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Psoriasis image identification using k-means clustering with morphological processing
Measurement 44 (2011) 895–905
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Measurement journal homepage: www.elsevier.com/locate/measurement
Psoriasis image identification using k-means clustering with morphological processing Li-Hong Juang a,⇑, Ming-Ni Wu b a b
Department of Applied Mechanics, Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia Department of Information Management, National Taichung Institute of Technology, Taichung, Taiwan, ROC
a r t i c l e
i n f o
Article history: Received 23 March 2010 Received in revised form 19 December 2010 Accepted 16 February 2011 Available online 1 March 2011 Keywords: Psoriasis image k-means clustering Morphological reconstruction Dilation Erosion
a b s t r a c t We present a preliminary design and experimental results of psoriasis objects tracking method for color-skin images that utilizes k-means clustering with morphological processing technique. The method is capable of solving unable exactly contoured psoriasis objects problem in color-skin image by adding the morphological reconstruction operation. The key idea of the proposed image processing procedure is the k-means clustering method helps the rough segmentation, then the dilation and erosion method are adapted to refine previous results. In this paper we investigate the possibility of employing this approach for psoriasis image application. The application of the proposed method for tracking psoriasis is demonstrated to help pathologists distinguish exactly its size and region. In this paper, we propose a psoriasis image segmentation procedure to improve the accuracy. The experimental results demonstrate that the misclassification error is very small between the proposed result and hand drawing. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Psoriasis [1] disease is a kind of disorder characterized by scaly papules and plaques, which usually are transmitted genetically with a dominant mode with variable penetrance but the origin is unknown until nowadays. Patients with psoriasis are more emotionally than physically disabling. Psoriasis will erode the self-image and forces the victim becoming a life of concealment and self-consciousness. So, when a patient has only a few asymptomatic chronic plaques, the disease will be more serious than it appears. The disease will be lifelong and characterized by chronic recurrent exacerbations and remissions, which are emotionally and physically debilitating. The lesions of psoriasis are quite distinctive; they initially have as red scaling papules that coalesce to form round-to-oval plaques, which can be viewed from the surrounding normal skin. It is silvery white and reveals bleeding points when removed, there usually be several variations in the mor⇑ Corresponding author. Tel.: +60 75534555; fax: +60 75566159. E-mail address: [email protected] (L.-H. Juang). 0263-2241/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.measurement.2011.02.006
phology of psoriasis. In this research, we will focus on the chronic plaque psoriasis with following characteristics. It usually be a well-defined plaque that is the most common presentation of psoriasis, which can appear anywhere on the cutaneous surface with a temporary brown, white, or red macula remains when the plaque subsides. Furthermore, they will enlarge to a certain size and then tend to remain stable for months or years. The percentage of the area of psoriasis is the major index to evaluate the disease expanded condition. Due to psoriasis being a chronic disease, it is very important to track the condition of the patient and select a proper treatment. In this research, we mainly design a imaging process that segments the image into normal and abnormal skin regions, then the area of the psoriasis vulgaris can be estimated. Imaging is a basic aspect of medical sciences for visualization of anatomical structures and functional or metabolic information of the human body [2]. Structural and functional imaging of human body is important for understanding the human body anatomy, physiological processes, function of organs, and behavior of whole or a part of organ under the influence of abnormal physiological
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conditions or a disease [3,4]. For the last two decades, radiological sciences have witnessed a revolutionary progress in medical imaging [5–19] and computerized medical image processing [20,21], some important radiological tools in diagnosis and treatment evaluation and intervention of critical diseases have much significant improvement for health care. So, medical imaging in diagnostic radiology is evolving as a result of the significant contributions of a number of different disciplines from basic sciences, engineering, and medicine. Therefore, computerized image reconstruction, processing and analysis methods have been developed for medical imaging applications. The application-domain knowledge has been used in developing models for accurate analysis and interpretation. Segmentation is a major step in medical image analysis and classification for radiological evaluation or computeraided diagnosis. Image segmentation is to the process of partitioning an image into distinct region by grouping together neighborhood pixels based on some pre-defined similarity criterion. The similarity principle can be determined using specific properties or features of pixels representing objects in the image. So, segmentation is a pixel classification technique that allows the formation of regions of similarities in the image. Image segmentation methods can be widely classified into three categories: Edge-based methods, where the edge information is used for boundaries of objects. The boundaries are then analyzed and modified, if necessary, to form closed regions belonging to the objects in the image; pixel-based direct classification method, where heuristics or estimation method derived from the histogram statistics of the image are used for forming closed regions belonging to the objects in the image; Region-based method, where pixels are analyzed directly for a region growing process based on a pre-defined similarity principle to form closed region belonging to the objects in the image. When the regions are defined, features can be computed to represent regions for characterization, analysis and classification. These features will include shape and texture information of the regions as well as statistical properties, like variance and mean of gray values. In this paper, we will propose an image tracking method by using k-means clustering with morphological processing for psoriasis region. This proposed method helps pathologists distinguish exactly psoriasis size and region. For this reason, the paper is separately as follows. First, as above introduction, the brief review about psoriasis is guided. Second, the mathematical preliminaries and basic theorem for the image algorithms employed in the segmentation processing are derived. Third, the series of image tracking tests based on the developed process technique are tried and compare the other method [1]. Finally, some conclusions are made and discussed.
2. The procedure of the image processing technique In this research, we would propose an image process procedure to segment psoriasis images using k-means clustering with morphological processing for psoriasis region. Due to the variations of skin color of the psoriasis and normal regions for different patients being very vari-
able, the feature signatures acquired from one image may not be good for other images. To be accurate segmentation, a proper image process procedure for an image can be manually selected to fit the best accuracy. But, as the number of images increase, this region selection process may become tedious. It may be more useful tool if the system can analyze the images and locate suitable regions. Therefore, a proper image process procedure is proposed to facilitate the image segmentation process. The proposed technique consists of six major elements: k-mean clustering, gray-level, median filtering, binary imaging, Sobel edge process, and morphological reconstruction. The image process procedure for psoriasis image segmentation is shown in Fig. 1. The followings are the relative image processing algorithm description. 2.2. k-Means clustering process In this research, k-mean clustering process first was used to classify the object from original color-skin image. The pixel-based direct classification method is to use histogram statistics to define single or multiple thresholds to classify an image pixel-by-pixel. The threshold for classifying pixels into classes is acquired from the analysis of the histogram of the image. A simple approach is to examine the histogram for bimodal distribution. If the histogram is bimodal, the threshold can be set to the gray value corresponding to the deepest point in the histogram valley. If false, the image can be partitioned into two or more regions using some heuristics about the properties of the image. The histogram of each partition can then be used to determine thresholds. By comparing the gray value of each pixel to the selected threshold, a pixel can be classified into one or the two classes. An image f(x, y) can be segmented into two classes using a gray value threshold T then
gðx; yÞ ¼
1 if f ðx; yÞ > T 0
if f ðx; yÞ 6 T;
ð1Þ
where g(x, y) is the segmented image with two classes of binary gray values ‘‘1’’ and ‘‘0’’ and T is the threshold selected at the valley point from the histogram. A simple approach for determining the gray value threshold T is to analyze the histogram for the peak values and then finding the deepest valley point between the two consecutive major peaks. If a histogram is clearly bi-modal, this method would give good results. To determine an optimal global gray value threshold for image segmentation, parametric distribution based methods can be applied to the histogram of an image [19]. We assume that the histogram of an image to be segmented has two Gaussian distributions belonging to two respective classes such as background and object. Therefore the histogram can be represented by a mixture probability density function p(z) written as
pðzÞ ¼ P1 p1 ðzÞ þ P2 p2 ðzÞ;
ð2Þ
where p1(z) and p2(z) are the Gaussian distributions of class 1 and 2, respectively, with the class probabilities of P1 and P2 so that P1 + P2 = 1. Using a gray value threshold
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T, a pixel in the image f(x, y) is classified to class 1 or class 2 in the segmented image g(x, y) into
gðx; yÞ ¼
Class 1 if f ðx; yÞ > T
ð3Þ
Class 2 if f ðx; yÞ 6 T
Let us define the error probabilities of misclassifying a pixel for
E1 ðTÞ ¼
Z
T
p2 ðzÞdz
ð4Þ
p1 ðzÞdz;
ð5Þ
1
and
E2 ðTÞ ¼
Z
T
1
where E1(T) and E2(T) are, respectively, the probability of erroneously classifying a class 1 pixel to class 2 and a class 2 pixel to class 1. The overall probability of error in pixel classification using the threshold t is then written as
EðTÞ ¼ P2 ðTÞE1 ðTÞ þ P1 ðTÞE2 ðTÞ:
ð6Þ
For image segmentation, the objective is to find an optimal threshold T that minimizes the overall probability of error in pixel classification. The optimization process requires the parameterization of the probability density distributions and likelihood of both classes. These parameters can be determined from a model or set of training images [19]. We assume ri and li to be the standard deviation and mean of the Gaussian probability density function of the class i (i = 1,2 for two class) such that 2 2 P1 P2 2 2 pðzÞ ¼ pffiffiffiffiffiffiffi eðzl1 Þ =2r1 þ pffiffiffiffiffiffiffi eðzl1 Þ =2r2 : 2pr1 2pr2
ð7Þ
The optimal global threshold T can be determined by finding a general solution that minimizes Eq. (6) with the mixture distribution in Eq. (7) and so satisfies the following quadratic equation [19]:
AT 2 þ BT þ C ¼ 0;
ð8Þ
where A ¼ r21 r22 ; B ¼ 2 l1 r22 l2 r21 , and C ¼ r21 2 2 2 2 2 l2 r2 l1 þ 2r1 r2 lnðr2 P1 =r1 P2 Þ. If the variances of both classes is assumed to be equal to r2, the optimal threshold T can be obtained as
T¼
l1 þ l2 2
þ
r2 l1 l2
ln
P2 : P1
ð9Þ
It should be noted that in case of equal likelihood of classes, the above expression for determining the optimal threshold is simply reduced to the average of the mean values of two classes. Clustering is for the process of grouping data points with similar feature vectors together in a single cluster while data points with dissimilar feature vectors are placed in different clusters. Therefore the data points that are close to each other in the feature space are clustered together. The similarity of feature vectors can be represented by an appropriate distance measure such as Euclidean or Mahalanobis distance [20]. Each cluster is represented by its mean (centeroid) and variance (spread) associated with the distribution of the corresponding feature vectors of the data points in the cluster. The formation of clusters is optimized with respect to an objective function involving prespecified distance and similarity measures along with additional constraints like smoothness. The k-means clustering is a popular approach to partition d-dimensional data into k clusters such that an objective function providing the desired properties of the distribution of feature vectors of clusters in terms of similarity and distance measures is optimized. A generalized k-means clustering algorithm initially places k clusters at arbitrarily selected cluster centroids vi, i = 1, . . . , 2, k and modifies centroids for the formation of new cluster shapes optimizing the objective function. The k-means clustering algorithm includes the following steps: 1. Selecting the number of clusters k with initial cluster centroids vi, i = 1, . . . , 2, k.
Fig. 1. Flowchart for psoriasis image segmentation processing.
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2. Partitioning the input data points into k clusters by assigning each data point xj to the closest cluster centroid vi using the selected distance measure, for example, Euclidean distance, defined as
dij ¼ kxj v i k;
ð10Þ
where X = {x1, x2, . . . , xn} is the input data set. 3. Computing a cluster assignment matrix U representing the partition of the data points with the binary membership value of the jth data point to the ith cluster such that U ¼ buij c, where
uij 2 f0; 1g for all i; j k X
uij ¼ 1 for all j and 0 <
i¼1
n X
uij < n for alli:
ð11Þ
j¼1
4. Re-computing the centroids using the membership values Pby
vi ¼
n j¼1 uij xj Pn j¼1 uij
for all i:
k X n X i¼1
kxj v i k2 :
ð13Þ
j¼1
It can be spotted from the above algorithm that the kmeans clustering method is quite sensitive to the initial cluster assignment and the choice of the distance measure. Additional criterion like within-cluster and between-cluster variances can be included in the objective function as constraints to force the algorithm to adapt the number of clusters k, as necessary for optimization of the objective function. In this research, k-means clustering method was used to classify color-skin image, so clustering objects are color, not gray-level image that is easily and fast classified. 2.3. Gray-level process In this image process procedure, after k-mean clustering process, then gray-level process was used to convert a RGB color-skin image to intensity gray-level image. Usually, intensity I, saturation S and hue I can be used for color to gray-level converting which can be express as [19]
I¼
RþGþB ; 3
ð14Þ
3 ðminðR:G:BÞÞ; S¼1 ðR þ G þ BÞ H¼
h
if B 6 G
360 h if B > G
ð15Þ
GÞ þ ðR BÞ
½ðR GÞ þ ðR BÞðG BÞ1=2
) ;
ð17Þ
2.4. Median filtering After color to gray-level converting, the gray-level image will remain some small fragile noise caused by real skin texture. So a median filter was used to filter out them. Median filter is an order-statistics filter that replaces the original image gray value of a pixel by the median of gray value of pixels for the specified neighborhood. A median filter operation for a smoothed image f(x, y) computed from the acquired image g(x, y) is written as
f ðx; yÞ ¼ medianfgði; jÞg;
ð18Þ
ði;jÞ2N
where N is the pre-specified neighborhood of the pixel (x, y). The gray value of the central pixel f(0, 0) is replaced by the median of gray values of all pixels in the neighborhood. 2.5. Binary imaging After median filter process, binary imaging process was used to form the object contour. A binary image means an image only has black and white. A gray-level image can be turned into a binary image by first choosing a gray-level T in the original image, then turning every pixel into black or white according to whether its gray value is greater than or less that T:
A pixel turns
white if x > T black
if x T
;
ð19Þ
where x representatives gray value. 2.6. Sobel edge process After binary imaging process, Sobel edge process was used to sharpen edges in the psoriasis image. Basically, edge is defined by the change in gray values of pixels in the neighborhood which can be expressed by a derivative or a difference operation. Sobel edge process is a first-order derivative operator for computing the gradient information in a specific direction. Usually, the derivative operator is encoded into a weight mask. Sobel edge process uses two weight masks, respectively, in computing the first-order gradient in x-direction as follows:
2
1 2 1
6 4 0 1
0 2
3
7 0 5; 1
ð20Þ
and in y-direction as follows:
2 ;
ð16Þ
3 1 0 1 6 7 4 2 0 2 5: 1 0 1
where
1 ½ðR 2 2
where angle h is measured with respect to the red axis in the ISH coordinate space and R, G and B are respect to red, green and blue in RGB coordinate space respectively.
ð12Þ
5. If cluster centroids or the assignment matrix does not change from the previous iteration, stop; otherwise go to Step 2. The k-means clustering method optimizes the sum-ofsquared-error based objective function Jw(U, v) then
Jw ðU; v Þ ¼
( h ¼ cos1
ð21Þ
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(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
Fig. 2. The first-case psoriasis images: (a) original image [1], (b) k-mean process image, (c) gray-level process image, (d) median filter process image, (e) binary process image, (f) Sobel process image, (g) morphological reconstruction image, (h) added into original image, and (i) hand-drawing contour image.
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Each of the two weight masks of 3 3 pixels will be used for convolution to compute respective gradient images. The resultant gradient image can be added
to the original image and rescaled using the full dynamic range of gray values for spatial image enhancement.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
Fig. 3. The second-case psoriasis images: (a) original image [1], (b) k-mean process image, (c) gray-level process image, (d) median filter process image, (e) binary process image, (f) Sobel process image, (g) morphological reconstruction image, (h) added into original image, and (i) hand-drawing contour image.
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(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
Fig. 4. The third-case psoriasis images: (a) original image [1], (b) k-mean process image, (c) gray-level process image, (d) median filter process image, (e) binary process image, (f) Sobel process image, (g) morphological reconstruction image, (h) added into original image, and (i) hand-drawing contour image.
2.7. Morphological reconstruction After Sobel edge process, morphological reconstruction was used to finalize the shape of psoriasis region. Morpho-
logical processing is based on the set theory to provide basic tools to deal with images for filtering, thinning and pruning operations that are useful for the description of region shape involving boundary and skeleton
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(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
Fig. 5. The fourth-case psoriasis images: (a) original image [1], (b) k-mean process image, (c) gray-level process image, (d) median filter process image, (e) binary process image, (f) Sobel process image, (g) morphological reconstruction image, (h) added into original image, and (i) hand-drawing contour image.
representation. Dilation and erosion are the two fundamental operations in morphological processing. Our Mor-
phological processing algorithms are based on the specific combination of the dilation and erosion opera-
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(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
Fig. 6. The fifth-case psoriasis images: (a) original image [1], (b) k-mean process image, (c) gray-level process image, (d) median filter process image, (e) binary process image, (f) Sobel process image, (g) morphological reconstruction image, (h) added into original image, and (i) hand-drawing contour image. _
tions. First we define two sets A and B belonging to an ndimensional space Zn. The dilation of set A by B, D(A, B) can be denoted by A B and defined as
DðA; BÞ ¼ A B ¼
[
A þ b;
ð22Þ
where B ¼ ½Bjb 2 Bg is the reflection set of B with respect to its origin. The erosion of set A by set B, E(A, B) can be denoted by A H B and defined as
EðA; BÞ ¼ AHB ¼ \ A b; b2B
b2B
ð24Þ
and
and _
A B ¼ fxjðB Þx \ A – 0g;
ð23Þ
AHB ¼ fxjðBÞx # Ag:
ð25Þ
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The above equation states that the erosion of a set A by a set B comprises all points x such that the set B located at x is entirely inside A. Usually, dilation and erosion are dual operation to each other, that is, _
A B ¼ ðAc H B Þc ;
ð26Þ
and _
AHB ¼ ðAc B Þc ;
ð27Þ
c
where A represents the complement of set A. After finishing morphological processing, we need to add the morphological reconstruction image with original color-skin image, then acquire the psoriasis segmentation image. 2.8. Segmentation test According to the image process procedure as shown in Fig. 1, it takes six steps to finish psoriasis image segmentation from k-mean clustering, gray-level, median filtering, binary imaging, Sobel edge process, to morphological reconstruction. In this research, we use psoriasis image five cases for segmentation test as shown in Figs. 2b–6b (288 288). For k-mean clustering, the color-skin image segmentation is same as pseudo color mapping, which is defined as a method that converts colors into a single integer index that is used to select a color from a list of specified colors in a data collection. It contains a weighting vector [L1, L2, L3] for RGB color format and a list of R colors. An index of 1 corresponds to the first color on this list; the mapping process is as the followings: 1. Normalize the weighting vector L by dividing it by its component summary. 2. Calculate J = round((R 1)(L1C1 + L2C2 + L3C3) + 1), where [C1, C2, C3] = [red, green, blue]. 3. Use J as an index to select one of the entries in the color list. 4. The selected color needs to display on the workstation more accurately. In histogram-based pixel classification method for image segmentation, the RGB values are partitioned into
Table 1 Accuracy for psoriasis image segmentation processing. Figure no.
Accuracy (%)
Fig. Fig. Fig. Fig. Fig.
97.23 94.49 90.22 88.45 87.54
2 3 4 5 6
two or more clusters depending on the peaks in the histogram to obtain thresholds. A color image may have additional color components in a specific representation such as Red, Green and Blue components in the RGB color coordinate system that can be added to the feature vector. The basic concept of segmentation by pixel classification can be extended to clustering the gray values of feature vector of pixels in the image. This approach is particularly useful when images with pixels representing a feature vector consisting of multiple parameters of interest are to be segmented. Figs. 2b–6b show the results after k-mean clustering process, respectively. The difference between psoriasis color (dark red) and skin color (light red) is small, so kmean clustering process is very fast. Multi-modality medical images may also require segmentation using a multi-dimensional feature space with multiple parameters of interest. Images can be segmented by pixel classification through clustering of all features of interest. The number of clusters in the multi-dimensional feature space thus represents the number of classes in the image. As the image is classified into cluster classes, segmented regions are obtained by checking the neighborhood pixels for the same class label. However, clustering may produce disjoint regions with holes or regions with a single pixel. After the image data are clustered and pixels are classified, some post-processing algorithm such as gray-level, median filtering, binary imaging, Sobel edge process, and morphological reconstruction algorithm are usually applied to obtain the final segmented regions. Figs. 2c–6c show to converts Lab color space image into the gray-level image, where the Lab space consists of a luminosity layer ‘L’, chromaticity-layer ‘a’ indicating where color falls along the red–green axis, and chromaticity-layer ‘b’ indicating where the color falls along the blue–yellow axis. All of the color information is in the ‘a’ and ‘b’ layers. The difference between two colors can be measured by using the Euclidean distance metric. The color skin has almost no color difference, so its converting gray value is also very fast. Then, Figs. 2d–6d show the results after median filtering, respectively. The median filter was mainly used to filter out some small fragile noise caused by real skin texture. It seems that there is more small fragile noise, so its processing will take some time. And then, Figs. 2e–6e show the results after binary imaging, due to the psoriasis image already gray, so its processing is also very fast. Again then, Figs. 2f–6f show the results after Sobel edge process, due to the psoriasis image already binary, so its processing is also very fast. Finally, Figs. 2g–6g show the results after morphological reconstruction, because it involves dilation and erosion process, its processing will take some time. Figs. 2h–6h show the psoriasis segmentation image results from adding the morphological reconstruction image with original color-skin image. To compute the psoriasis seg-
Table 2 Time complexity for psoriasis image segmentation processing steps. Step
k-mean
Gray-level
Median filter
Binary image
Sobel
MR
Time complexity (O)
N
N
N2
N
N
N2
MR: morphological reconstruction.
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mentation accuracy, we need to make the psoriasis region contour by hand drawing as shown in Figs. 2i–6i, which are assumed 100% accuracy. Table 1 shows the accuracy for psoriasis image segmentation processing. In general, the average accuracy is good above 90%. The experimental results demonstrate that the misclassification error is very small between the proposed result and hand drawing. We also compute the time complexity for psoriasis image segmentation processing step, the result is shown in Table 2. The results show the proposed procedure has lower time complexity (O) except median filtering and morphological reconstruction process, that is, it saves lots computing time. N is lower time complexity and N2 is normal time complexity. To prove the proposed method is best on accuracy, and computing time, we took the method [1], ‘‘Segmentation of psoriasis vulgaris images using multiresolution-based orthogonal Subspace Techniques’’, from its experiments for the comparison, its time complexity is more than N4. The results show the proposed method saves lots computing time and has the best accuracy due to our lower time complexity. The higher time complexity means more spending computing time and low accuracy. 3. Conclusions We have proposed a realization of psoriasis region tracking method of color-skin image using k-means clustering with morphological processing technique. A preliminary evaluation on psoriasis image shows encouraging results. k-means clustering with morphological segmentation algorithm for tracking objects in medical images is performed to be very promising for medical image segmentation applications. The regions related to psoriasis can be exactly separated from the color-skin image. This proposed method will be able to help pathologists distinguish exactly psoriasis size and region. References [1] J.S. Taur, G.H. Lee, C.W. Tao, C.C. Chen, C.W. Yang, Segmentation of psoriasis vulgaris images using multiresolution-based orthogonal subspace techniques, IEEE Trans. Syst. Man Cybernet.—Part B: Cybernet. 36 (2) (2006) 390–402. [2] A. Rangarajan, I.T. Hsiao, G. Gindi, A Bayesian joint mixture framework for the integration of anatomical in functional image reconstruction, J. Math. Imag. Vis. 12 (2000) 199–217.
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[3] F.M. Enzinger, S.W. Weiss, Malignant vascular tumors, in: F.M. Enzinger, S.W. Weiss (Eds.), Soft Tissue Tumors, third ed., Mosby, St Louis, MO, 1995, pp. 655–677. [4] L.V.D. Hauwe, F. Ramon, Lymphatic tumors, in: A.M. De Schepper (Ed.), Imaging of Soft Tumors, second ed., Springer, Heidelberg, 2001, pp. 246–254. [5] K.Y. Tu, T.B. Chen, H.H.S. Lu, R.S. Liu, K.L. Chen, C.M. Chen, J.C. Chen, Empirical studies of cross-reference maximum likelihood estimate reconstruction for positron emission tomography, Biomed. Eng. – Appl. Basis Commun. 13 (1) (2001) 1–7. [6] C.M. Kao, X. Pan, C.T. Chen, W.H. Wong, Image restoration and reconstruction with a Bayesian approach, Med. Phys. 25 (5) (1998) 600–613. [7] G.N. Hounsfield, Computerized transverse axial scanning tomography. Part 1: description of the system, Br. J. Radiol. 46 (1973) 1016–1022. [8] B. Lipinski, H. Herzog, E.R. Kops, W. Oberschelp, H.W. MullerGartner, Expectation maximization reconstruction of positron emission tomography images using anatomical magnetic resonance information, IEEE Trans. Med. Imag. 16 (2) (1997) 129– 136. [9] A. Bazille, M.A. Guttman, E.R. Mcveigh, E.A. Zerhouni, Impact of semiautomated versus manual image segmentation errors on myocardial strain calculation by magnetic resonance tagging, Invest. Radiol. 29 (4) (1994) 427–433. [10] H. Anger, Use of gamma-ray pinhole camera for vivo studies, Nature 170 (1952) 200–204. [11] X. Ouyang, W.H. Wang, V.E. Johnson, X. Hu, C.T. Chen, Incorporation of correlated structural images in PET image reconstruction, IEEE Trans. Med. Imag. 13 (2) (1994) 627–640. [12] Y.S. Akgul, C. Kambhamettu, M. Stone, Extraction and tracking of the tongue surface from ultrasound image sequences, in: Proceedings IEEE Computer Vision Pattern Recognition, Santa Barbara, CA, 1998, pp. 298–303. [13] U.R. Abeyratne, A.P. Petropulu, J.M. Reid, On modeling the tissue response from ultrasonic B-scan images, IEEE Trans. Med. Imag. 1 (2) (1996) 479–490. [14] T.L. Faber, E.M. Stokely, Orientation of 3D structures in medical images, IEEE Trans. Pattern Anal. Mach. Intel. 2 (2) (1980) 127–135. [15] G.J. Grewera, J.K. Udupa, Shape based interpolation of multidimensional grey-level images, IEEE Trans. Med. Imag. 15 (6) (1996) 881–892. [16] F.S. Cohen, G. Georgiou, E. Halpern, WOLD decomposition of the backscatter echo in ultrasound images of soft tissue organs, IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 1 (2) (1997) 460–472. [17] K.D. Donohue, F. Forsberg, C.W. Piccoli, B.B. Goldberg, Classification of breast masses with ultrasonic scattering structure templates, IE EE Trans. Ultrason. Ferroelectr. Freq. Contr. 1 (2) (1999) 300–310. [18] G. Georgiou, F.S. Cohen, Statistical characterization of diffuse scattering in ultrasound images, IEEE Trans. Ultrason. Ferroelectr. Freq. Contr. 1 (2) (1998) 57–64. [19] R.C. Gonzalez, R.E. Woods, Digital Image Processing, second ed., Prentice-Hall, Englewood Cliffs, NJ, 2002 (Competitive). [20] A.P. Dhawan, L. Arata, Segmentation of medical images through competitive learning, Comput. Methods Prog. Biomed. 40 (2) (1993) 203–215. [21] R.O. Duda, P.E. Hart, Pattern Classification and Scene Analysis, Wiley, New York, 1973.
Contents lists available at ScienceDirect
Measurement journal homepage: www.elsevier.com/locate/measurement
Psoriasis image identification using k-means clustering with morphological processing Li-Hong Juang a,⇑, Ming-Ni Wu b a b
Department of Applied Mechanics, Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia Department of Information Management, National Taichung Institute of Technology, Taichung, Taiwan, ROC
a r t i c l e
i n f o
Article history: Received 23 March 2010 Received in revised form 19 December 2010 Accepted 16 February 2011 Available online 1 March 2011 Keywords: Psoriasis image k-means clustering Morphological reconstruction Dilation Erosion
a b s t r a c t We present a preliminary design and experimental results of psoriasis objects tracking method for color-skin images that utilizes k-means clustering with morphological processing technique. The method is capable of solving unable exactly contoured psoriasis objects problem in color-skin image by adding the morphological reconstruction operation. The key idea of the proposed image processing procedure is the k-means clustering method helps the rough segmentation, then the dilation and erosion method are adapted to refine previous results. In this paper we investigate the possibility of employing this approach for psoriasis image application. The application of the proposed method for tracking psoriasis is demonstrated to help pathologists distinguish exactly its size and region. In this paper, we propose a psoriasis image segmentation procedure to improve the accuracy. The experimental results demonstrate that the misclassification error is very small between the proposed result and hand drawing. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Psoriasis [1] disease is a kind of disorder characterized by scaly papules and plaques, which usually are transmitted genetically with a dominant mode with variable penetrance but the origin is unknown until nowadays. Patients with psoriasis are more emotionally than physically disabling. Psoriasis will erode the self-image and forces the victim becoming a life of concealment and self-consciousness. So, when a patient has only a few asymptomatic chronic plaques, the disease will be more serious than it appears. The disease will be lifelong and characterized by chronic recurrent exacerbations and remissions, which are emotionally and physically debilitating. The lesions of psoriasis are quite distinctive; they initially have as red scaling papules that coalesce to form round-to-oval plaques, which can be viewed from the surrounding normal skin. It is silvery white and reveals bleeding points when removed, there usually be several variations in the mor⇑ Corresponding author. Tel.: +60 75534555; fax: +60 75566159. E-mail address: [email protected] (L.-H. Juang). 0263-2241/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.measurement.2011.02.006
phology of psoriasis. In this research, we will focus on the chronic plaque psoriasis with following characteristics. It usually be a well-defined plaque that is the most common presentation of psoriasis, which can appear anywhere on the cutaneous surface with a temporary brown, white, or red macula remains when the plaque subsides. Furthermore, they will enlarge to a certain size and then tend to remain stable for months or years. The percentage of the area of psoriasis is the major index to evaluate the disease expanded condition. Due to psoriasis being a chronic disease, it is very important to track the condition of the patient and select a proper treatment. In this research, we mainly design a imaging process that segments the image into normal and abnormal skin regions, then the area of the psoriasis vulgaris can be estimated. Imaging is a basic aspect of medical sciences for visualization of anatomical structures and functional or metabolic information of the human body [2]. Structural and functional imaging of human body is important for understanding the human body anatomy, physiological processes, function of organs, and behavior of whole or a part of organ under the influence of abnormal physiological
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conditions or a disease [3,4]. For the last two decades, radiological sciences have witnessed a revolutionary progress in medical imaging [5–19] and computerized medical image processing [20,21], some important radiological tools in diagnosis and treatment evaluation and intervention of critical diseases have much significant improvement for health care. So, medical imaging in diagnostic radiology is evolving as a result of the significant contributions of a number of different disciplines from basic sciences, engineering, and medicine. Therefore, computerized image reconstruction, processing and analysis methods have been developed for medical imaging applications. The application-domain knowledge has been used in developing models for accurate analysis and interpretation. Segmentation is a major step in medical image analysis and classification for radiological evaluation or computeraided diagnosis. Image segmentation is to the process of partitioning an image into distinct region by grouping together neighborhood pixels based on some pre-defined similarity criterion. The similarity principle can be determined using specific properties or features of pixels representing objects in the image. So, segmentation is a pixel classification technique that allows the formation of regions of similarities in the image. Image segmentation methods can be widely classified into three categories: Edge-based methods, where the edge information is used for boundaries of objects. The boundaries are then analyzed and modified, if necessary, to form closed regions belonging to the objects in the image; pixel-based direct classification method, where heuristics or estimation method derived from the histogram statistics of the image are used for forming closed regions belonging to the objects in the image; Region-based method, where pixels are analyzed directly for a region growing process based on a pre-defined similarity principle to form closed region belonging to the objects in the image. When the regions are defined, features can be computed to represent regions for characterization, analysis and classification. These features will include shape and texture information of the regions as well as statistical properties, like variance and mean of gray values. In this paper, we will propose an image tracking method by using k-means clustering with morphological processing for psoriasis region. This proposed method helps pathologists distinguish exactly psoriasis size and region. For this reason, the paper is separately as follows. First, as above introduction, the brief review about psoriasis is guided. Second, the mathematical preliminaries and basic theorem for the image algorithms employed in the segmentation processing are derived. Third, the series of image tracking tests based on the developed process technique are tried and compare the other method [1]. Finally, some conclusions are made and discussed.
2. The procedure of the image processing technique In this research, we would propose an image process procedure to segment psoriasis images using k-means clustering with morphological processing for psoriasis region. Due to the variations of skin color of the psoriasis and normal regions for different patients being very vari-
able, the feature signatures acquired from one image may not be good for other images. To be accurate segmentation, a proper image process procedure for an image can be manually selected to fit the best accuracy. But, as the number of images increase, this region selection process may become tedious. It may be more useful tool if the system can analyze the images and locate suitable regions. Therefore, a proper image process procedure is proposed to facilitate the image segmentation process. The proposed technique consists of six major elements: k-mean clustering, gray-level, median filtering, binary imaging, Sobel edge process, and morphological reconstruction. The image process procedure for psoriasis image segmentation is shown in Fig. 1. The followings are the relative image processing algorithm description. 2.2. k-Means clustering process In this research, k-mean clustering process first was used to classify the object from original color-skin image. The pixel-based direct classification method is to use histogram statistics to define single or multiple thresholds to classify an image pixel-by-pixel. The threshold for classifying pixels into classes is acquired from the analysis of the histogram of the image. A simple approach is to examine the histogram for bimodal distribution. If the histogram is bimodal, the threshold can be set to the gray value corresponding to the deepest point in the histogram valley. If false, the image can be partitioned into two or more regions using some heuristics about the properties of the image. The histogram of each partition can then be used to determine thresholds. By comparing the gray value of each pixel to the selected threshold, a pixel can be classified into one or the two classes. An image f(x, y) can be segmented into two classes using a gray value threshold T then
gðx; yÞ ¼
1 if f ðx; yÞ > T 0
if f ðx; yÞ 6 T;
ð1Þ
where g(x, y) is the segmented image with two classes of binary gray values ‘‘1’’ and ‘‘0’’ and T is the threshold selected at the valley point from the histogram. A simple approach for determining the gray value threshold T is to analyze the histogram for the peak values and then finding the deepest valley point between the two consecutive major peaks. If a histogram is clearly bi-modal, this method would give good results. To determine an optimal global gray value threshold for image segmentation, parametric distribution based methods can be applied to the histogram of an image [19]. We assume that the histogram of an image to be segmented has two Gaussian distributions belonging to two respective classes such as background and object. Therefore the histogram can be represented by a mixture probability density function p(z) written as
pðzÞ ¼ P1 p1 ðzÞ þ P2 p2 ðzÞ;
ð2Þ
where p1(z) and p2(z) are the Gaussian distributions of class 1 and 2, respectively, with the class probabilities of P1 and P2 so that P1 + P2 = 1. Using a gray value threshold
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T, a pixel in the image f(x, y) is classified to class 1 or class 2 in the segmented image g(x, y) into
gðx; yÞ ¼
Class 1 if f ðx; yÞ > T
ð3Þ
Class 2 if f ðx; yÞ 6 T
Let us define the error probabilities of misclassifying a pixel for
E1 ðTÞ ¼
Z
T
p2 ðzÞdz
ð4Þ
p1 ðzÞdz;
ð5Þ
1
and
E2 ðTÞ ¼
Z
T
1
where E1(T) and E2(T) are, respectively, the probability of erroneously classifying a class 1 pixel to class 2 and a class 2 pixel to class 1. The overall probability of error in pixel classification using the threshold t is then written as
EðTÞ ¼ P2 ðTÞE1 ðTÞ þ P1 ðTÞE2 ðTÞ:
ð6Þ
For image segmentation, the objective is to find an optimal threshold T that minimizes the overall probability of error in pixel classification. The optimization process requires the parameterization of the probability density distributions and likelihood of both classes. These parameters can be determined from a model or set of training images [19]. We assume ri and li to be the standard deviation and mean of the Gaussian probability density function of the class i (i = 1,2 for two class) such that 2 2 P1 P2 2 2 pðzÞ ¼ pffiffiffiffiffiffiffi eðzl1 Þ =2r1 þ pffiffiffiffiffiffiffi eðzl1 Þ =2r2 : 2pr1 2pr2
ð7Þ
The optimal global threshold T can be determined by finding a general solution that minimizes Eq. (6) with the mixture distribution in Eq. (7) and so satisfies the following quadratic equation [19]:
AT 2 þ BT þ C ¼ 0;
ð8Þ
where A ¼ r21 r22 ; B ¼ 2 l1 r22 l2 r21 , and C ¼ r21 2 2 2 2 2 l2 r2 l1 þ 2r1 r2 lnðr2 P1 =r1 P2 Þ. If the variances of both classes is assumed to be equal to r2, the optimal threshold T can be obtained as
T¼
l1 þ l2 2
þ
r2 l1 l2
ln
P2 : P1
ð9Þ
It should be noted that in case of equal likelihood of classes, the above expression for determining the optimal threshold is simply reduced to the average of the mean values of two classes. Clustering is for the process of grouping data points with similar feature vectors together in a single cluster while data points with dissimilar feature vectors are placed in different clusters. Therefore the data points that are close to each other in the feature space are clustered together. The similarity of feature vectors can be represented by an appropriate distance measure such as Euclidean or Mahalanobis distance [20]. Each cluster is represented by its mean (centeroid) and variance (spread) associated with the distribution of the corresponding feature vectors of the data points in the cluster. The formation of clusters is optimized with respect to an objective function involving prespecified distance and similarity measures along with additional constraints like smoothness. The k-means clustering is a popular approach to partition d-dimensional data into k clusters such that an objective function providing the desired properties of the distribution of feature vectors of clusters in terms of similarity and distance measures is optimized. A generalized k-means clustering algorithm initially places k clusters at arbitrarily selected cluster centroids vi, i = 1, . . . , 2, k and modifies centroids for the formation of new cluster shapes optimizing the objective function. The k-means clustering algorithm includes the following steps: 1. Selecting the number of clusters k with initial cluster centroids vi, i = 1, . . . , 2, k.
Fig. 1. Flowchart for psoriasis image segmentation processing.
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2. Partitioning the input data points into k clusters by assigning each data point xj to the closest cluster centroid vi using the selected distance measure, for example, Euclidean distance, defined as
dij ¼ kxj v i k;
ð10Þ
where X = {x1, x2, . . . , xn} is the input data set. 3. Computing a cluster assignment matrix U representing the partition of the data points with the binary membership value of the jth data point to the ith cluster such that U ¼ buij c, where
uij 2 f0; 1g for all i; j k X
uij ¼ 1 for all j and 0 <
i¼1
n X
uij < n for alli:
ð11Þ
j¼1
4. Re-computing the centroids using the membership values Pby
vi ¼
n j¼1 uij xj Pn j¼1 uij
for all i:
k X n X i¼1
kxj v i k2 :
ð13Þ
j¼1
It can be spotted from the above algorithm that the kmeans clustering method is quite sensitive to the initial cluster assignment and the choice of the distance measure. Additional criterion like within-cluster and between-cluster variances can be included in the objective function as constraints to force the algorithm to adapt the number of clusters k, as necessary for optimization of the objective function. In this research, k-means clustering method was used to classify color-skin image, so clustering objects are color, not gray-level image that is easily and fast classified. 2.3. Gray-level process In this image process procedure, after k-mean clustering process, then gray-level process was used to convert a RGB color-skin image to intensity gray-level image. Usually, intensity I, saturation S and hue I can be used for color to gray-level converting which can be express as [19]
I¼
RþGþB ; 3
ð14Þ
3 ðminðR:G:BÞÞ; S¼1 ðR þ G þ BÞ H¼
h
if B 6 G
360 h if B > G
ð15Þ
GÞ þ ðR BÞ
½ðR GÞ þ ðR BÞðG BÞ1=2
) ;
ð17Þ
2.4. Median filtering After color to gray-level converting, the gray-level image will remain some small fragile noise caused by real skin texture. So a median filter was used to filter out them. Median filter is an order-statistics filter that replaces the original image gray value of a pixel by the median of gray value of pixels for the specified neighborhood. A median filter operation for a smoothed image f(x, y) computed from the acquired image g(x, y) is written as
f ðx; yÞ ¼ medianfgði; jÞg;
ð18Þ
ði;jÞ2N
where N is the pre-specified neighborhood of the pixel (x, y). The gray value of the central pixel f(0, 0) is replaced by the median of gray values of all pixels in the neighborhood. 2.5. Binary imaging After median filter process, binary imaging process was used to form the object contour. A binary image means an image only has black and white. A gray-level image can be turned into a binary image by first choosing a gray-level T in the original image, then turning every pixel into black or white according to whether its gray value is greater than or less that T:
A pixel turns
white if x > T black
if x T
;
ð19Þ
where x representatives gray value. 2.6. Sobel edge process After binary imaging process, Sobel edge process was used to sharpen edges in the psoriasis image. Basically, edge is defined by the change in gray values of pixels in the neighborhood which can be expressed by a derivative or a difference operation. Sobel edge process is a first-order derivative operator for computing the gradient information in a specific direction. Usually, the derivative operator is encoded into a weight mask. Sobel edge process uses two weight masks, respectively, in computing the first-order gradient in x-direction as follows:
2
1 2 1
6 4 0 1
0 2
3
7 0 5; 1
ð20Þ
and in y-direction as follows:
2 ;
ð16Þ
3 1 0 1 6 7 4 2 0 2 5: 1 0 1
where
1 ½ðR 2 2
where angle h is measured with respect to the red axis in the ISH coordinate space and R, G and B are respect to red, green and blue in RGB coordinate space respectively.
ð12Þ
5. If cluster centroids or the assignment matrix does not change from the previous iteration, stop; otherwise go to Step 2. The k-means clustering method optimizes the sum-ofsquared-error based objective function Jw(U, v) then
Jw ðU; v Þ ¼
( h ¼ cos1
ð21Þ
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(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
Fig. 2. The first-case psoriasis images: (a) original image [1], (b) k-mean process image, (c) gray-level process image, (d) median filter process image, (e) binary process image, (f) Sobel process image, (g) morphological reconstruction image, (h) added into original image, and (i) hand-drawing contour image.
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Each of the two weight masks of 3 3 pixels will be used for convolution to compute respective gradient images. The resultant gradient image can be added
to the original image and rescaled using the full dynamic range of gray values for spatial image enhancement.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
Fig. 3. The second-case psoriasis images: (a) original image [1], (b) k-mean process image, (c) gray-level process image, (d) median filter process image, (e) binary process image, (f) Sobel process image, (g) morphological reconstruction image, (h) added into original image, and (i) hand-drawing contour image.
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(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
Fig. 4. The third-case psoriasis images: (a) original image [1], (b) k-mean process image, (c) gray-level process image, (d) median filter process image, (e) binary process image, (f) Sobel process image, (g) morphological reconstruction image, (h) added into original image, and (i) hand-drawing contour image.
2.7. Morphological reconstruction After Sobel edge process, morphological reconstruction was used to finalize the shape of psoriasis region. Morpho-
logical processing is based on the set theory to provide basic tools to deal with images for filtering, thinning and pruning operations that are useful for the description of region shape involving boundary and skeleton
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(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
Fig. 5. The fourth-case psoriasis images: (a) original image [1], (b) k-mean process image, (c) gray-level process image, (d) median filter process image, (e) binary process image, (f) Sobel process image, (g) morphological reconstruction image, (h) added into original image, and (i) hand-drawing contour image.
representation. Dilation and erosion are the two fundamental operations in morphological processing. Our Mor-
phological processing algorithms are based on the specific combination of the dilation and erosion opera-
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(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
Fig. 6. The fifth-case psoriasis images: (a) original image [1], (b) k-mean process image, (c) gray-level process image, (d) median filter process image, (e) binary process image, (f) Sobel process image, (g) morphological reconstruction image, (h) added into original image, and (i) hand-drawing contour image. _
tions. First we define two sets A and B belonging to an ndimensional space Zn. The dilation of set A by B, D(A, B) can be denoted by A B and defined as
DðA; BÞ ¼ A B ¼
[
A þ b;
ð22Þ
where B ¼ ½Bjb 2 Bg is the reflection set of B with respect to its origin. The erosion of set A by set B, E(A, B) can be denoted by A H B and defined as
EðA; BÞ ¼ AHB ¼ \ A b; b2B
b2B
ð24Þ
and
and _
A B ¼ fxjðB Þx \ A – 0g;
ð23Þ
AHB ¼ fxjðBÞx # Ag:
ð25Þ
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The above equation states that the erosion of a set A by a set B comprises all points x such that the set B located at x is entirely inside A. Usually, dilation and erosion are dual operation to each other, that is, _
A B ¼ ðAc H B Þc ;
ð26Þ
and _
AHB ¼ ðAc B Þc ;
ð27Þ
c
where A represents the complement of set A. After finishing morphological processing, we need to add the morphological reconstruction image with original color-skin image, then acquire the psoriasis segmentation image. 2.8. Segmentation test According to the image process procedure as shown in Fig. 1, it takes six steps to finish psoriasis image segmentation from k-mean clustering, gray-level, median filtering, binary imaging, Sobel edge process, to morphological reconstruction. In this research, we use psoriasis image five cases for segmentation test as shown in Figs. 2b–6b (288 288). For k-mean clustering, the color-skin image segmentation is same as pseudo color mapping, which is defined as a method that converts colors into a single integer index that is used to select a color from a list of specified colors in a data collection. It contains a weighting vector [L1, L2, L3] for RGB color format and a list of R colors. An index of 1 corresponds to the first color on this list; the mapping process is as the followings: 1. Normalize the weighting vector L by dividing it by its component summary. 2. Calculate J = round((R 1)(L1C1 + L2C2 + L3C3) + 1), where [C1, C2, C3] = [red, green, blue]. 3. Use J as an index to select one of the entries in the color list. 4. The selected color needs to display on the workstation more accurately. In histogram-based pixel classification method for image segmentation, the RGB values are partitioned into
Table 1 Accuracy for psoriasis image segmentation processing. Figure no.
Accuracy (%)
Fig. Fig. Fig. Fig. Fig.
97.23 94.49 90.22 88.45 87.54
2 3 4 5 6
two or more clusters depending on the peaks in the histogram to obtain thresholds. A color image may have additional color components in a specific representation such as Red, Green and Blue components in the RGB color coordinate system that can be added to the feature vector. The basic concept of segmentation by pixel classification can be extended to clustering the gray values of feature vector of pixels in the image. This approach is particularly useful when images with pixels representing a feature vector consisting of multiple parameters of interest are to be segmented. Figs. 2b–6b show the results after k-mean clustering process, respectively. The difference between psoriasis color (dark red) and skin color (light red) is small, so kmean clustering process is very fast. Multi-modality medical images may also require segmentation using a multi-dimensional feature space with multiple parameters of interest. Images can be segmented by pixel classification through clustering of all features of interest. The number of clusters in the multi-dimensional feature space thus represents the number of classes in the image. As the image is classified into cluster classes, segmented regions are obtained by checking the neighborhood pixels for the same class label. However, clustering may produce disjoint regions with holes or regions with a single pixel. After the image data are clustered and pixels are classified, some post-processing algorithm such as gray-level, median filtering, binary imaging, Sobel edge process, and morphological reconstruction algorithm are usually applied to obtain the final segmented regions. Figs. 2c–6c show to converts Lab color space image into the gray-level image, where the Lab space consists of a luminosity layer ‘L’, chromaticity-layer ‘a’ indicating where color falls along the red–green axis, and chromaticity-layer ‘b’ indicating where the color falls along the blue–yellow axis. All of the color information is in the ‘a’ and ‘b’ layers. The difference between two colors can be measured by using the Euclidean distance metric. The color skin has almost no color difference, so its converting gray value is also very fast. Then, Figs. 2d–6d show the results after median filtering, respectively. The median filter was mainly used to filter out some small fragile noise caused by real skin texture. It seems that there is more small fragile noise, so its processing will take some time. And then, Figs. 2e–6e show the results after binary imaging, due to the psoriasis image already gray, so its processing is also very fast. Again then, Figs. 2f–6f show the results after Sobel edge process, due to the psoriasis image already binary, so its processing is also very fast. Finally, Figs. 2g–6g show the results after morphological reconstruction, because it involves dilation and erosion process, its processing will take some time. Figs. 2h–6h show the psoriasis segmentation image results from adding the morphological reconstruction image with original color-skin image. To compute the psoriasis seg-
Table 2 Time complexity for psoriasis image segmentation processing steps. Step
k-mean
Gray-level
Median filter
Binary image
Sobel
MR
Time complexity (O)
N
N
N2
N
N
N2
MR: morphological reconstruction.
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mentation accuracy, we need to make the psoriasis region contour by hand drawing as shown in Figs. 2i–6i, which are assumed 100% accuracy. Table 1 shows the accuracy for psoriasis image segmentation processing. In general, the average accuracy is good above 90%. The experimental results demonstrate that the misclassification error is very small between the proposed result and hand drawing. We also compute the time complexity for psoriasis image segmentation processing step, the result is shown in Table 2. The results show the proposed procedure has lower time complexity (O) except median filtering and morphological reconstruction process, that is, it saves lots computing time. N is lower time complexity and N2 is normal time complexity. To prove the proposed method is best on accuracy, and computing time, we took the method [1], ‘‘Segmentation of psoriasis vulgaris images using multiresolution-based orthogonal Subspace Techniques’’, from its experiments for the comparison, its time complexity is more than N4. The results show the proposed method saves lots computing time and has the best accuracy due to our lower time complexity. The higher time complexity means more spending computing time and low accuracy. 3. Conclusions We have proposed a realization of psoriasis region tracking method of color-skin image using k-means clustering with morphological processing technique. A preliminary evaluation on psoriasis image shows encouraging results. k-means clustering with morphological segmentation algorithm for tracking objects in medical images is performed to be very promising for medical image segmentation applications. The regions related to psoriasis can be exactly separated from the color-skin image. This proposed method will be able to help pathologists distinguish exactly psoriasis size and region. References [1] J.S. Taur, G.H. Lee, C.W. Tao, C.C. Chen, C.W. Yang, Segmentation of psoriasis vulgaris images using multiresolution-based orthogonal subspace techniques, IEEE Trans. Syst. Man Cybernet.—Part B: Cybernet. 36 (2) (2006) 390–402. [2] A. Rangarajan, I.T. Hsiao, G. Gindi, A Bayesian joint mixture framework for the integration of anatomical in functional image reconstruction, J. Math. Imag. Vis. 12 (2000) 199–217.
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