Bio-Medical Materials and Engineering 24 (2014) 129–143 DOI 10.3233/BME-130793 IOS Press
129
Texture feature extraction based on wavelet transform and gray-level co-occurrence matrices applied to osteosarcoma diagnosis1 Hu Shana, Xu Chaoa, Guan WeiQiaoa, Tang Yonga,b,*and Liu Yana,* a
Department of Biomedical Engineering, ZhongShan School of Medicine, Sun Yat-Sen University, GuangZhou, 510060, PR China. b Computer College, South China Normal University, GuangZhou, 510631, PR China.
Abstract. Osteosarcoma is the most common malignant bone tumor among children and adolescents. In this study, image texture analysis was made to extract texture features from bone CR images to evaluate the recognition rate of osteosarcoma. To obtain the optimal set of features, Sym4 and Db4 wavelet transforms and gray-level co-occurrence matrices were applied to the image, with statistical methods being used to maximize the feature selection. To evaluate the performance of these methods, a support vector machine algorithm was used. The experimental results demonstrated that the Sym4 wavelet had a higher classification accuracy (93.44%) than the Db4 wavelet with respect to osteosarcoma occurrence in the epiphysis, whereas the Db4 wavelet had a higher classification accuracy (96.25%) for osteosarcoma occurrence in the diaphysis. Results including accuracy, sensitivity, specificity and ROC curves obtained using the wavelets were all higher than those obtained using the features derived from the GLCM method. It is concluded that, a set of texture features can be extracted from the wavelets and used in computer-aided osteosarcoma diagnosis systems. In addition, this study also confirms that multi-resolution analysis is a useful tool for texture feature extraction during bone CR image processing. Keywords: Feature selection, gray-level co-occurrence matrix, osteosarcoma diagnosis, texture feature, wavelet transform
1. Introduction Osteosarcoma is the most common primary malignant bone tumor and the sixth most common type of cancer among children and adolescents, for whom the prognosis remains unfavorable despite treatment protocols combining chemotherapy and surgery. At present, the early diagnosis of osteosarcoma relies mainly on X-ray (CR/DR) while the final diagnosis depends on biopsies. However, as the manifestation of osteosarcoma is complex in CR images, atypical cases can easily be misdiagnosed [1]. To fully exploit the information in a CR image, it is necessary to use digital image processing technology to extract and analyze this information.
1* Co-corresponding author. Liu Yan, Email: [email protected] ,Tel: 0086-020-87331856, Fax: 0086-020-87331854 Tang Yong, Email: [email protected], Tel: 0086-020-85215327, Fax: 0086-020-87331854
0959-2989/14/$27.50 © 2014 – IOS Press and the authors. All rights reserved
130
S. Hu et al. / Texture feature extraction based on wavelet transform and gray-level co-occurrence matrices
Texture is an important characteristic used for identifying regions of interest (ROIs) in an image, which expresses either the fine structure or the macroscopic structure. In the last 30 years, many methods have been developed for analyzing texture, such as statistical, structural, model-based and signal processing approaches. Among them, statistical analysis is the most fundamental method for textural feature extraction, where the spatial distributions of gray-scale values are analyzed and the textural features are calculated using the statistical properties, such as 1-D features based on gray-level intensity histograms and 2-D features based on co-occurrence matrices [2,3]. A typical method that uses co-occurrence matrices is the gray-level co-occurrence matrices (GLCM) method proposed by Haralick et al. in the 1970s [4]. This method has been widely used in many texture analysis applications and it remains to be an important feature extraction method in the domain of medical image texture analysis [5-7]. The GLCM method tabulates how often different combinations of pixel brightness values (gray levels) occur in an image, and 14 features are extracted from the GLCMs to characterize the texture. In recent years, researchers have proposed many texture extraction methods based on analysis of multiple scales according to human vision. Multi-resolution analysis has been proved to be useful for image processing. The goal of multi-resolution analysis is to decompose the original image into sub-bands that preserve high- and low-frequency information, and to analyze these sub-bands in the frequency domain. By using a family of functions localized in terms of time and frequency, wavelet transforms can centralize the energy of the original image within only a few coefficients after wavelet decomposition. These coefficients have high local relativity in three directions of different sub-band images: horizontal, vertical, and diagonal. Thus, wavelet transforms can be used to extract texture information from images. Several studies have demonstrated the successful use of wavelet transforms as multi-resolution tools for texture analysis in medical image processing [8-13]. The present study compared the use of GLCM with wavelet transforms, including the Daubechies wavelet and Symlet wavelet, for the textural analysis of osteosarcoma CR images. Some significant features were also selected by statistical methods to create a classifier, that categorized bone images as normal or abnormal. The main aim of this study was to determine the distinguishing traits using these methods.
Fig.1. Schematic of the proposed system
Figure 1 shows a schematic of the system proposed in this study. First, the images were pre-processed to select ROIs. Then feature extraction was performed for each cropped sub-image. The texture features obtained from GLCM were calculated at fixed pixel distances (d=1) and the orientation was classified into four different directions (Ʌ ൌ Ͳι ǡ Ͷͷι ǡ ͻͲι ǡ ͳ͵ͷι ). For the wavelet transforms, the features were computed at four decomposition levels based on Daubechies wavelet and
S. Hu et al. / Texture feature extraction based on wavelet transform and gray-level co-occurrence matrices
131
Symlet wavelet. In the next stage, statistical methods, i.e., one-way ANOVA and rank-sum test, were applied to feature selection using the wavelet transforms. Finally, a support vector machine (SVM) algorithm was used to classify the images as normal or abnormal. The classification accuracy, sensitivity, specificity and Receiver Operating Characteristic (ROC) curves were used to evaluate the effectiveness of these features for the computer-aided diagnosis of osteosarcoma. 2. Material and methods 2.1. Dataset The bone CR images were provided by Guangdong General Hospital, The First Affiliated Hospital and The Second Affiliated Hospital of Sun Yat-sen University. The images were stored in DICOM format and the database contained a total of 141 cases, including 70 osteosarcoma cases and 71 normal cases. The patients with osteosarcoma were all measured in the progressive stage, as determined by biopsies. In all cases, CR images of the long bone were available and captured in situ. The images were divided into two classes: epiphysis and diaphysis, depending on which part of the bone was imaged. In the osteosarcoma cases, 33 epiphysis images and 37 diaphysis images were collected, whereas in the normal cases, 28 epiphysis images and 43 diaphysis images were collected. However, these images were acquired from different conditions with respect to the type of machine and the resolution. The ROIs included different orders of magnitude of pixels, which would result in adverse effects in the feature extraction. Image preprocessing was necessary to minimize the errors caused by these differences.
Fig.2. The regions of interest for the epiphysis (a) and diaphysis (b)
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S. Hu et al. / Texture feature extraction based on wavelet transform and gray-level co-occurrence matrices
First, the image was cropped with a rectangle to obtain the sub-image with the ROI, where the rectangle was the widest possible rectangle filled completely by the epiphysis or diaphysis, as shown in Figure 2. Second, the same areas in different sub-images could contain different numbers of pixels, thus the resolution of the images was adjusted to ensure that the same number of pixels were contained in the same area of each sub-image. Both of them were completed manually using Photoshop software. 2.2. Wavelet transforms The wavelet transform [14] decomposed the signal as a linear operation for different scaling components and it could be obtained by filter convolution with a varying signal and scaling. For discrete signals, the discrete wavelet transform (DWT) was obtained by the discretization of time, translation and scale parameters. The wavelet ɗሺሻ is a linear combination of the scaling and translating of the scaling functionɔሺሻ, which satisfies a two-scale differential equation, using Eqs.(1) and (2): ɔሺሻ ൌ ξʹ σ ݄ሺ݇ሻ߮ ሺʹ ݔെ ݇ሻ
(1)
ɗሺሻ ൌ ξʹ σ ݃ሺ݇ሻ߮ ሺʹ ݔെ ݇ሻ
(2)
where ݄ is the low-pass filter and ݃ is the high-pass filter. These two filters are quadrature mirror filters, which satisfy݃ሺ݇ሻ ൌ ሺെͳሻ ݄ሺͳ െ ݇ሻ. To apply the wavelet transform to image processing, two-dimensional (2-D) wavelets are required from the vector product of ɗሺሻand ɔሺሻǡwhich are defined using Eqs.(3)-(6): ɔሺǡ ሻ ൌ ɔሺሻɔሺሻ
(3)
ɗு ሺǡ ሻ ൌ ɗሺሻɔሺሻ
(4)
ɗ ሺǡ ሻ ൌ ɔሺሻɗሺሻ
(5)
ɗ ሺǡ ሻ ൌ ɗሺሻɗሺሻ
(6)
where ɔሺǡ ሻ is a 2-D scaling function,ɗு , ɗ ǡ andɗ are three 2-D wavelets, and ܪ,ܸ , andܦrepresent the horizontal, vertical and diagonal directions, respectively. Different mother wavelets have different supporting lengths and regularities, therefore the results of texture feature extraction depend highly on the selection of the mother wavelet and the number of levels. The Daubechies wavelet is a compactly supported orthogonal wavelet which is significant in the wavelet field. The Symlet wavelet has a construction similar to that of the Daubechies wavelet, but its symmetry is higher. Several studies have compared the effect of various wavelets on the extraction of texture features [15-18]. In the present study, the Db4 and Sym4 wavelets were selected to extract features from bone CR images and to compare their effects. The number of decomposed levels determines the amount of details during textural extraction. The first level has the finest texture, and the fineness decreases as the number of decomposed levels increases. Synthesizing the texture at various levels can reflect an image’s texture. However, the computational cost increases when more levels are decomposed. In the present study, when the image was decomposed from the histogram of coefficients, it was found that the image achieved better
S. Hu et al. / Texture feature extraction based on wavelet transform and gray-level co-occurrence matrices
133
equalization at level 4. As shown in Figure 3, the ROI (a) is decomposed with the Db4 wavelet, and (b) and (c) are the histograms of coefficients in the vertical direction for level 1 and level 4, respectively. Therefore, after considering the computational costs, these images were decomposed at four levels. Three features are extracted at each level and in each direction (horizontal, vertical, and diagonal), i.e., the mean, variance and energy, which are defined using Eqs.(7)-(9), where Cij is the coefficient matrix at point (i,j). ଵ
തതതത Mean: ܥ ௌ ൌ Variance: ܸௌ ൌ
ൈ
ଵ ൈ
Energy: ݁ௌ ൌ
σୀ σୀ ܥ
(7)
ଶ തതതത σୀ σୀሺܥ െ ܥ ௌ ሻ ଵ
ൈ
σୀ σୀหܥ ห
ଶ
(8) (9)
134
S. Hu et al. / Texture feature extraction based on wavelet transform and gray-level co-occurrence matrices
Fig.3.(a) The regions of interest for the epiphysis. (b) Histogram of the coefficients in the vertical direction for level 1. (c) Histogram of the coefficients in the vertical direction for level 4.
2.3. Gray-level co-occurrence matrices GLCM is a matrix defined for an image based on the distributions of co-occurring values at a given offset. This matrix calculates how often a pixel with a gray-level value i occurs horizontally, vertically, or diagonally relative to adjacent pixels with a value j. The correlations of the gray-level values between two specific points with a given offset can describe the image features in terms of orientation, distance, and variation, representing the roughness and pattern of texture. A co-occurrence matrix C is defined for an ܰ௫ ൈ ܰ௬ image with ܰ gray-level values. Let ܮ௫ ൌ ሼͳǡʹǡ ǥ ǡ ܰ௫ ሽ be the horizontal spatial domain, ܮ௬ ൌ ሼͳǡʹǡ ǥ ǡ ܰ௬ ሽ be the vertical spatial domain, and ܩൌ ሼͲǡͳǡ ǥ ǡ ܰ െ ͳሽ be the set of gray levels. Image ܫcan be written as ܫǣ ܮ௫ ൈ ܮ௬ ՜ ܩ. An element of GLCM is ܲሺ݅ǡ ݆ǡ ݀ǡ ߠሻ, which means the two gray-level values ݅ and݆ co-occur at two pixels with an offset of ݀ pixels and a direction of , where ݀ ൌ ͳǡʹǡ͵ǡ ǥ and Ʌ ൌ Ͳι ǡ Ͷͷι ǡ ͻͲι ǡ ͳ͵ͷι . Haralick defined 14 second-order statistical features [4]. All of them could be extracted from a GLCM. Similar to Haralick and Fu [19], the mean values were calculated for four different directions (Ʌ ൌ Ͳι ǡ Ͷͷι ǡ ͻͲι ǡ ͳ͵ͷι ), where the gray degree was 256, the window size of texture was 55, and d=1. In the previous study [20], the authors reported that not all of these features were equally effective for image texture analysis. Therefore, based on experiments, five features were selected, i.e., energy, contrast, correlation, homogeneity and entropy. They are described by Eqs.(10)-(14): Energy: ݂ଵ ൌ ටσ σሼሺ݅ǡ ݆ሻሽଶ
(10)
Contrast: ݂ଶ ൌ σ σሺ݅ െ ݆ሻଶ ሺ݅ǡ ݆ሻ
(11)
Correlation: ݂ଷ ൌ
σ σೕሺሻሺǡሻିఓೣ ఓ
Homogeneity: ݂ସ ൌ σ σ
ఙೣ ఙ ଵ
(12)
ሺ݅ǡ ݆ሻ
(13)
Entropy: ݂ହ ൌ െ σ σ ሺ݅ǡ ݆ሻ ݈݃ሼሺ݅ǡ ݆ሻሽ
(14)
ଵାሺିሻమ
S. Hu et al. / Texture feature extraction based on wavelet transform and gray-level co-occurrence matrices
135
2.4. Feature selection Feature selection is an important issue in building classification systems. The redundancy and interdependency of features lead to misclassification. Meanwhile, additional computations are associated with high costs. As a result, it is advantageous to limit the number of input features in a classifier to obtain a predictive and less computationally intensive model. 2.4.1. Two-group independent samples-test For the 141 cases, 39 texture features were obtained using the Db4 wavelet and 39 texture features using the Sym4 wavelet. The following conclusions could be drawn. The mean value was the superposition of the fluctuation of the texture feature values. Theoretically, this value was close to 0, which could not reflect the textural information in the image. Therefore, this feature was excluded from the subsequent experiments. The independent samples t-test showed that the energy and variance of the other sub-bands were very similar, in addition to the low-frequency sub-band at level 4. These two values were simultaneously effective and ineffective when used to distinguish between normal and pathological bone images. This was because the energy values and variance values were similar when the mean value was close to 0. Therefore, energy was selected as the unique feature to reflect the textural information. However, the low-frequency sub-band at level 4 was approximately the same as that in the original image, therefore it could not be used to extract texture features. As a result, this sub-band was excluded in the study. In conclusion, when the original image was decomposed into four levels, the energy features were extracted in vertical, horizontal, and diagonal directions at each level. Therefore, 12 features were extracted using the Db4 wavelet and 12 features using the Sym4 wavelet. 2.4.2. One-way ANOVA and rank-sum test Before classification, it is useful to determine whether a set of features can discriminate among the labeled classes. As classical statistical inference is a well-established statistical test, two statistical tests were used in this step: one-way ANOVA and rank-sum test. The ANOVA test was used to compute the variation between features within a class and between classes. The test was considered to be statistically significant if the variation between classes was relatively high compared with the variation within a class. ANOVA used the variance to determine whether the means were different, but it should satisfy the conditions of the normality test and homogeneity test. If either condition was not met, the rank-sum test was then used. With the methods described before, the texture features extracted from the bone CR images were subject to one-way ANOVA test and rank-sum test. Table 1 shows the numbers of features are clinically significant after the two tests, where Vn, Hn, and Dn represent the energy values for the vertical, horizontal, and diagonal directions, respectively, at level n. An example of features extracted using Sym4 in epiphysis is as follows. First, normality test and homogeneity test were applied to all features, for normality test and homogeneity test , =0.1. Next, for features satisfied both of these two conditions, one-way ANOVA test was applied. Afterwards, five features, V2, H2, H3, D3, and D4 were selected, p
129
Texture feature extraction based on wavelet transform and gray-level co-occurrence matrices applied to osteosarcoma diagnosis1 Hu Shana, Xu Chaoa, Guan WeiQiaoa, Tang Yonga,b,*and Liu Yana,* a
Department of Biomedical Engineering, ZhongShan School of Medicine, Sun Yat-Sen University, GuangZhou, 510060, PR China. b Computer College, South China Normal University, GuangZhou, 510631, PR China.
Abstract. Osteosarcoma is the most common malignant bone tumor among children and adolescents. In this study, image texture analysis was made to extract texture features from bone CR images to evaluate the recognition rate of osteosarcoma. To obtain the optimal set of features, Sym4 and Db4 wavelet transforms and gray-level co-occurrence matrices were applied to the image, with statistical methods being used to maximize the feature selection. To evaluate the performance of these methods, a support vector machine algorithm was used. The experimental results demonstrated that the Sym4 wavelet had a higher classification accuracy (93.44%) than the Db4 wavelet with respect to osteosarcoma occurrence in the epiphysis, whereas the Db4 wavelet had a higher classification accuracy (96.25%) for osteosarcoma occurrence in the diaphysis. Results including accuracy, sensitivity, specificity and ROC curves obtained using the wavelets were all higher than those obtained using the features derived from the GLCM method. It is concluded that, a set of texture features can be extracted from the wavelets and used in computer-aided osteosarcoma diagnosis systems. In addition, this study also confirms that multi-resolution analysis is a useful tool for texture feature extraction during bone CR image processing. Keywords: Feature selection, gray-level co-occurrence matrix, osteosarcoma diagnosis, texture feature, wavelet transform
1. Introduction Osteosarcoma is the most common primary malignant bone tumor and the sixth most common type of cancer among children and adolescents, for whom the prognosis remains unfavorable despite treatment protocols combining chemotherapy and surgery. At present, the early diagnosis of osteosarcoma relies mainly on X-ray (CR/DR) while the final diagnosis depends on biopsies. However, as the manifestation of osteosarcoma is complex in CR images, atypical cases can easily be misdiagnosed [1]. To fully exploit the information in a CR image, it is necessary to use digital image processing technology to extract and analyze this information.
1* Co-corresponding author. Liu Yan, Email: [email protected] ,Tel: 0086-020-87331856, Fax: 0086-020-87331854 Tang Yong, Email: [email protected], Tel: 0086-020-85215327, Fax: 0086-020-87331854
0959-2989/14/$27.50 © 2014 – IOS Press and the authors. All rights reserved
130
S. Hu et al. / Texture feature extraction based on wavelet transform and gray-level co-occurrence matrices
Texture is an important characteristic used for identifying regions of interest (ROIs) in an image, which expresses either the fine structure or the macroscopic structure. In the last 30 years, many methods have been developed for analyzing texture, such as statistical, structural, model-based and signal processing approaches. Among them, statistical analysis is the most fundamental method for textural feature extraction, where the spatial distributions of gray-scale values are analyzed and the textural features are calculated using the statistical properties, such as 1-D features based on gray-level intensity histograms and 2-D features based on co-occurrence matrices [2,3]. A typical method that uses co-occurrence matrices is the gray-level co-occurrence matrices (GLCM) method proposed by Haralick et al. in the 1970s [4]. This method has been widely used in many texture analysis applications and it remains to be an important feature extraction method in the domain of medical image texture analysis [5-7]. The GLCM method tabulates how often different combinations of pixel brightness values (gray levels) occur in an image, and 14 features are extracted from the GLCMs to characterize the texture. In recent years, researchers have proposed many texture extraction methods based on analysis of multiple scales according to human vision. Multi-resolution analysis has been proved to be useful for image processing. The goal of multi-resolution analysis is to decompose the original image into sub-bands that preserve high- and low-frequency information, and to analyze these sub-bands in the frequency domain. By using a family of functions localized in terms of time and frequency, wavelet transforms can centralize the energy of the original image within only a few coefficients after wavelet decomposition. These coefficients have high local relativity in three directions of different sub-band images: horizontal, vertical, and diagonal. Thus, wavelet transforms can be used to extract texture information from images. Several studies have demonstrated the successful use of wavelet transforms as multi-resolution tools for texture analysis in medical image processing [8-13]. The present study compared the use of GLCM with wavelet transforms, including the Daubechies wavelet and Symlet wavelet, for the textural analysis of osteosarcoma CR images. Some significant features were also selected by statistical methods to create a classifier, that categorized bone images as normal or abnormal. The main aim of this study was to determine the distinguishing traits using these methods.
Fig.1. Schematic of the proposed system
Figure 1 shows a schematic of the system proposed in this study. First, the images were pre-processed to select ROIs. Then feature extraction was performed for each cropped sub-image. The texture features obtained from GLCM were calculated at fixed pixel distances (d=1) and the orientation was classified into four different directions (Ʌ ൌ Ͳι ǡ Ͷͷι ǡ ͻͲι ǡ ͳ͵ͷι ). For the wavelet transforms, the features were computed at four decomposition levels based on Daubechies wavelet and
S. Hu et al. / Texture feature extraction based on wavelet transform and gray-level co-occurrence matrices
131
Symlet wavelet. In the next stage, statistical methods, i.e., one-way ANOVA and rank-sum test, were applied to feature selection using the wavelet transforms. Finally, a support vector machine (SVM) algorithm was used to classify the images as normal or abnormal. The classification accuracy, sensitivity, specificity and Receiver Operating Characteristic (ROC) curves were used to evaluate the effectiveness of these features for the computer-aided diagnosis of osteosarcoma. 2. Material and methods 2.1. Dataset The bone CR images were provided by Guangdong General Hospital, The First Affiliated Hospital and The Second Affiliated Hospital of Sun Yat-sen University. The images were stored in DICOM format and the database contained a total of 141 cases, including 70 osteosarcoma cases and 71 normal cases. The patients with osteosarcoma were all measured in the progressive stage, as determined by biopsies. In all cases, CR images of the long bone were available and captured in situ. The images were divided into two classes: epiphysis and diaphysis, depending on which part of the bone was imaged. In the osteosarcoma cases, 33 epiphysis images and 37 diaphysis images were collected, whereas in the normal cases, 28 epiphysis images and 43 diaphysis images were collected. However, these images were acquired from different conditions with respect to the type of machine and the resolution. The ROIs included different orders of magnitude of pixels, which would result in adverse effects in the feature extraction. Image preprocessing was necessary to minimize the errors caused by these differences.
Fig.2. The regions of interest for the epiphysis (a) and diaphysis (b)
132
S. Hu et al. / Texture feature extraction based on wavelet transform and gray-level co-occurrence matrices
First, the image was cropped with a rectangle to obtain the sub-image with the ROI, where the rectangle was the widest possible rectangle filled completely by the epiphysis or diaphysis, as shown in Figure 2. Second, the same areas in different sub-images could contain different numbers of pixels, thus the resolution of the images was adjusted to ensure that the same number of pixels were contained in the same area of each sub-image. Both of them were completed manually using Photoshop software. 2.2. Wavelet transforms The wavelet transform [14] decomposed the signal as a linear operation for different scaling components and it could be obtained by filter convolution with a varying signal and scaling. For discrete signals, the discrete wavelet transform (DWT) was obtained by the discretization of time, translation and scale parameters. The wavelet ɗሺሻ is a linear combination of the scaling and translating of the scaling functionɔሺሻ, which satisfies a two-scale differential equation, using Eqs.(1) and (2): ɔሺሻ ൌ ξʹ σ ݄ሺ݇ሻ߮ ሺʹ ݔെ ݇ሻ
(1)
ɗሺሻ ൌ ξʹ σ ݃ሺ݇ሻ߮ ሺʹ ݔെ ݇ሻ
(2)
where ݄ is the low-pass filter and ݃ is the high-pass filter. These two filters are quadrature mirror filters, which satisfy݃ሺ݇ሻ ൌ ሺെͳሻ ݄ሺͳ െ ݇ሻ. To apply the wavelet transform to image processing, two-dimensional (2-D) wavelets are required from the vector product of ɗሺሻand ɔሺሻǡwhich are defined using Eqs.(3)-(6): ɔሺǡ ሻ ൌ ɔሺሻɔሺሻ
(3)
ɗு ሺǡ ሻ ൌ ɗሺሻɔሺሻ
(4)
ɗ ሺǡ ሻ ൌ ɔሺሻɗሺሻ
(5)
ɗ ሺǡ ሻ ൌ ɗሺሻɗሺሻ
(6)
where ɔሺǡ ሻ is a 2-D scaling function,ɗு , ɗ ǡ andɗ are three 2-D wavelets, and ܪ,ܸ , andܦrepresent the horizontal, vertical and diagonal directions, respectively. Different mother wavelets have different supporting lengths and regularities, therefore the results of texture feature extraction depend highly on the selection of the mother wavelet and the number of levels. The Daubechies wavelet is a compactly supported orthogonal wavelet which is significant in the wavelet field. The Symlet wavelet has a construction similar to that of the Daubechies wavelet, but its symmetry is higher. Several studies have compared the effect of various wavelets on the extraction of texture features [15-18]. In the present study, the Db4 and Sym4 wavelets were selected to extract features from bone CR images and to compare their effects. The number of decomposed levels determines the amount of details during textural extraction. The first level has the finest texture, and the fineness decreases as the number of decomposed levels increases. Synthesizing the texture at various levels can reflect an image’s texture. However, the computational cost increases when more levels are decomposed. In the present study, when the image was decomposed from the histogram of coefficients, it was found that the image achieved better
S. Hu et al. / Texture feature extraction based on wavelet transform and gray-level co-occurrence matrices
133
equalization at level 4. As shown in Figure 3, the ROI (a) is decomposed with the Db4 wavelet, and (b) and (c) are the histograms of coefficients in the vertical direction for level 1 and level 4, respectively. Therefore, after considering the computational costs, these images were decomposed at four levels. Three features are extracted at each level and in each direction (horizontal, vertical, and diagonal), i.e., the mean, variance and energy, which are defined using Eqs.(7)-(9), where Cij is the coefficient matrix at point (i,j). ଵ
തതതത Mean: ܥ ௌ ൌ Variance: ܸௌ ൌ
ൈ
ଵ ൈ
Energy: ݁ௌ ൌ
σୀ σୀ ܥ
(7)
ଶ തതതത σୀ σୀሺܥ െ ܥ ௌ ሻ ଵ
ൈ
σୀ σୀหܥ ห
ଶ
(8) (9)
134
S. Hu et al. / Texture feature extraction based on wavelet transform and gray-level co-occurrence matrices
Fig.3.(a) The regions of interest for the epiphysis. (b) Histogram of the coefficients in the vertical direction for level 1. (c) Histogram of the coefficients in the vertical direction for level 4.
2.3. Gray-level co-occurrence matrices GLCM is a matrix defined for an image based on the distributions of co-occurring values at a given offset. This matrix calculates how often a pixel with a gray-level value i occurs horizontally, vertically, or diagonally relative to adjacent pixels with a value j. The correlations of the gray-level values between two specific points with a given offset can describe the image features in terms of orientation, distance, and variation, representing the roughness and pattern of texture. A co-occurrence matrix C is defined for an ܰ௫ ൈ ܰ௬ image with ܰ gray-level values. Let ܮ௫ ൌ ሼͳǡʹǡ ǥ ǡ ܰ௫ ሽ be the horizontal spatial domain, ܮ௬ ൌ ሼͳǡʹǡ ǥ ǡ ܰ௬ ሽ be the vertical spatial domain, and ܩൌ ሼͲǡͳǡ ǥ ǡ ܰ െ ͳሽ be the set of gray levels. Image ܫcan be written as ܫǣ ܮ௫ ൈ ܮ௬ ՜ ܩ. An element of GLCM is ܲሺ݅ǡ ݆ǡ ݀ǡ ߠሻ, which means the two gray-level values ݅ and݆ co-occur at two pixels with an offset of ݀ pixels and a direction of , where ݀ ൌ ͳǡʹǡ͵ǡ ǥ and Ʌ ൌ Ͳι ǡ Ͷͷι ǡ ͻͲι ǡ ͳ͵ͷι . Haralick defined 14 second-order statistical features [4]. All of them could be extracted from a GLCM. Similar to Haralick and Fu [19], the mean values were calculated for four different directions (Ʌ ൌ Ͳι ǡ Ͷͷι ǡ ͻͲι ǡ ͳ͵ͷι ), where the gray degree was 256, the window size of texture was 55, and d=1. In the previous study [20], the authors reported that not all of these features were equally effective for image texture analysis. Therefore, based on experiments, five features were selected, i.e., energy, contrast, correlation, homogeneity and entropy. They are described by Eqs.(10)-(14): Energy: ݂ଵ ൌ ටσ σሼሺ݅ǡ ݆ሻሽଶ
(10)
Contrast: ݂ଶ ൌ σ σሺ݅ െ ݆ሻଶ ሺ݅ǡ ݆ሻ
(11)
Correlation: ݂ଷ ൌ
σ σೕሺሻሺǡሻିఓೣ ఓ
Homogeneity: ݂ସ ൌ σ σ
ఙೣ ఙ ଵ
(12)
ሺ݅ǡ ݆ሻ
(13)
Entropy: ݂ହ ൌ െ σ σ ሺ݅ǡ ݆ሻ ݈݃ሼሺ݅ǡ ݆ሻሽ
(14)
ଵାሺିሻమ
S. Hu et al. / Texture feature extraction based on wavelet transform and gray-level co-occurrence matrices
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2.4. Feature selection Feature selection is an important issue in building classification systems. The redundancy and interdependency of features lead to misclassification. Meanwhile, additional computations are associated with high costs. As a result, it is advantageous to limit the number of input features in a classifier to obtain a predictive and less computationally intensive model. 2.4.1. Two-group independent samples-test For the 141 cases, 39 texture features were obtained using the Db4 wavelet and 39 texture features using the Sym4 wavelet. The following conclusions could be drawn. The mean value was the superposition of the fluctuation of the texture feature values. Theoretically, this value was close to 0, which could not reflect the textural information in the image. Therefore, this feature was excluded from the subsequent experiments. The independent samples t-test showed that the energy and variance of the other sub-bands were very similar, in addition to the low-frequency sub-band at level 4. These two values were simultaneously effective and ineffective when used to distinguish between normal and pathological bone images. This was because the energy values and variance values were similar when the mean value was close to 0. Therefore, energy was selected as the unique feature to reflect the textural information. However, the low-frequency sub-band at level 4 was approximately the same as that in the original image, therefore it could not be used to extract texture features. As a result, this sub-band was excluded in the study. In conclusion, when the original image was decomposed into four levels, the energy features were extracted in vertical, horizontal, and diagonal directions at each level. Therefore, 12 features were extracted using the Db4 wavelet and 12 features using the Sym4 wavelet. 2.4.2. One-way ANOVA and rank-sum test Before classification, it is useful to determine whether a set of features can discriminate among the labeled classes. As classical statistical inference is a well-established statistical test, two statistical tests were used in this step: one-way ANOVA and rank-sum test. The ANOVA test was used to compute the variation between features within a class and between classes. The test was considered to be statistically significant if the variation between classes was relatively high compared with the variation within a class. ANOVA used the variance to determine whether the means were different, but it should satisfy the conditions of the normality test and homogeneity test. If either condition was not met, the rank-sum test was then used. With the methods described before, the texture features extracted from the bone CR images were subject to one-way ANOVA test and rank-sum test. Table 1 shows the numbers of features are clinically significant after the two tests, where Vn, Hn, and Dn represent the energy values for the vertical, horizontal, and diagonal directions, respectively, at level n. An example of features extracted using Sym4 in epiphysis is as follows. First, normality test and homogeneity test were applied to all features, for normality test and homogeneity test , =0.1. Next, for features satisfied both of these two conditions, one-way ANOVA test was applied. Afterwards, five features, V2, H2, H3, D3, and D4 were selected, p
