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This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/copyright Author's personal copy Computerized Medical Imaging and Graphics 34 (2010) 160–166 Contents lists available at ScienceDirect Computerized Medical Imaging and Graphics journal homepage: www.elsevier.com/locate/compmedimag A discrimination method for the detection of pneumonia using chest radiograph Norliza Mohd. Noor a,∗ , Omar Mohd. Rijal b , Ashari Yunus c , S.A.R. Abu-Bakar d a Department of Electrical Engineering, College of Science and Technology, UTM International Campus, Universiti Teknologi Malaysia, Jalan Semarak, 54100 Kuala Lumpur, Malaysia b Institute of Mathematical Sciences, University Malaya, Lembah Pantai, 50603 Kuala Lumpur, Malaysia c Institute of Respiratory Medicine, Jalan Pahang, 50586 Kuala Lumpur, Malaysia d Faculty of Elect. Eng., Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor, Malaysia a r t i c l e i n f o Article history: Received 3 April 2009 Received in revised form 5 August 2009 Accepted 17 August 2009 Keywords: Detection Texture measures Pneumonia Principal component analysis (PCA) Discriminant analysis Digital chest X-ray a b s t r a c t This paper presents a statistical method for the detection of lobar pneumonia when using digitized chest X-ray films. Each region of interest was represented by a vector of wavelet texture measures which is then multiplied by the orthogonal matrix Q2 . The first two elements of the transformed vectors were shown to have a bivariate normal distribution. Misclassification probabilities were estimated using probability ellipsoids and discriminant functions. The result of this study recommends the detection of pneumonia by constructing probability ellipsoids or discriminant function using maximum energy and maximum column sum energy texture measures where misclassification probabilities were less than 0.15. © 2009 Elsevier Ltd. All rights reserved. 1. Introduction The chest X-ray of a patient is frequently used as the initial indicator of pneumonia mainly due to cost consideration despite the existence of better and more expensive medical imaging modalities [1]. Depending on the experience of the medical practitioner, types of lung diseases and their stage of infection may be difficult to identify from the chest X-ray. Respiratory infections are the most common of all infections. The most serious respiratory infection, pneumonia, shows the highest mortality rate of all infectious diseases and is the sixth leading cause of death in people over 65 years of age [2]. In 2004, 58,564 people died of pneumonia in the United States of America [3]. Pneumonia is a serious infection or inflammation of the lungs. Pneumonia can have over 30 different causes which include various chemicals, bacteria, viruses, mycoplasmas and other infectious agents such as pneumocystis (fungi). Symptoms of pneumonia include fever, coughing, shortness of breath, chest pain and loss of appetite [4]. Texture is an important item of information that humans use in analyzing a scene [5]. Textures may be considered as a global ∗ Corresponding author. Tel.: +60 3 2615 4589/19 327 4854; fax: +60 3 2615 4315. E-mail addresses: [email protected] (N.Mohd. Noor), [email protected] (O.Mohd. Rijal), [email protected] (A. Yunus), [email protected] (S.A.R. AbuBakar). 0895-6111/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.compmedimag.2009.08.005 repetition of a basic pattern defined over a local region, however, the basic pattern is difficult to define. This problem has led to the creation of several measures of textures, and the choice of texture measure is closely related to the issue of visual perception [6]. There are studies involving texture features extracted from wavelet coefficients. Unser [7], Fauzi and Lewis [8,9] and Sengur et al. [10] used mean of energy as the wavelet-based texture features. Boukerroui et al. [11] used angular second moment and correlation as the texture feature to extract feature and segmentation for breast tumors in ultrasonic imaging. Agani et al. [12] used four texture features namely, entropy, contrast, angular second moment and inverse difference moment derived from the co-occurrence matrix in diagnosis of myocardial infarction tissue from echocardiography images and retrieval in small dimension images. Muneeswaran et al. [13] used five texture measures which are Norm-2 energy, Norm-1 energy, standard deviation of the energy, average residual and entropy for rotational and scale invariant feature set for textural image classification. Kazuhiko et al. [14] developed computer aided diagnosis for interstitial pneumonia using chest X-ray with relatively good result. Their study used second order statistics in distinguishing normal images and interstitial pneumonia images. The second order statistics used in this method is derived from the co-occurrence matrix and run-length matrix and the features obtained from these matrices attempts to quantify microscopic variation of density. Recently, Oliveira et al. [15] has developed a computer aided diagnosis method using Haar wavelet to extract features from chest Author's personal copy N.Mohd. Noor et al. / Computerized Medical Imaging and Graphics 34 (2010) 160–166 161 radiographs and distance-dependent weighting for image classification in detection of childhood pneumonia with high sensitivity and specificity. They have designed a prototype system, named Pneumo-CAD that is able to detect pneumonia present against pneumonia absent in chest X-ray images to aid pneumonia diagnosis in children. In this paper a novel discrimination method to detect lobar pneumonia using a digitized chest radiograph is proposed. The discrimination method uses texture measure. Each patient therefore is represented by a vector of texture measures. These vectors of texture measures were found to be normally distributed. Twodimensional probability ellipsoids and appropriate discriminant functions estimate the following error probability; and ˛ = P(Type 1 Error) = P(PNEU|NL), ˇ = P(Type 2 Error) = P(NL|PNEU), for a selected texture measure. Fig. 1. (a) Chest X-ray of a pneumonia patient, and (b) a subset image of the infected area. The Institute of Respiratory Medicine, Kuala Lumpur. 2. Materials and methods This study involved collaboration with the Institute of Respiratory Medicine (IPR), Malaysia, which is the Malaysian national referral centre for respiratory diseases. Cases that arrived at the IPR may be considered a random sample since an individual case may come from any of the Malaysian hospitals or clinics. The chest X-ray films from IPR were then digitized into DICOM format using the X-ray Film Scanner Kodak LS 75 with the following specifications: pixel spot size of 100 m, 12 bit per pixel, image size of 2016 × 2048 pixels. An example of a digitized X-ray film is shown in Fig. 1. Each of the ROI for a given image was subjected to the twodimensional Daubechies wavelet transform as shown in Fig. 2 [16,17]. The wavelet transform convert the image into four subsets, labeled LL, LH, HL and HH representing the trend, horizontal, vertical and diagonal detail coefficients. The twelve texture measures considered were; (i) Mean Energy, E = 1 N j 1 N2 j (iii) Contrast = j where = 1 N2 j (vi) Standard 1 N2 j k (iv) Homogeneity, H = |Cjk |2 k |Cjk |2 log |Cjk |2 j (Cjk − ) 2 k Cjk k deviation (|Cjk |2 − ) 2 of where = STDE = energy, 1 N2 k j |Cjk |2 k (vii) Maximum wavelet coefficient value, max = max(Cjk ) (viii) Minimum wavelet coefficient value, min = min(Cjk ) ⎛ (ix) Maximum value of energy, Emax = max ⎝ 2.1. Texture measures (ii) Entropy = − 1 N2 (v) Standard deviation of value, STDV = j ⎞ |Cjk |2 ⎠ k (x) Maximum row sum energy (xi) Maximum column sum energy (xii) Average number of zero-crossings where Cjk is the element of sub-image (say, LL) found in row-j and column-k [18,19]. Hence, twelve texture measures in each of LL, LH, HL and HH yields 48 descriptors or features, u, that will be used to detect pneumonia. 2.2. Modified principal component method k 2 (j − k) Cjk j k Cjk 1+|j−k| A sample of thirty images were concurrently read and interpreted for the presence of lobar pneumonia with no secondary ailment (PNEU) by two independent pulmonologists who are trained according to the World Health Organization (WHO) guideline [20,21] and the affected region (ROI) was identified (Fig. 1). Fig. 2. (a) Region of interest, (b) the transformed image where four image subset was formed. Author's personal copy 162 N.Mohd. Noor et al. / Computerized Medical Imaging and Graphics 34 (2010) 160–166 This process was repeated for a sample of another thirty individuals labeled as pneumonia-absent group or normal (NL) who came for a routine medical check-up. These sixty cases (30 cases each for PNEU and NL) will be used as the control group. Another forty cases (20 cases each for PNEU and NL), were similarly obtained and will be used as the test group to estimate misclassification probabilities. The standard principal component method is generally used for purposes of reducing dimension in multivariable problems. Geometrically the principal component transformation merely rotates the data (vectors) such that the Euclidean distance between the vectors is unchanged. This rotation is achieved by means of an orthogonal transformation. Unfortunately, if there exist two over- Fig. 3. 1st two component of pseudo-PC scatter plot for PNEU ( ) and NL( ). Author's personal copy N.Mohd. Noor et al. / Computerized Medical Imaging and Graphics 34 (2010) 160–166 Fig. 3. (Continued ). 163 Author's personal copy 164 N.Mohd. Noor et al. / Computerized Medical Imaging and Graphics 34 (2010) 160–166 lapping groups achieving reduction in dimension does nothing to increase the separation of the two groups. A modified principal component (ModPC) method is now proposed in order to investigate the possibility of both reduction in dimension and increased separation between groups. This proposed method is applied to the problem of differentiating pneumonia cases from normal lung. The data used were divided into two sets (u1 , u2 , · · ·, u60 ) is the control data set and (u61 , u2 , · · ·, u100 ) is the test data set. Let u1 , u2 , · · ·, u30 where u ∈ G1 represent the texture measures for pneumonia samples and u31 , u32 , · · ·, u60 where u ∈ G2 represent the texture measures for normal lung samples. The main problem of the ModPC method is the choice of an orthogonal transformation. Let M be an orthogonal matrix such that ur is transformed to u∗r = Mur (r = 1, · · ·, 100). 1 Let n−1 Sj be the estimate of the covariance matrix for group Gj (j = 1, 2). For example, 30 S1 = (ur − u)(ur − u) T where u = r=1 (u1 + u2 + · · · + u30 ) 30 and Recall G(v) = ln g1 (v) g2 (v) where g1 (v) denote the probability distribution for PNEU, say N2 ( , ˙1 ), and g2 (v) denote the probability distribution for 1 NL, say N2 ( , ˙2 ). The equality of covariance matrices was 2 tested using the Box’s Test [22], and if ˙1 = ˙2 , G(v) is the linear discriminant function (LDF), otherwise, G(v) is the quadratic discriminant function (QDF). The number of times G(v) < 0 for vj (j = 61, . . ., 80) gives an estimate of ˇ. Henceforth ˛ is similarly derived. For both of LDF and QDF, the criterion G(v) < 0 is true assuming equal a priori probabilities and costs of misclassification d(i|j) which is the cost of misclassifying observation-j (i = 1, 2 and j = 1, 2). 2.3. Testing for normality Given v1 , v2 , · · ·, vn ∈ 2 . The statistics v = n (vj − v)(vj − v) T (v1 +···+vn ) n and Sv = T and yj = (vj − v) ((n − 1)Sv −1 )(vj − v) for j = 1, j=1 S2 is similarly defined for u31 , u32 , · · ·, u60 . The spectral decomposition of the estimated covariance matrix are, 1 S1 = Q1 1 Q1T for G1 n−1 and . . ., n were calculated. If vj is normally distributed then yj (j = 1, . . ., n) must come from a chi-squared distribution with two degrees of freedom. Effectively, testing normality of v1 , v2 , · · ·, vn is equivalent to testing whether yj (j = 1, . . ., n) comes from a chi-squared distribution using the Kolmogorov–Smirnov test [23]. In all cases studied the Kolmogorov–Smirnov test confirms that yj has a chi-squared distribution, henceforth, indicating that vj is bivariate normal. 2.4. Confidence region of the first two components of v 1 S2 = Q2 2 Q2 T for G2 n−1 where n = 30, Qj (j = 1, 2) is the appropriate matrix of eigenvectors, and j (j = 1, 2) is the corresponding diagonal matrix of eigenvalues. Henceforth, the matrix M may be chosen in two ways, namely M = Q1 or M = Q2 . For a selected M matrix, take the first two components of ur ∗ (r = 1,. . .,100) which explain at least 90% of the variability, relabel it as vr (r = 1,. . .,100) and perform the following: for the (v +···+v ) vectors v1 , v2 , · · ·, v30 , ∈ 2 calculate the statistics v1 = 1 30 30 and Sv1 = (b) Estimation of ˛ and ˇ from discriminant function: 30 T (vj − v1 )(vj − v1 ) . The vectors v1 , v2 , · · ·, v30 were j=1 found to be bivariate normal. Henceforth the pneumonia ellipsoid T (v − v1 ) ((n − 1)Sv1 −1 )(v − v1 ) = c was drawn where c was selected from a standard chi-square table. Further, the estimate of g1 (v), which is the probability distribution for G1 is also obtained. The above was repeated for v31 , v32 , · · ·, v60 yielding the NL ellipsoid and the corresponding estimate of g2 (v) which is the probability distribution for G2 . Finally the estimate of the discriminant function G(v) = ln g1 (v) g2 (v) may be derived. The two error probabilities ˛ and ˇ may be estimated by using the test set v61 , v62 , · · ·, v80 from G1 and v81 , v82 , · · ·, v100 from G2 in two ways; (a) Estimation of ˛ and ˇ from the probability ellipsoid: (i) The number of times vj (j = 61, . . ., 80) falls into the NL ellipsoid gives an estimate of ˇ. (ii) The number of times vj (j = 81, . . ., 100) falls into the PNEU ellipsoid gives an estimate of ˛. A 2D plot of the first two components of v together with its corresponding approximate confidence region (an ellipse) was used to investigate clustering of the two groups of individuals. If two clusters of points are discovered on the 2D plot and each cluster is contained in a separate confidence ellipse then the texture measures used (u) is regarded as a useful feature for discrimination. The 95% probability ellipsoid was drawn for each group, PNEU and NL (see Fig. 3). Since v is bivariate normal, therefore a value for c may be selected from standard chi-squared tables. The quadratic form, T for example, (v − v1 ) ((n − 1)S1 −1 )(v − v1 ) is approximately a chisquared random variable where the approximation is considered good if n ≥ 25 [22]. 3. Results When all the vectors of texture measures were multiplied by Q2 (obtained from NL data), a modified principal component method for the detection of pneumonia gave at most misclassification probabilities of 0.15. Given that Q2 was selected, the probability ellipsoid may be used as a graphical method of detection and the discriminant functions used as a formal detection method. The selected texture measures to be used as features for purposes of discrimination are maximum energy and maximum column sum energy. The selection of the type of texture measure and the matrix Qj (j = 1, 2) for the probability ellipsoid is given in Table 1 whilst Table 2 gave similar results using the discriminant function. Table 1 clearly shows that using Q1 gave large ˇ errors, whilst using Q2 , maximum energy and maximum column sum energy showed acceptable levels of ˛ and ˇ (≤0.15). It is of interest to note that using all twelve features, resulted in ˛ = 0.20 and Author's personal copy N.Mohd. Noor et al. / Computerized Medical Imaging and Graphics 34 (2010) 160–166 Table 1 Estimated misclassification probabilities using ellipsoids. Texture measures Mean of energy Entropy Std. dev. of intensity value Std. dev. of energy Maximum value Minimum value Maximum Energy Max. row sum energy Max. column sum energy Zero-crossing Contrast Homogeneity All 12 features Q1 (PNEU ellipsoids) Q2 (NL ellipsoids) ˛ ˇ ˛ ˇ 0 0 0 0 0.05 0.05 0 0 0 0 0 0 0 0.45 0.65 0.6 0.45 0.7 0.65 0.6 0.65 0.6 0.3 0.75 0.7 0.7 0.55 0.45 0.6 0.55 0 0.65 0.15 0.1 0.15 0.15 0.05 0.05 0.2 0.2 0.45 0.65 0.2 0.25 0.25 0.15 0.2 0.1 0.85 0.2 0.4 0.25 ˛ = P(Type I Error) = P (PNEU|NL). ˇ = P(Type II Error) = P (NL|PNEU) Table 2 Estimated misclassification probabilities from LDF/QDF. Texture measures Mean of energy Entropy Std. dev. of intensity value Std. dev. of energy Maximum value Minimum value Maximum energy Max. row sum energy Max. column sum energy Zero-crossing Contrast Homogeneity All 12 features Q1 (PNEU) Q2 (NL) ˛ ˇ ˛ ˇ 0.8000 0.3000 0.0500 0.9000 0.1000 0.6500 0.1000 0.1000 0.1000 0.0500 0.1500 0.9000 0.2500 0.1000 0.4000 0.3500 0.0500 0.0000 0.2500 0.1000 0.1500 0.1000 0.7500 0.1500 0.0000 0.0000 0.5000 0.3500 0.0500 1.0000 0.1000 0.7500 0.1500 0.1000 0.1500 0.4500 0.8500 0.9000 0.2000 0.2500 0.3000 0.3000 0.0500 0.1500 0.2000 0.1000 0.1500 0.1000 0.6000 0.1000 0.0000 0.1000 ˛ = P(Type I Error) = P (PNEU|NL). ˇ = P(Type II Error) = P (NL|PNEU). ˇ = 0.25. Table 2 shows that when using maximum value, maximum energy, maximum row sum energy, maximum column sum energy, without the need to choose between Q1 and Q2, both ˛ and ˇ are less than 0.15. A general result that could be summarized from both Tables 1 and 2 is that both probability ellipsoids and discriminant function can be simultaneously used if Q2 and maximum energy and maximum column sum energy texture measure were selected. 165 The ˛ and ˇ errors are used as indicators of group separation. Estimates of ˛ and ˇ were obtained by counting the number of test data being misclassified. The use of discriminant functions is to be preferred over the use of probability ellipsoids, especially in the case where the data is normally distributed. Fixing a ceiling of 0.15 for both ˛ and ˇ shows that the matrix Q2 allows the combined use of the probability ellipsoids and discriminant function, when maximum energy and maximum column sum energy texture measures are considered. In other words, the probability ellipsoids could provide a first estimate of misclassification probabilities graphically whilst the discriminant function provides the final optimal detection procedure when using Q2 . Texture measures are widely applied [8–15], but only [15] appear to use texture measure for the detection of pneumonia. However [15], studied detection of childhood pneumonia using mean of energy as the texture measure with sensitivity (100%) and specificity (80%) being considered as measures of performance. In contrast this study focuses on the detection of pneumonia for adults using statistical methods where the Type I Error and Type II Error are considered as measures of performance. The proposed detection method may only be used to differentiate PNEU from NL. In general extra information may be derived from the images, for example, the possible existence of pulmonary tuberculosis or lung cancer. There is a need to reselect the orthogonal transformation when the detection of the other diseases is of interest. 5. Conclusion This study proposes a novel statistical method for the detection of pneumonia when texture measures extracted from digital images of chest X-rays are used as feature vectors in a discrimination procedure. The texture measures maximum energy and maximum column sum energy when used as feature vectors in the proposed discrimination method yields low misclassification probabilities not exceeding 0.15. If the matrix Q2 is applied together with the maximum energy and the maximum column sum energy texture measures, the probability ellipsoids may be used graphically for initial data exploration and the LDF or QDF used as formal methods of detecting pneumonia. Acknowledgements We would like to acknowledge the contribution from The Institute of Respiratory Medicine, Kuala Lumpur. This research was funded under an E-Science Fund from the Ministry of Science, Technology and Innovation and Universiti Teknologi Malaysia. 4. Discussion Thirty cases each for PNEU and NL constituted the control group whilst twenty cases each for PNEU and NL formed the test group. For each of these 100 cases (images), a region of interest was identified and consequently the Daubechies transform was applied yielding appropriate vectors of texture measures. Each of the 100 vectors of texture measures were subjected to an orthogonal transformation in particular the matrix Q2 was applied. Henceforth, probability ellipsoids and discriminant function were constructed from the control group data. The ˛ and ˇ errors were in turned estimated with the test data. Two probability ellipsoids of the modified principal components that are both compact with minimal overlapping are regarded as showing significant separation. A compact probability ellipsoid is one in which all points are within the ellipsoid. Fig. 3 shows that every pair of ellipsoids (for a given texture measure) appears to have the same degree of overlap. References [1] Schilham AMR, Ginneken B, Loog M. A computer aided diagnosis system for detection of lung nodules in chest radiographs with an evaluation on a public database. Med Image Anal 2006;10:247–58, doi:10.1016/j.media.2005.09.003. [2] Centers for Disease Control and Prevention. National Center for Health Statistics: Preliminary Data for 2005. USA; September 2007. [3] Improving Life, One Breath at a Time. Lung Disease Data: 2008. New York: American Lung Association; 2008: pp. 68. [4] Karetzky M, Cunha BA, Brandstetter RD. The Pneumonias. New York: SpringerVerlag; 1993. [5] Alparone L, Benelli G, Vagniluca A. Texture-based analysis techniques for the classification of radar images. IEEE Proc 1990;137(4):276–82 (Pt.F.). [6] Levine MD. Vision in Man and Machine. 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Norliza Mohd Noor is currently pursuing her Ph.D. at the Universiti Teknologi Malaysia (UTM) under the supervision of Assoc. Prof. Dr Syed Abdul Rahman Syed Abu Bakar. She received her B.Sc. Electrical Engineering from Texas Tech University of Lubbock, Texas and Master of Electrical Engineering from UTM in 1985 and 1996 respectively. She currently attached to the Dept. of Electrical Engineering, College of Science and Technology, UTM International Campus, Kuala Lumpur. She is a senior member of IEEE Omar Mohd Rijal received his B.Sc. Maths (Operational Research) from New University of Ulster, Ireland (1979) and Ph.D. (Applied Statistics) from University of Glasgow, UK in 1984. He has been attached to the Institute of Mathematical Sciences, University of Malaya since 1984 and was appointed as the associate professor in 1998. His research interests are applied statistics, image and data analysis for medical, industrial and remote sensing applications Ashari Yunus is a Consultant Respiratory Physician at the Institute of Respiratory Medicine, Kuala Lumpur. He received his M.D. from National University of Malaysia, and MMED from Science University of Malaysia. He has completed the Advanced Respiratory Training: RPAH & SVH (Sydney). He is also a member of the expert panel Malaysian heart and lung transplant unit S. A. R. Abu-Bakar (Syed Abdul Rahman Syed Abu Bakar) received the B.Sc. degree from Clarkson University in Potsdam, New York (USA), in 1990, and an MSEE degree from Georgia Tech in 1991 (USA), and the Ph.D. degree from the University of Bradford, England in 1997. In 1992, he joined the Faculty of Electrical Engineering as a lecturer and currently he is an associate professor in the same faculty as well as the head for the Computer Vision, Video and Image Processing research lab. His current research interests include image processing with application in medical imaging, biometrics, agricultural and industrial applications, and computer vision especially in the area of security and surveillance. He has published more than 90 scientific papers both at national and international levels. He is also a senior member of IEEE