomogeneous region for each color channel. In the RSM mod-le, the histogram thresholding technique can successfully detecthe valleys in the histogram of each color channel and can bepplied in the formation of all possible cells, which are usedo split the image into multiple homogeneous regions. The end-oints of these cells can be obtained by taking the adjacent valleys
n the histogram of each color channel to form the intensityanges of the homogeneous regions for each color channel andhus produce multiple homogeneous regions. The merging tech-ique is applied to merge perceptually close homogeneous regionsnd obtain better initialization for the FCM clustering technique.inally, the initial cluster centers and the number of clustersre obtained and used as initialization for the FCM clusteringechnique.
The rest of the paper is organized as follows. Section 2 presentsn detail the RSM and FCM clustering modules of the proposedpproach and provide illustrations of the implementation proce-
ure of the RFHA technique. Section 3 analyzes the experimentalesults obtained from the RFHA and compares them with existingegmentation approaches. Section 4 concludes the results of thisaper.
ting 13 (2013) 2017–2036
2. Proposed approach
The iterative optimization of the FCM clustering technique isessentially a local searching method that has a tendency to fall ontolocal minimum points. However, the FCM clustering technique isvery sensitive to the initialization condition of the initial clustercenters and the number of clusters [23]. Thus, the image segmen-tation results produced by the FCM clustering technique dependon the initialization condition. Usually, good initialization condi-tions can only be obtained by running repetitive experiments basedon certain experiences. As a result, a laborious process is gener-ally required to obtain good initialization conditions for the FCMclustering technique [23].
In this paper, an adaptive unsupervised clustering that utilizesthe RSM module as the initialization scheme for the FCM cluster-ing technique is proposed. The proposed method RFHA aims toimprove the conventional FCM clustering technique by eliminat-ing the limitations of the conventional FCM clustering technique. Ablock diagram of the proposed RFHA technique is shown in Fig. 1to provide a general idea of the proposed RFHA technique in amore comprehensive manner. As shown in Fig. 1, the proposedRFHA technique consists of two modules: RSM and FCM cluster-ing. These two modules are presented in detail in Sections 2.1 and2.2 respectively.
This study uses the RSM module as an initialization scheme thatallows users to determine cluster numbers and centroids automat-ically and adaptively. The obtained cluster numbers and centroidsserve as the initialization conditions for the FCM clustering mod-ule. Compared with the widely used random initialization scheme,the initialization scheme based on the RSM module requires aless laborious process and consistently produces good initializa-tion conditions for the FCM clustering module. The capability ofthe RSM module to determine cluster numbers and centroids auto-matically and adaptively is due to the capacity of the RSM moduleto detect them based on the global information in the histogramof the input images. Different types of input images have differenttypes of global information. Therefore, the RSM module eventu-ally detects different cluster numbers and centroids depending onthe numbers and intensity values of the significant peaks that arepresent in the histograms of the input images.
More specifically, each pixel in a color image with RGB repre-sentation consists of a mixture of intensity of the red, green, andblue color channels. Hence, the histogram of the red, green, andblue color channels could produce global information on the entireimage. The basic analysis approach to a histogram is that a homo-geneous region tends to form a significant peak in the histogramand that the valley between the adjacent significant peaks couldbe used as the threshold between these homogeneous regions.Thus, the histogram thresholding is used as a popular segmenta-tion technique that searches for peaks and valleys in the histogramfor gray-scale images [35,36]. However, the typical segmentationapproach based on the histogram analysis could work well only ifthe significant peaks in the histogram can be recognized correctly.
For a color image, the pixels belonging to a homogeneous regionmust have a certain range of intensity for each color channel. Foreach homogeneous region, the pixels belonging to that homoge-neous region have the intensity values within the intensity rangesof that homogeneous region for each color channel. In the RSMmodule, we apply the histogram thresholding technique to deter-mine the significant peaks in the histogram of each color channeland then obtain the valleys between adjacent significant peaks inthe histogram of each color channel. The valleys in the histogram
of each color channel are used to form the endpoints of each colorchannel of the cells, which correspond to the intensity ranges ofeach color channel of the homogeneous regions. As a result, all pos-sible cells with different volumes are formed. These cells are used
K.S. Tan et al. / Applied Soft Computing 13 (2013) 2017–2036 2019
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Fig. 1. Block diagram of
o split the image into multiple homogeneous regions. The colorepresenting each homogeneous region is obtained by averagingll the pixels within their particular cells. The merging techniques applied to merge these homogeneous regions and avoid theormation of perceptually close homogenous regions. Finally, thenitialization condition of the initial cluster centers and numbersre obtained and used to initialize the FCM clustering module.
Similar to the AS module in [26], aside from providing the ini-ialization condition for the FCM clustering module, the standaloneSM module could be used in color image segmentation. Extensivevaluation of the qualitative and quantitative performances of theSM module is provided in Section 3 to investigate the performancef the standalone RSM module in color image segmentation.
.1. RSM module
In this paper, the RSM technique is used to initialize the FCMlustering technique in view of its drawbacks. The histogramhresholding technique is proposed to obtain the cell endpointsf each color channel. The formed cells are used to split the imagento multiple homogeneous regions. The merging technique is thenpplied to merge perceptually close homogeneous regions andbtain better initialization for the FCM clustering technique. TheSM technique is performed as follows:
i. Apply the moving average filter with a span of 5 to the histogramof each color channel, as described by the following equation:
where n(k) is the number of pixels in the histogram of each colorchannel with intensity k and s(k) is the corresponding value inthe resultant histogram of each color channel with intensity kafter applying the moving average filter.
(Note: Based on the analysis performed using numerousimages, the span of the moving average filter can be set from2 to 8. The span of the moving average filter smaller than 2
could not remove certain small peaks residing in the histogramof each color channel, whereas the span of the moving averagefilter larger than 8 could remove certain significant peaks in thehistogram of each color channel. As a result, 5 was set as the
oposed RFHA technique.
span of the moving average filter by taking the average valuebetween the two extreme values.)
ii. Identify all the peaks and valleys in s(k) produced by the his-togram of each color channel based on the fuzzy rule base inEq. (2) and then remove the peaks and valleys in s(k) producedby the histogram of each color channel based on the fuzzy rulebase in Eq. (3):
IF(s(k) > s(k − 1)&s(k) > s(k + 1))
THEN(k is peak)
IF(s(k) < s(k − 1)&s(k) < s(k + 1))
THEN(k is valley),
(2)
IF(k is peak) AND (s(k + 1) > s(k − 1))
THEN(s(k) = s(k + 1))
IF(k is peak) AND (s(k + 1) < s(k − 1))
THEN(s(k) = s(k − 1))
IF(k is valley) AND (s(k + 1) > s(k − 1))
THEN(s(k) = s(k − 1))
IF(k is valley) AND (s(k + 1) < s(k − 1))
THEN(s(k) = s(k + 1))
(3)
ii. Identify the significant peaks by examining the turning pointswith positive to negative gradient changes in s(k) produced bythe histogram of each color channel.
iv. Determine the valleys in the histogram of each color channel bytaking the minimum value between any adjacent peaks in thehistogram of each color channel.
v. Form all possible cells with different volumes. The volume ofeach cell depends on the endpoints of each color channel of thecell. The endpoints of each color channel of a cell are obtainedby taking the adjacent valleys in the histogram of each colorchannel.
vi. Assign each pixel to only one cell with the condition that theintensity of each color channel of the pixel is within the end-points of each color channel of the cell.
ii. Form all the initial cluster centers by averaging all pixels within
their particular cells using the following equation:
cj = 1pj
∑xi ∈ Xj
xi, (4)
2020 K.S. Tan et al. / Applied Soft Computing 13 (2013) 2017–2036
d Mer
vi
i
x
2
d[acmf
W
wcctt
Fig. 2. (a) Original image Lena, (b) image after the Region Splitting an
where 1 ≤ j ≤ M and M is the number of clusters whose Pj > 0. Xjis the pixel set assigned to the jth cluster, Pj is the number ofpixels assigned to the jth cluster, and xi is the ith pixel in thatcluster.
ii. Calculate for the Manhattan distance D for any two out of theseM cluster centers with the following equation:
D(cj, ck) =∣∣Rj − Rk
∣∣ +∣∣Gj − Gk
∣∣ +∣∣Bj − Bk
∣∣ , ∀j /= k (5)
where 1 ≤ j ≤ M and 1 ≤ k ≤ M. Rj, Gj, and Bj are the intensities ofthe red, green, and blue color channels of the jth cluster cen-ter, respectively, and Rk, Gk, and Bk are the intensities of thered, green, and blue color channels of the kth cluster center,respectively.
(Note: The Manhattan distance is a better distance measure-ment than the Euclidean distance. The former exhibits a morestable visual color similarity, whereas the latter tends to pro-duce a wider variation of color perception with the same colordistance.)
x. Find the shortest distance between two nearest cluster centers.x. Merge the nearest clusters to form new clusters and refresh the
cluster center using Eq. (4) only if the shortest distance betweentwo nearest cluster centers is less than the threshold Manhat-tan distance for the merging process, dc. Otherwise, stop themerging process.
i. Reduce the number of cluster centers, M to (M − 1), and repeatSteps viii to x until shortest distance between two nearest clus-ter centers is not less than dc.
.2. Fuzzy C-means clustering module
The FCM clustering technique is a Hill-Climbing techniqueeveloped by Dunn in 1973 [37] and improved by Bezdek in 198138]. This technique attempts to partition every image pixel into
collection of M fuzzy cluster centers with respect to some givenriteria [39]. Let N be the total number of pixels in that image and
be the exponential weight of membership degree. The objectiveunction Wm of the FCM clustering technique is defined as
m(U, C) =N∑
i=1
M∑j=1
umji d2
ji, (6)
here uji is the membership degree of the ith pixel to the jth cluster
enter and dji is the distance between the ith pixel and the jth clusterenter. If Ui = (u1i, u2i, . . ., uMi)T is the set of membership degree ofhe ith pixel associated with each cluster center, xi is the ith pixel inhe image, and cj is the jth cluster center, then U = (U1, U2, . . ., UN)
ging (RSM) technique, and (c) final segmentation result of the image.
is the membership degree matrix and C = (c1, c2, . . ., cM) is the setof cluster centers.
The objective function Wm of the FCM clustering techniquereveals the clustering quality of the output images in terms of thedegree of compactness and uniformity of the cluster centers. Specif-ically, a smaller value of Wm indicates a more compact and uniformcluster center set that leads to more desirable clustering results.However, a closed-form solution for calculating the minimum valueof Wm does not exist because different types of input images consistof different pixel distributions. Hence, different expressions of theobjective function Wm are produced. Consequently, formula thatmay be specifically used to calculate the minimum value of Wm forall types of images during the FCM clustering process does not exist.
To achieve minimization of the objective function Wm, the alter-native strategy is to carry out the FCM clustering technique in aniterative manner. The FCM clustering technique can be describedas follows:
Set the iteration terminating threshold ε to a small positivenumber in the range [0,1] and the number of iteration q to 0. Cal-culate U(q) according to C(q) using the following equation:
uji = 1∑k=1M (dji/dki)
2/m−1(7)
where 1 ≤ j ≤ M and 1 ≤ i ≤ N. If dji = 0, then uji = 1. Moreover, theother membership degrees of this pixel are set to 0.
Calculate C(q+1) according to U(q) with the following equation:
cj =∑i=1
N umji
xi∑i=1N um
ji
(8)
where 1 ≤ j ≤ M.Update U(q+1) according to C(q+1) using Eq. (7).Compare U(q+1) with U(q). If || U(q+1) − U(q)|| ≤ �, stop iteration.
Otherwise, q = q + 1, and go back to Step ii.
2.3. Illustration of the implementation procedure
In this section, we apply the proposed clustering approach toperform color image segmentation with the image Lena (Fig. 2(a)).The histograms of its red, green, and blue color channels are shownin Fig. 3(a), (b), and (c), respectively. The significant peaks detectedin the histograms of the color channels are also indicated in thesame figures. As shown in Fig. 3, the proposed histogram thresh-
olding technique could locate significant peaks in the histogramsof its red, green, and blue color channels. After the significant peaksare identified, the minimum value between adjacent significantpeaks is identified to be the valley. The valleys detected in the
K.S. Tan et al. / Applied Soft Computing 13 (2013) 2017–2036 2021
F (a) rel
hFvavciiwmniF
ig. 3. Significant peaks detected in the histograms of its respective color channels:egend, the reader is referred to the web version of the article.)
istograms of its red, green, and blue color channels are shown inig. 4(a), (b), and (c), respectively. All possible cells with differentolumes are formed. For each cell, the endpoints of its red, green,nd blue color channels take the intensity values of the adjacentalleys obtained from the histograms of its red, green, and blueolor channels, respectively (Fig. 5). These cells are used to split themage into multiple homogeneous regions. The color represent-ng each homogeneous region is obtained by averaging all pixels
ithin their particular cells. The merging process is carried out to
erge all perceptually close cluster centers and obtain a reasonable
umber of clusters for all kinds of input images. The segmentedmage after running the proposed RSM technique is illustrated inig. 2(b). Finally, the initial cluster centers and numbers are used
d, (b) green, and (c) blue. (For interpretation of the references to color in this figure
as initialization for the FCM clustering technique to perform colorimage segmentation. The segmented image of the RFHA approachis shown in Fig. 2(c).
3. Experiment results
According to the algorithm description, the minimum dc is theonly parameter of the RFHA approach that is used as the crite-
rion to measure color similarity between any two cluster centers.This parameter denotes the minimum Manhattan distance betweenany two cluster centers. Loo and Tan [40] analyzed the color dis-tance measurement in the RGB color space and revealed that the
2022 K.S. Tan et al. / Applied Soft Computing 13 (2013) 2017–2036
F b) gret
MEscLwac
iniA
ig. 4. Valleys detected in the histograms of its respective color channels: (a) red, (he reader is referred to the web version of the article.)
anhattan distance is a better distance measurement than theuclidean distance. The former exhibits a more stable visual colorimilarity, whereas the latter tends to produce wider variations ofolor perception with the same color distance. As shown in Table 1,oo and Tan [40] revealed that the Manhattan distance is below 71,here the same color is observed with a very low intensity vari-
nce. As a result, we set dc to be 71 to merge the perceptually closeluster centers.
In this study, the performance of the proposed RFHA technique
s compared with the conventional randomly initialized FCM tech-ique and several adaptive unsupervised segmentation techniques,
ncluding Ant Colony-Fuzzy C-means Hybrid Algorithm (AFHA) andJNDH. The randomly initialized FCM technique is selected because
en, and (c) blue. (For interpretation of the references to color in this figure legend,
of its superior performance in the C-means family [24]. The ran-domly initialized FCM technique cannot determine the number ofclusters adaptively. Thus, we set the number of clusters of the ran-domly initialized FCM technique with the final number of clustersobtained using the proposed RFHA technique. This minor modi-fication on the randomly initialized FCM technique ensures faircomparison with the proposed RHFA technique in the followingsection.
The AFHA technique is introduced [26] by incorporating the
AS technique into the FCM clustering technique. AFHA is selectedfor comparison because of its better segmentation results com-pared with other state-of-the-art segmentation technique, such asX-means, Mean Shift, Normalized Cut, and Han and Shi’s method
K.S. Tan et al. / Applied Soft Computing 13 (2013) 2017–2036 2023
Fig. 5. Formation of a
Table 1Categories of color similarity in terms of the Manhattan distance [40].
dc Visual inspection result
10–30 Same color31–70 Same color, low intensity variance71–90 Same color series91–120 Same color series, low intensity variance121–150 Different colors, small color range
[ttmrtp
tppuNrtpmofbvat
j
TP
151–190 Different colors, wider color rangeAbove 190 Very randomly occurring color
26]. AJNDH [27] is also selected for comparison because it is one ofhe newest techniques. Thus, we are interested to know whetherhe proposed RFHA technique could generally produce better seg-
entation results than the AJNDH technique. The segmentationesults of the AS and RSM initialization schemes are also inves-igated because they can be used to perform the segmentationrocess on color images.
The configuration and parameter settings of all the aforemen-ioned peer algorithms taken from the literature, as well as theroposed RSM and RFHA techniques, are given in Table 2. Thearameter settings for the peer algorithms are the same as thosesed in the original papers. For the AS and AFHA techniques, P,, ˛, ˇ, �, r, �, and dc represent the minimum number of pixels
equired to form an initial cluster center, image size, parametero control the relative weight of the pheromone concentration,arameter to control the relative weight of the heuristic value,inimum probability for pixel classification, cluster radius, evap-
ration rate of pheromone concentration, and minimum distanceor merging cluster, respectively [26]. For the AJNDH technique,oth � and � represent the similarity and merging threshold
1 2alues used to calculate the Just Noticeable Difference (JND) andgglomeration histograms, respectively [27]. For the randomly ini-ialized FCM, AFHA, and RFHA techniques incorporated with the
able 2arameter settings of the compared segmentation algorithms.
Algorithm Year Cluster numbers
Randomly initialized FCM [22] 1986 Non-adaptive
AS [25] 2011 Adaptive
AFHA [25] 2011 Adaptive
AJNDH [26] 2011 Adaptive
RSM – Adaptive
RFHA – Adaptive
ll possible cells.
FCM clustering technique, the parameter m employed to control thefuzziness of the membership as well as the terminating thresholdε are set as 2 and 0.001, respectively, as preferred in previous stud-ies [23,41]. Finally, the randomly initialized FCM technique is notequipped with the mechanism to determine the number of clustersadaptively and automatically. Thus, to ensure reasonable compari-son, we set the number of clusters of the randomly initialized FCMtechnique to be the same as the final number of clusters obtainedusing the proposed RFHA technique.
In this section, the segmentation results of the randomly ini-tialized FCM, AS, AFHA, AJNDH, and RFHA techniques are firstevaluated visually. Almost all of the abovementioned techniques(except for the randomly initialized FCM) can adaptively initializethe distribution of cluster centers. Thus, the final cluster numbersproduced by the different techniques are compared.
The segmentation results in our work are greatly dependent oncluster quality. Thus, the cluster quality produced by the randomlyinitialized FCM, AS, AFHA, AJNDH, and RFHA techniques shouldbe evaluated. To evaluate cluster quality, several important clus-ter validity criteria featured in previous works on fuzzy clusteringare highlighted. One of the most fundamental benchmarks usedto evaluate cluster quality is the mean square error (MSE). A goodclustering approach should always generate results with small dis-tortions, where the cluster centers should be placed in such a waythat they reduce the distances to data pieces as much as possi-ble when the cluster number is fixed. The MSE evaluation functioncould be described as follows:
MSE = 1N
M∑j=1
∑i ∈ S
∥∥xi − cj
∥∥2(9)
where N is the number of output image pixels, M is the number ofclusters produced during the clustering process, Sj represents theset of pixels in the jth cluster, cj denotes the intensity levels of the
Parameter settings
m = 2, ε = 0.001P = 0.008 × N, ̨ = 0.5, ̌ = 2, � = 0.4, r = 80, � = 0.8, dc = 28m = 2, ε = 0.001, P = 0.008 × N, ̨ = 0.5, ̌ = 2, � = 0.4, r = 80, � = 0.8, dc = 28�1 = 2567, �2 = �1 + 100dc = 71m = 2, ε = 0.001, dc = 71
2024 K.S. Tan et al. / Applied Soft Computing 13 (2013) 2017–2036
F est imA
pi
tamhaT
F
F
F
a
Q
epiTdttirlt
ig. 6. The image Lena: (a) original image, the rest are segmentation results of the tFHA, (e) AJNDH, (f) RSM, and (g) RFHA.
ixels in the jth cluster center, and xi is the intensity levels of theth pixel in the jth cluster center.
Three benchmark analyses are used to evaluate the segmen-ation results of the randomly initialized FCM, AS, AFHA, AJNDH,nd RFHA techniques. These benchmark analyses are used to esti-ate the empirical goodness of the segmentation results with some
uman characterizations on the properties of ideal segmentationnd which require no prior knowledge of correct segmentation.hese analyses are described as follows:
F(I) proposed by Liu and Yang [42],
(I) =√
M∑M
j=1e2j√
Nj
, (10)
’(I) proposed by Borsotti et al. [43],
′(I) =∑M
j=1e2j
√∑MaxAreaa=1 [S(a)]1+(1/a)
(1000 × N)√
Nj
(11)
nd Q(I) further refined from F(I) by Borsotti et al. [43],
(I) = 11000 × N
√M
M∑j=1
[e2
j
1 + log Nj+
(S(Nj)
Nj
)2]
(12)
For the above formulae, I is an image and N is the total pix-ls in I. The segmentation can be described as an assignment ofixels in the image I into M regions. Cj denotes the set of pixels
n region j, whereas Nj = |Cj| denotes the number of pixels in Cj.he value of ej, which represents homogeneity within a region, isefined as the Euclidean distance between the RGB color vectors ofhe pixels of region j and the color vector attributed to region j inhe segmented image. Finally, S(a) denotes the number of regions in
mage I that has an area of exactly a and MaxArea denotes the largestegion in the segmented image. Although the above three formu-ae differ, these functions are used to penalize the segmentationhat form too many regions and have non-homogeneous regions
age produced by the following algorithms: (b) randomly initialized FCM, (c) AS, (d)
by giving them larger values. In this paper, 140 images obtainedfrom public image segmentation databases are used as the testeddataset.
3.1. Qualitative evaluation on segmentation results
The performance of the proposed RFHA and the other conven-tional techniques are visually evaluated by using 7 out of the 140tested images. The segmentation results for the images Lena, Birds,Swimmer, Red Church, Diver, Lake, and Moon are shown in Figs. 6–12,respectively. Generally, the RFHA technique produces better seg-mentation results compared with the randomly initialized FCM,AS, AFHA, AJNDH, and RSM techniques for the images shown inFigs. 6–12. The segmented regions of the resultant images pro-duced by the RFHA technique are more homogeneous comparedwith those produced by the randomly initialized FCM, AS, AFHA,AJNDH, and RSM techniques. In addition, the RFHA technique couldsuccessfully reduce the classification error and preserve some of theimportant features of the input color images.
For example, in the image Lena (Fig. 6), the RFHA techniqueoutperforms the randomly initialized FCM, AS, AFHA, and AJNDHtechniques by producing a more homogeneous background. Seem-ingly, the background of the resultant image produced by the RSMtechnique is more homogenous than that produced by the RFHAtechnique. However, a considerable number of pixels of the back-ground are mistakenly assigned as the color of the hat’s featherby the RSM technique. For the image Birds (Fig. 7), a classificationerror exists. The white feathers of the birds have been mistak-enly assigned to the sky by the randomly initialized FCM, AS,AFHA, and AJNDH techniques, although some of these techniquesproduce more homogenous backgrounds with fewer clusters. How-ever, both the RSM and RFHA techniques have successfully avoided
this classification error.
For the image Swimmer (Fig. 8), the AJNDH, RSM, and RFHAtechniques produce better segmentation results than the ran-domly initialized FCM, AS, and AFHA techniques by assigning the
K.S. Tan et al. / Applied Soft Computing 13 (2013) 2017–2036 2025
F est imA
sttsoF
FA
ig. 7. The image Birds: (a) original image, the rest are segmentation results of the tFHA, (e) AJNDH, (f) RSM, and (g) RFHA.
wimming trunk of the swimmer with the desired red color. Bothhe AJNDH and RFHA techniques show better segmentation results
han the RSM technique because some of the pixels in the coach’shirt are mistakenly assigned to the background. This error can bebserved in the resultant image produced by the RSM technique inig. 8(f). Compared with the AJNDH technique, the RFHA technique
ig. 8. The image Swimmer: (a) original image, the rest are segmentation results of the tS, (d) AFHA, (e) AJNDH, (f) RSM, and (g) RFHA.
age produced by the following algorithms: (b) randomly initialized FCM, (c) AS, (d)
produces a more homogenous region on the swimmer’s leg. Forthe Red Church image (Fig. 9), the randomly initialized FCM, AS,
and AFHA techniques produce a more homogenous sky with fewerclusters. However, as shown in Fig. 9(b), (c), and (d), large portionsof the pixels on the red church roof are mistakenly assigned as thegray color pixels in the segmented images produced by these three
est image produced by the following algorithms: (b) randomly initialized FCM, (c)
2026 K.S. Tan et al. / Applied Soft Computing 13 (2013) 2017–2036
F f the
A
tcpchR
F(
ig. 9. The image Red Church: (a) original image, the rest are segmentation results oS, (d) AFHA, (e) AJNDH, (f) RSM, and (g) RFHA.
echniques. The AJNDH, RSM, and RFHA techniques prevent suchlassification errors. Furthermore, the RSM and RFHA techniques
roduce a more homogenous roof region consisting of two clustersompared with the AJNDH technique, which produces a lessomogenous roof region consisting of three clusters. Thus, theSM and RFHA techniques outperform the AJNDH technique.
ig. 10. The image Diver: (a) original image, the rest are segmentation results of the testd) AFHA, (e) AJNDH, (f) RSM, and (g) RFHA.
test image produced by the following algorithms: (b) randomly initialized FCM, (c)
For the image Diver (Fig. 10), classification errors can beobserved on the resultant images produced by the AS and AFHA
techniques. Compared with the randomly initialized FCM, AJNDH,RSM, and RFHA techniques, the AS and AFHA techniques fail toclassify the pixels in the diving suit, the yellow object and thewhite object into three distinctive clusters. For the segmented
image produced by the following algorithms: (b) randomly initialized FCM, (c) AS,
K.S. Tan et al. / Applied Soft Computing 13 (2013) 2017–2036 2027
F e test
(
ielaer
F(
ig. 11. The image Lake: (a) original image, the rest are segmentation results of thd) AFHA, (e) AJNDH, (f) RSM, and (g) RFHA.
mage produced by the RSM technique, an obvious classificationrror can be observed as well. All the pixels of the yellow object
ocated at the right hand side of the image are mistakenly assigneds part of the rock located below it. No significant classificationrrors are observed in the resultant images produced by theandomly initialized FCM and AJNDH techniques. However, the
ig. 12. The image Moon: (a) original image, the rest are segmentation results of the testd) AFHA, (e) AJNDH, (f) RSM, and (g) RFHA.
image produced by the following algorithms: (b) randomly initialized FCM, (c) AS,
RFHA technique performs slightly better because it produces amore homogenous region on the white object and on the rock,
which are located at the right hand side of the image.
The AFHA, RSM, and RFHA techniques produce a more homo-geneous region with four clusters on the image Lake (Fig. 11)compared with that produced by the AS and AJNDH techniques,
image produced by the following algorithms: (b) randomly initialized FCM, (c) AS,
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Table 3Number of clusters produced by different techniques.
ote: The values in boldface represent the best results obtained for the comparison.
hich produce a less homogenous lake region with five clusters.n the resultant images produced by the randomly initialized FCMechnique, a considerable number of pixels at the ground regionave been mistakenly assigned as the lake region. An obvious clas-ification error exists in the segmented images produced by theSM technique. Some pixels of the cyan colored sky are mistakenlyssigned as part of the cloud. Furthermore, the proposed RFHA tech-ique performs slightly better than the AFHA technique because itroduces a more homogenous region on the mountain surface.
Finally, all the segmented images produced by the randomly ini-ialized FCM, AS, AFHA, and AJNDH techniques in the image MoonFig. 12) experience a severe classification error. These techniquesave inaccurately assigned the pixels of the moon as part of theky. The RSM and RFHA techniques are successful in avoiding thislassification error by assigning the moon and the sky as sepa-ate clusters. The RSM technique produces an obvious ring regionround the moon. Therefore, the RFHA technique demonstratesetter performance than the RSM technique.
Aside from the visual inspection results on the seven images,dditional 20 supplementary images were analyzed to support thendings mentioned previously. The results are shown in Fig. 13f Appendix A. The RFHA technique produces more homogeneousegmented regions and significantly reduces classification errors.hus, the proposed RFHA technique outperforms the randomly ini-ialized FCM, AS, AFHA, AJNDH, and RSM techniques.
.2. Evaluation of cluster number
Based on the qualitative results shown in the previous section,he proposed RFHA technique can adaptively initialize the clus-er center distribution and the centroid values. The proposed RSM
echanism offers a superior cluster center initialization mech-nism that guarantees effective classification capability and lessistortion during the segmentation process. Except for the ran-omly initialized FCM technique, all of the peer algorithms haveheir own unique mechanism for cluster center initialization.hus, the dependence of the segmentation results on the num-er of clusters produced by each technique should be discussed.he number of clusters produced by each technique is tabulatedn Table 3.
Table 3 shows that the number of clusters produced by the ran-omly initialized FCM, RSM, and RFHA techniques is always theame. Similar findings can be observed for the AS and AFHA tech-iques. This observation inevitably casts doubt on the value of theybridization techniques adopted because the increment in theomputation time and the complexity in the hybridization schemere unlikely to trade significant performance gains in terms of the
umber of clusters produced. Two important facts are highlightedo clarify the doubt mentioned above.
The finding that the cluster numbers of the RSM and RFHA tech-iques are same is rational because the RSM module serves as
ting 13 (2013) 2017–2036
the initialization scheme of the FCM module in the RFHA tech-nique. Specifically, in the proposed RFHA technique, the clusternumbers and centroids produced by the RSM module are fed intothe subsequent FCM module to overcome the dependency of theFCM module on the initialization condition. Similar explanation isapplicable for the AS and AFHA techniques. Meanwhile, the ran-domly initialized FCM technique is not equipped with the adaptivemechanism in determining the cluster number. Thus, a slight mod-ification is made. The cluster number of the randomly initializedFCM technique is set to the same value as that of the RSM and RFHAtechniques to ensure reasonable experimental comparison.
The second observation that should be highlighted is the pos-sibility of significant qualitative and quantitative differences inthe segmentation results produced by different algorithms despitehaving the same cluster number. While the number of clustersproduced is necessary, it is an insufficient performance metric toreveal the overall clustering performances of the aforementionedalgorithms. The randomly initialized FCM, RSM, and RFHA tech-niques have the same cluster number. However, Sections 3.3 and3.4 show that the other performance metrics used to access theclustering quality (i.e. the MSE values) and homogeneity [i.e. theF(I), F’(I), and Q(I) values] of the segmented images are significantlydifferent among the randomly initialized FCM, RSM, and RFHA tech-niques. A similar finding is also observed for the AS and AFHAtechniques.
This section investigates the effect of cluster number on thequality of segmentation results. Table 3 shows that the randomlyinitialized FCM, RSM, and RFHA techniques produce fewer clus-ters than the AS, AFHA, and AJNDH techniques for the images Lena,Red Church, and Lake. Thus, the randomly initialized FCM, RSM,and RFHA techniques could generally produce better and largerhomogenous regions in the images Lena, Red Church, and Lake byhaving fewer clusters. For the image Swimmer, the randomly ini-tialized FCM, AJNDH, RSM, and RFHA techniques yield larger andbetter homogeneous regions in the segmented image than the ASand AFHA techniques by producing fewer clusters.
As for the images Birds and Moon, the AS, AFHA, and AJNDHtechniques produce larger homogenous regions by obtaining fewerclusters than the randomly initialized FCM, RSM, and RFHA tech-niques. However, considerable pixels are mistakenly assigned tothe background (i.e. sky) in the segmented images produced by theAS, AFHA, and AJNDH techniques, resulting in classification errors.These classification errors are successfully avoided by the RSM andRFHA techniques, indicating that the suitable number of clusters isobtained by both techniques. The randomly initialized FCM tech-nique shares the same number of clusters with the RSM and RFHAtechniques. However, it suffers the same classification error pro-duced by the AS, AFHA, and AJNDH techniques because the initialcluster centers obtained in the randomly initialized FCM tech-nique are not properly initialized through the randomized process.Finally, for the image Diver, the AS and AFHA techniques producefewer clusters, but the quality of the segmentation result is lessacceptable than those produced by the randomly initialized FCM,AJNDH, RSM, and RFHA techniques. Thus, severe classification erroris observed (Fig. 10). Among the randomly initialized FCM, AJNDH,and RFHA techniques, the randomly initialized FCM and RFHA tech-niques outperform the AJNDH technique by producing better andlarger homogeneous regions for the image Diver (Fig. 10).
Table 3 shows that fewer clusters do not guarantee crediblesegmentation results. A tradeoff is found between the number ofclusters produced and the quality of segmentation results, whereinan insufficient number of clusters produced during the segmen-
tation process could lead to classification errors, as shown in theimages Birds, Moon, and Diver. Effective segmentation could beobtained by achieving more homogeneity in the regions whilekeeping a reasonable number of clusters.
K.S. Tan et al. / Applied Soft Computing 13 (2013) 2017–2036 2029
Table 4Comparison of clustering quality between the proposed RFHA and other conventional techniques based on the MSE evaluation function.
The MSE values of the randomly initialized FCM, AS, AFHA,JNDH, RSM, and RFHA techniques are tabulated in Table 4. The bestesults obtained are in boldface, whereas the second best results aren boldface and italics. This notation is employed for other resultsresented in this paper. Table 4 shows that the proposed RFHA tech-ique consistently produces relatively smaller MSE values than thether approaches (i.e., ranked as the best or second best, exceptor the image of Lena). The smaller values indicate that the clus-ering quality of the proposed RFHA technique is better than thether approaches. This observation is consistent with the visualnspection results in Section 3.1. Although the RSM technique couldroduce more homogeneous regions in some parts of the tested
mages, the MSE values of these images are always larger than thoseroduced by the RFHA technique. Thus, despite the fact that fewerlusters are produced by the RSM technique, the RFHA techniqueould consistently produce better cluster distribution than the RSMechnique.
Apart from the images shown in Figs. 6–12, the MSE values ofhe randomly initialized FCM, AS, AFHA, AJNDH, RSM, and RFHAechniques for 20 supplementary images (Fig. 13 of Appendix A)re tabulated in Table 10 of Appendix B. The relatively smaller MSEalues in the 20 images indicate that the proposed RFHA techniqueutperforms the randomly initialized FCM, AS, AFHA, AJNDH, and
SM techniques. The capability of the RFHA technique to produceonsistently smaller MSE values proves that it has the advantagef producing clustering results with less distortion compared withhe other techniques.
able 6omparison of segmentation results of the F’(I) evaluation function.
3.4. Quantitative evaluation of segmentation results
The quantitative results obtained for the F(I), F’(I), and Q(I) eval-uation functions are tabulated in Tables 5–7, respectively. Theproposed RFHA technique produces the best (smallest) F(I), F’(I),and Q(I) values for the images Birds, Swimmer, and Moon, and thesecond best values for the images Lena, Red Church, Diver, andLake. Among the values derived for the image Lake, the Q(I) valueobtained is the best (smallest). By generating smaller values for theF(I), F’(I), and Q(I) evaluation functions, the segmented regions pro-duced by the proposed RFHA technique are more homogeneous anddemonstrate less distortion compared with the other techniques.Consequently, significant segmentation results are attained. Theseresults support the favorable qualitative findings obtained by theproposed RFHA technique in the previous section. In addition, theseresults prove that the proposed RFHA technique outperforms therandomly initialized FCM, AS, AFHA, AJNDH, and RSM techniquesboth qualitatively and quantitatively.
The results tabulated in Tables 5–7 show that the other tech-niques produce good F(I), F’(I), and Q(I) evaluation functions onlyfor specific images. For example, the AFHA technique produces thesecond smallest F(I) value for the image Swimmer but fails to pro-duce the same result for the image Lena. Similar findings couldbe observed for the other evaluation functions such as F’(I) andQ(I) on the other images. The randomly initialized FCM, AS, AFHA,
AJNDH, and RSM techniques suffer from the same problem as well.Furthermore, the effective performance achieved by these tech-niques in terms of the F(I), F’(I), and Q(I) evaluation functions isnot consistently matched with the qualitative evaluation results
each performance metric is calculated and displayed in Table 9. Theaverage improvement produced by the proposed RFHA techniquecompared with the peer algorithm in each performance metric is
Table 8Performance comparison of segmentation results based on average values of MSE,F(I), F’(I), and Q(I) for 140 standard images.
Algorithm Benchmark quantitative evaluation function
resented in Section 3.1. For example, although the randomly ini-ialized FCM technique could produce the second best F(I), F’(I),nd Q(I) values in the image Birds, a significant classification errors observed, wherein the white feathers of the birds are mistakenlyssigned to the sky. Similar problems could be observed in the seg-entation results of the images Swimmer and Moon produced by
he AFHA technique. Although the F(I), F’(I), and Q(I) values pro-uced by the proposed RFHA technique are relatively small, thisechnique successfully prevents such classification errors. Further-
ore, the proposed RFHA technique can preserve the importanteatures of the input color images during the segmentationrocess.
In addition, the obtained F(I), F’(I), and Q(I) values suggesthat the randomly initialized FCM, AS, AFHA, AJNDH, and RSMechniques produce inconsistent quantitative performance on theame image. To illustrate, the AJNDH technique produces theest F(I) and F’(I) values for the image Lena but fails to maintainffective performance in terms of the Q(I) value. This techniques ranked as the second least effective among the techniques.he same problem can be observed for the randomly initial-zed FCM, AS, AFHA, and RSM techniques as well. However, theroposed RFHA technique consistently produces promising F(I),’(I), and Q(I) evaluation functions for all images. This proves theobustness of the proposed RFHA technique in maintaining con-istent and effective performance for any type of analysis andmage.
To support the abovementioned findings, the F(I), F’(I), and Q(I)alues of 20 supplementary images (Fig. 13 of Appendix A) forhe randomly initialized FCM, AS, AFHA, AJNDH, RSM, and RFHAechniques are tabulated in Table 11 of Appendix C. All the eval-ation functions favor segmentation by the RFHA technique, ashown by the smaller values of the three evaluation benchmarks.he AFHA and AJNDH techniques produce smaller F(I), F’(I), and(I) values than the RFHA technique in certain images. However,
he difference in these values is not significant. In addition, despitehe smaller F(I), F’(I), and Q(I) values produced by the AFHA andJNDH techniques, the segmentation region produced by the RFHA
echnique is more homogenous when inspected visually. Mean-hile, the randomly initialized FCM technique exhibits slightly
ffective performance in certain images by producing F(I), F’(I),nd Q(I) values that are comparable with those of the RFHA tech-ique. The effective performance of the randomly initialized FCMechnique in certain images is due to the fact that the num-er of clusters used in the randomly initialized FCM technique iset to the number of clusters obtained by the RFHA technique.owever, the randomly initialized FCM technique fails to be per-
istent in exhibiting effective performance in all images becausehe unstable randomized mechanism is used for the initializationrocess of the cluster center. By contrast, the initialization pro-
ess of the cluster center is performed using a more systematicrocedure of RSM in the proposed RFHA technique, which canuarantee a more accurate and reasonable estimation of the initialluster.
5.0855 9.1017 3.44181.3058 1.3763 0.7073
Finally, the AS and RSM techniques both show the most infe-rior performance in the segmentation process. This observationis reasonable because the original purpose of both AS and RSMtechniques is used as the basis for obtaining the non-optimal initialclusters for the segmentation process, prior to the implementationof the subsequent step of the FCM technique. Without this imple-mentation, the AS and RSM techniques cannot obtain the optimumfinal cluster centers. However, the superior performance of theRFHA technique over the AFHA and AJNDH techniques proves theexcellent performance of the RSM technique in determining theinitial clusters during the segmentation process.
To evaluate further the segmentation results produced by theproposed RFHA technique and the other current existing segmen-tation techniques, the average values of MSE, F(I), F’(I), and Q(I) for140 natural images taken from the public segmentation databaseare tabulated in Table 8. The AS and RSM techniques are discardedin this average quantitative evaluation based on the previous anal-yses that reveal their ineffective performance and their failure toguarantee the acquisition of the optimum final cluster centers inthe segmentation process. Based on the average values of MSE, F(I),F’(I), and Q(I), the performance of the techniques could be rankedas follows:
RFHA > AJNDH > randomly initialized FCM > AFHA
The proposed RFHA technique produces the smallest average val-ues of MSE, F(I), F’(I), and Q(I). By contrast, the AFHA techniqueyields the largest average values of MSE, F(I), and F’(I), as well asa large value of Q(I). Based on the average MSE values, the pro-posed RFHA technique is superior to the other techniques becauseit can produce more compact and stable clusters during the clus-tering process. In addition, the capabilities of the proposed RFHAtechnique in producing small values of F(I), F’(I), and Q(I) at a consis-tent pace during the segmentation process prove that the proposedRFHA technique is an excellent color image segmentation tech-nique.
To emphasize further the excellent performance of the proposedRFHA technique, the average improvement produced by the pro-posed RFHA technique compared with the other peer algorithms in
K.S. Tan et al. / Applied Soft Computing 13 (2013) 2017–2036 2031
Table 9Average improvement produced by the RFHA technique over the peer algorithms based on average values of MSE, F(I), F’(I), and Q(I) for 140 standard images.
Algorithm Average improvement of the RFHA technique in each performance metric
MSE F(I) F’(I) Q(I)
.46%
.95%
.33%
c
A
wvdr
tivbpFronctAQ1Awfa
TttsuaAdsphpniTRit
FCM vs. RFHA 10.17% 9AFHA vs. RFHA 11.97% 10AJNDH vs. RFHA 4.92% 3
alculated using the following equation:
verage improvement = Result (peer algorithm) − Result (RFHA)Result (peer algorithm)
× 100% (13)
here Result (peer algorithm) and Result (RFHA) represent thealues of the performance metrics [i.e. MSE, F(I), F’(I), Q(I)] pro-uced by the peer algorithms and the proposed RFHA technique,espectively.
Compared with the other peer algorithms, the proposed RFHAechnique could obtain promising segmentation results, with 12%mprovement in clustering quality (as represented by the MSEalue) and 63.16% reduction in classification errors (as representedy the F(I), F’(I), and Q(I) values) (Table 9). For the MSE analysis, theroposed RFHA technique is superior to the randomly initializedCM, AFHA, and AJNDH techniques by 10.17%, 11.97%, and 4.92%,espectively. For the F(I) analysis, the proposed RFHA techniqueutperforms the randomly initialized FCM, AFHA, and AJNDH tech-iques by 9.46%, 10.95%, and 3.33%, respectively. A similar trendould be observed in the F’(I) analysis, wherein the proposed RFHAechnique outperforms the randomly initialized FCM, AFHA, andJNDH techniques by 9.46%, 11.14%, and 3.41%, respectively. In the(I) analysis, the RFHA technique shows a superiority of 13.43%,7.09%, and 63.16% over the randomly initialized FCM, AFHA, andJNDH techniques, respectively. The results in Table 9 are alignedith the results of quanlitative and quantitative analyses, which
urther validate the excellence of the proposed RFHA technique as color image segmentation technique.
From the results obtained, another observation could be drawn.he qualitative and quantitative experimental results indicate thathat standalone RSM module produces less satisfactory segmen-ation results compared with the proposed RFHA technique. Aimilar behavior has been observed in earlier studies. The AS mod-le adopted as the initialization scheme for the AFHA techniquelso delivers less effective segmentation results compared with theFHA technique [26]. The less effective performances of the stan-alone RSM and AS modules are mainly due to their inability toeek a compact clustering result in the feature space [26]. The poorerformance of the standalone RSM technique eventually led us toybridize the RSM module with the FCM clustering technique androduce the RFHA technique. The results show that the compact-ess of the clustering results of the RFHA technique is substantially
mproved as compared with that of the standalone RSM module.
his excellent performance is supported by the capability of theSM module to produce clusters numbers and centroids automat-
cally and adaptively, as well as the capability of the FCM moduleo seek a compact clustering result in the feature space.
9.46% 13.43%11.14% 17.09%
3.41% 63.16%
4. Conclusions
This paper presents the RFHA technique, an adaptive unsu-pervised clustering approach used to perform color imagesegmentation. We propose the RSM technique to determine theinitial cluster centers and numbers automatically and adaptivelyfor the initialization of the FCM clustering technique. In somecases, the RSM technique could produce credible segmentationresults. Therefore, this technique could be used as a segmenta-tion approach for regions of interest. However, the RSM techniquecould not guarantee the acquisition of the optimum final clustercenters. Hence, the FCM clustering technique is applied to obtainthe optimum final cluster centers. Experimental results show thatthe RFHA technique can obtain better segmentation results com-pared with other existing segmentation techniques by providingmore homogeneous segmented regions and avoiding classificationerrors.
Acknowledgements
The authors express their sincere thanks to the associate edi-tor and the reviewers for their significant contributions to theimprovement of the final paper. This research was supported by theFundamental Research Grant Scheme (FRGS), Ministry of HigherEducation (MOHE), Malaysia titled “Investigation of New ColorImage Illumination Estimation Concept for Development of NewColor Correction Techniques” and Universiti Sains Malaysia (USM)Postgraduate Fellowship Scheme.
Appendix A. Segmentation results of the 20 test imagesfrom the randomly initialized FCM, AS, AFHA, AJNDH, RSM,and RFHA techniques
Fig. 13 .
Appendix B. Comparison of segmentation results from therandomly initialized FCM, AS, AFHA, AJNDH, RSM, and RFHAtechniques based on the MSE evaluation function
Table 10.
Appendix C. Comparison of segmentation results from therandomly initialized FCM, AS, AFHA, AJNDH, RSM, and RFHA
techniques based on the F(I), F’(I), and Q(I) evaluationfunctions
Table 11 .
2032 K.S. Tan et al. / Applied Soft Computing 13 (2013) 2017–2036
Fig. 13. Image segmentation tests. First column: original images. Second column: randomly initialized FCM segmentation. Third column: AS segmentation. Fourth column:AFHA segmentation. Fifth column: AJNDH segmentation. Sixth column: RSM segmentation. Seventh column: RFHA segmentation. Test images from the first to the twentiethrows are Car, Smarties2, Tiffany, Onion, Hill, Castle, Bridge, Hill2, Kangaroo, Bird2, Sun Flower, Plane, Bonsai, Goat, Crown, White Church, Old Man, Eagle, Onion2, and Houserespectively.
K.S. Tan et al. / Applied Soft Computing 13 (2013) 2017–2036 2033
Fig. 13. (Continued).
2034 K.S. Tan et al. / Applied Soft Computing 13 (2013) 2017–2036
Fig. 13. (Continued).
Table 10Comparison of clustering quality of the MSE evaluation function.
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Khang Siang Tan received his B. Eng. degree in Mechatronic Engineering from Uni-versiti Sains Malaysia (USM), in 2009. He obtained his M.Sc. degree in Electricaland Electronic Engineering (major in image processing) from the same universityin 2011. During his M.Sc. study, he worked with the Imaging and Intelligent Sys-tems Research Team (ISRT), School of Electrical and Electronic Engineering, USM.His research interests include image enhancement and image segmentation.
Nor Ashidi Mat Isa received the B. Eng. degree in Electrical and Electronic Engi-neering with First Class Honors from USM in 1999. In 2003, he went on to receivehis Ph.D. degree in Electronic Engineering (major in Image Processing and Artifi-cial Neural Network). Currently, he serves as associate professor and lectures atthe School of Electrical and Electronic Engineering, USM. His research interestsinclude intelligent systems, image processing, neural network, biomedical engineer-ing, intelligent diagnostic systems, and algorithms. He has provided leadership tothe ISRT research group in publishing at both the national and international are-nas. Their contributions can be found in numerous journals, book chapters, andproceedings.
Wei Hong Lim received his B. Eng. degree in Mechatronic Engineering with FirstClass Honors from USM, Malaysia in 2011. He is currently pursuing his Ph.D. degreein Electrical and Electronic Engineering and is works with the ISRT, School of Elec-trical and Electronic Engineering, USM. His research interests include digital imageprocessing and artificial intelligence.
