New design of adaptive Gabor wavelet filter bank for medical image retrieval

IET Image ProcessingVolume 14, Issue 4 p. 679-687 Research ArticleFree Access New design of adaptive Gabor wavelet filter bank for medical image retrieval Aswini K. Samantaray, Corresponding Author Aswini K. Samantaray asamantaray@nitgoa.ac.in Department of Electrical & Electronics Engineering, National Institute of Technology Goa, Farmagudi, Goa, 403401 IndiaSearch for more papers by this authorAmol D. Rahulkar, Amol D. Rahulkar Department of Electrical & Electronics Engineering, National Institute of Technology Goa, Farmagudi, Goa, 403401 IndiaSearch for more papers by this author Aswini K. Samantaray, Corresponding Author Aswini K. Samantaray asamantaray@nitgoa.ac.in Department of Electrical & Electronics Engineering, National Institute of Technology Goa, Farmagudi, Goa, 403401 IndiaSearch for more papers by this authorAmol D. Rahulkar, Amol D. Rahulkar Department of Electrical & Electronics Engineering, National Institute of Technology Goa, Farmagudi, Goa, 403401 IndiaSearch for more papers by this author First published: 18 February 2020 https://doi.org/10.1049/iet-ipr.2019.1024Citations: 2AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Gabor wavelet is widely used in the analysis of texture feature. This study presents a novel feature descriptor based on the design of adaptive Gabor wavelet filter-bank for medical image retrieval. The design of proposed Gabor wavelet provides flexibility to extract the dominant directional features from medical images. First, peaks in the spectrum of medical image are analysed to determine the dominant directions present in the image. With these dominant directions, a bank of Gabor-filters is designed to extract the directional features effectively. Next, feature vector is derived by computing the energy and standard deviation from the Gabor filtered coefficients at a particular scale and orientation. The use of maximum likelihood estimation (MLE) is suggested to measure the similarity between the feature vectors of heterogeneous medical images. The performance of the proposed method is evaluated on three different publicly available databases namely NEMA, OASIS and EXACT09. The performance in terms of average retrieval precision (ARP), average retrieval rate (ARR) and computational time are compared with well-known existing methods. It is observed from experimental results that the proposed approach achieved ARP of 85.32, 85.24 and 77% and ARR of 31.33, 14.05 and 23.78% for NEMA, OASIS and EXACT09 databases respectively. 1 Introduction With the technology development in medical field, there is a rapid increase in medical image data. Due to this, medical image retrieval becomes more difficult and time consuming for diagnosis purpose [1]. Therefore, there is a growing interest in devising efficient methods for image retrieval from medical image databases. The traditional methods of image retrieval mainly depend on text describing the scene. Hence, they are keyword based searching methods. However, it is difficult and time consuming to trace each medical image by its unique scene. So, medical images are indexed by visual queries like colour, texture and shape rather than text based keywords [2]. Since last two decades, content based image retrieval (CBIR) became an active area of research. The capability of supporting visual contents is the key advantage of CBIR. However, some of the techniques produce unsatisfactory outcome due to distinctive characteristics of medical images. Hence, the main challenge of CBIR is to devise efficient methods with increased retrieval accuracy and reduced retrieval time. A typical medical image retrieval system consists of three important stages: preprocessing, feature extraction and similarity measurement. This paper focuses on the feature extraction step which is the key for a successful image retrieval system. Several methods have been proposed for the extraction of features from the medical images. Local binary pattern (LBP) [3] performs well in texture classification of medical images and has a low computational complexity. Several LBP variants are also proposed such as centre symmetric LBP [4], data driven LBP [5], local ternary patten (LTP) [6] and centre symmetric LTP [7] where a relationship is established between the centre pixel and its neighbourhood pixels. Likewise, other texture descriptors such as peak valley edge pattern [8] and local ternary co-occurrence pattern [9] are proposed for the extraction of features from the medical images. These descriptors also use the relationship between the centre pixel and its neighbourhood pixels. Murala and Wu. [10] proposed a local mesh pattern for medical image retrieval where the relationship between centre pixel and its neighbourhood is found along with the relationship between the neighbourhood pixels. However, the major limitations of these binary descriptors are that the size of the features increases with the increase in number of local neighbours. Recently, a significant contribution is observed from wavelet transform based approaches for medical image retrieval. Yelampalli et al. [11] used Daubechies wavelet-based local feature descriptor for the registration of medical images. Same authors used a binary feature descriptor to discriminate normal and abnormal chest computed tomography (CT) images [12]. In their next method [13], the registration of medical images is based on binary feature descriptor and modified affine transform. A local wavelet pattern for the retrieval of CT images is discussed in [14]. However, the decomposition level of wavelet transform depends on the nature of the images in the database in order to get better performance. Also, these methods suffer from limited directionality. The autocorrelation features are proposed in [15, 16] for the registration of medical images. The registration of medical images in these methods depends on continuous optimisation scheme with local minima. Other recent methods based on region features [17] and particle swarm optimisation [18, 19] are used in medical image retrieval. One of the widely used methods for extraction of texture feature is Gabor wavalet filter bank (FB) [20]. This FB is an efficient tool for the analysis of local time–frequency characteristics. The Gabor wavelet FB uses a set of specific (fixed) directions and scales to describe the texture features. It extracts the time–frequency coefficients for each direction and scale [21]. The direction set and scale set belong to the direction space and scale space, respectively. It is found that different modalities of images (which differed in terms of different rotation and background pixels) are present in medical image databases. Hence, it is difficult to extract textural information present in the medical images using fixed directions and scales [22]. In last few years, a number of filters are derived from Gabor filters, some of which are rotation invariant and can be used for texture classification [23, 24]. Manjunath and Ma. [25] used circular Gabor filters which are used for the classification of rotation invariant texture and texture segment. The experimental results of these methods show that these methods perform better in extraction of texture features. However, the computational complexity is high for this method to extract and analyse the texture information [26]. In order to solve this problem, Log-Gabor wavelet FB has been proposed by Gao et al. [27] which has a low computational complexity. However, the limitation of log-Gabor FB is its design with fixed orientations. It is observed from literature that Gabor wavelet FB and its variants (circular Gabor, log-Gabor) are widely used for texture extraction and analysis. However, it is difficult to design Gabor wavelet FB for different applications. It is because, the FB requires a number of optimal tuned parameters such as orientation, scale, aspect ratio, phase offset, standard deviation along Gaussian major and minor axes to design the filters. The effect of these different Gabor filter parameters has been investigated in [28] on texture retrieval. However, the explanation on the selection of these parameters is insufficient. In particular, the Gabor FB is designed with fixed set of scales and orientations. In addition, the smoothing parameters (standard deviation along Gaussian major and minor axes) also play an important role in the design of Gabor wavelet FB. With this fixed set of orientations and scales, the Gabor wavelet FB is unable to extarct the discriminative texture features from the medical images. It is because, the images in the medical database are of different size and modalities (heterogeneous). It is observed that the orientations used in the design of Gabor wavelet FB do not match with the most dominant texture orientations of heterogeneous medical images. Hence, the Gabor FB is unable to extract the dominant texture features from the medical images. Thus, it is necessary to design the Gabor filters with the dominant texture directions present in the heterogeneous medical images. With this, the performance of the medical image retrieval can be improved significantly. In this paper, a novel method for the extraction of texture features from medical images using an adaptive Gabor wavelet FB is presented. The block diagram of the proposed method is shown in Fig. 1. First, all the images are preprocessed using noise removal and image enhancement techniques to retain the minute details. Next, the dominant texture directions of the medical images are determined by analysing the dominant peaks present in the spectrum of the image. These directions are used to design a bank of Gabor filters to extract the time–frequency coefficients for each determined direction and scale. Since the orientation set used for designing the Gabor filters is different for different medical images, hence named as adaptive Gabor FB (AGFB). Next, a set of feature vectors are computed in terms of standard deviation and energy from the Gabor filtered images. In order to retrieve the image from the medical database, a match is found between the images by finding the similarity between the feature vectors. Maximum likelihood estimation (MLE) is suggested over distance based metrics for the purpose of similarity measurement. Fig. 1Open in figure viewerPowerPoint Block diagram of medical image retrieval system using the proposed method The rest of the paper is organised as follows. The overview of Gabor FB is described in Section 2. Section 3 describes the effect of orientation parameter and proposed design of Gabor FB for texture feature extraction. A similarity measurement metrics in terms of MLE is described in Section 4. Section 5 describes the extensive discussion of result analysis followed by conclusion in Section 6. 2 Gabor wavelet transform This is important to analyse the frequency and space characteristics of a signal simultaneously. It is well known that short time Fourier transform (STFT) can analyse the signal in both space and frequency domain. However, STFT uses fixed window size for which there is a low time–frequency resolution. Therefore, several filters including different wavelet filters have been proposed to provide space-frequency signal decomposition [11-19]. Gabor filters are generally used to obtain the local spatial and frequency information. The Gabor filters are widely used in many image processing applications such as texture analysis, edge extraction, object recognition and so on. A 2D Gabor function is a Gaussian modulated by a complex sinusoid and is given by [21] (1)and its Fourier transform is represented by (2)where , denote the Gaussian's major and minor widths, respectively, and f is the modulation frequency. The ratio of standard deviation along minor axis to standard deviation along major axis defines the spatial aspect ratio () which describes the ellipticity of the support of Gabor function. The parameter represents the phase offset which specifies the symmetricity of the function. The function is symmetric when or , antisymmetric when or and asymmetric when . The Gabor wavelet filters are obtained using (1) and are expressed as (3)where and m, n are the scales and orientation of the Gabor wavelet, respectively, with and . and are expressed as follows: (4)where and K is the total number of orientations. Gabor wavelet FB is commonly utilised for a particular set of scales and orientations. It is observed that these filters are not able to extract the important discriminative texture features from the medical images. This is because of a fixed set of orientations to design the filters. The number of filters in the bank is proportional to the number of orientations considered for the design with fixed scales. If more number of orientations are considered, more number of filters are obtained which leads to increase in computational complexity. Hence, in order to reduce computational complexity, a fixed direction set of either four and or six and is commonly considered for the design of the FB. However, it is observed that these directions are not the most dominant directions for medical images as medical images are heterogeneous in nature. In order to address this issue, the Gabor FB is designed with the dominant texture directions present in medical images. Hence, the different orientations for different medical images are used to design the Gabor FB adaptively. 3 Proposed design of AGFB It is known that the performance of the Gabor FB is controlled by a number of parameters (orientation, scale, aspect ratio, phase offset, standard deviation along Gaussian major and minor axes). The parameter in (4) is the orientation of the normal to the parallel stripes of the Gabor function. This is one of the important parameters which affects the performance of the filters. The design of the proposed AGFB is as follows. 3.1 Effect of orientation parameter on images It is known that a bank of Gabor filters with a number of different orientations are used to analyse the texture (to get the features) from the image. In order to understand the importance of orientation parameter, consider a bank of 16 Gabor filters at different orientations and one scale in frequency domain as given in Fig. 2. The first filter is at a orientation of , second is at , third is at and so on. Consider an image given in Fig. 3a which is a white circle in black background. When each filter of the Gabor FB shown in Fig. 2 is applied to the image shown in Fig. 3a, the edge of the circle is detected at an angle at which each Gabor filter is oriented as shown in Fig. 3c. This is because the Gabor filter extracts important information at points where the texture changes when it is applied to an image. Fig. 2Open in figure viewerPowerPoint Bank of 16 Gabor filters oriented at different angles Fig. 3Open in figure viewerPowerPoint Corresponding oriented edge features being detected when passed through individual oriented Gabor filters (a) Input image of a circle, (b) Bank of 16 Gabor filters, (c) Output circle as seen when passed through individual Gabor filter 3.2 Computation of orientation parameter In order to compute the orientation parameter, the spectral characteristics of an image are obtained using Fourier transform and is expressed as (5)where is an image. For convenience of the computation, the Fourier spectrum is converted into polar form , where r is the radial value and is the orientation. This is achieved by expressing each point obtained in (5) in polar co-ordinates . Next, orientation parameters are evaluated for each radial value r and is expressed using function . This function indicates the behaviour of the spectrum along a circle of radius r centred at origin. Similarly, radial values are evaluated for each value of orientation parameter and is expressed using function . This function describes the behaviour of the spectrum along a radial direction from the origin. The above two spectral descriptors are described by (6) and (7), respectively (6) (7)where the dimension of R is obtained by for an image of size . In this work, we concentrate on the orientation parameter, hence is the function of interest with origin shifted to the centre of the spectrum. So, by varying the values of , a 1D function can be generated which describes the textural energy content. The variation of orientation parameter gives the textural energy content along the concentric circles within the spectrum. By analysing the texture energy content with respect to , we get the peak value at each orientation. The prominent peaks of spectrum give the principal direction of the texture pattern, i.e. the principal direction is along horizontal or vertical or any other direction. From the above discussion, these descriptors give following information: • Location of the highest peak. • Mean and variance of amplitude as well as axial variations. • Distance between mean and highest value of the functions (). The detailed design of the proposed AGFB is as follows: Initially, the origin of the spectrum is shifted to the centre . Next, assume an arbitrary point at a distance R from the centre . The point with fixed radius R and varied is calculated by the following equations: (8) The radial direction from the centre of the spectrum to the point are determined by the slope of the line joining the centre to the point. Similarly, the process is repeated for other remaining points. A spectral energy is analysed which shows the energy distribution of the spectrum at all orientations. The prominent peaks are found from the obtained spectral energy distribution. These prominent peaks indicate the major textural energy content at different orientations. Thus, the length of the vector becomes . The values of the orientation parameter for which the spectral energy is maximum, are chosen as (9)where . Next, the selected orientations are used as the orientation parameter for the design of Gabor FB. The design of the proposed AGFB is given by the following equation: (10)where is the orientation of the prominent peaks in the spectrum of the medical image. Therefore, the Gabor filtered coefficient for a medical image is given by (11) Illustration: In order to illustrate the aforementioned design, consider an image and its Fourier spectrum as shown in Figs. 4a and b, respectively. It is seen that when the proposed scheme is applied to the image in Fig. 4a, all the peaks of the image are found as shown in Fig. 4b. It is clearly observed from Fig. 4b that we have the patterns in the horizontal direction with equal to and . We have also the strong patterns in the diagonal directions with equal to and , a stronger pattern in vertical direction with equal to . Fig. 4Open in figure viewerPowerPoint Frequency spectrum of a test image (a) Test image, (b) Its spectrum It is to be noted that out of two parameters and r, the orientation parameter is taken as the control parameter to design the Gabor FB for medical image retrieval. The total number of proposed filters in the FB is proportional to the number of orientations considered for the experiment with fixed scales. The peaks in the spectral representation of an medical image give the values of the orientations for designing the Gabor FB. A typical CT image and its spectrum are shown in Fig. 5. Fig. 5Open in figure viewerPowerPoint Frequency spectrum of a CT test image (a) CT image, (b) Its spectrum 3.3 Effect of orientation parameter on other Gabor filter parameter It is known that the standard deviation along the minor axis which defines the spatial aspect ratio can be adjusted according to the number of selected orientations [28]. The relation between the orientation parameter and the standard deviation along the minor axis is described by the following equations: (12)where and is the crossing point between two adjoining filters with adjacent orientations. By substituting the value of in (12), the standard deviation along minor axis can be rewritten as (13)where n represents the number of orientations. When the value of n is small, (13) produces wide filters which are not suitable to extract texture feature. However, when n value is large, . Hence, (13) can be approximated by (14) The computational complexity of the Gabor filter can be expressed as , where and are the standard deviations of the Gabor filter along major and minor axes, respectively, and M and N are the dimensions of the medical image. From (14), it is evident that larger is the value of n, larger is the value of which leads to larger spatial aspect ratio (). A larger value of increases the computational complexity. Therefore, in order to have low complexity, the value should be chosen to be small which further keeps the small value of spatial aspect ratio and therefore the number of orientations. The variation of Gabor filter parameters (aspect ratio, phase offset, orientation and standard deviation along Gaussian major and minor axes) and their effects on different medical images are shown in Fig. 6. The medical images of rows 1 and 2 are for phase offset of (asymmetry) and rows 3 and 4 are for phase offset of (antisymmetry). It is observed from the resultant images of these rows that the filters are unable to extract the features effectively. Rows 5 and 6 show the Gabor filtered image with phase offset (symmetry). It is observed that the texture are clearly detected as compared to the images shown in rows 1–4. It is because, medical images are symmetric in nature. Hence, a phase offset of is selected for the design of Gabor wavelet FB. In order to decide the effect of spatial aspect ratio, Gabor filters with an aspect ratios of 1, 0.5, 0.2 and 0.3 are applied to the columns 1, 2, 3, 4 of Fig. 6, respectively. In columns 1 and 2, though the filters are able to extract the some texture features, they are not able to extract minute textural details which are important in case of medical image analysis. Although all the texture features from the medical images in column 3 are extracted, the texture features are not clearly distinguishable. However, the filters are able to extract all the detailed texture features from the medical images in column 4. The minute details of the medical images are retained efficiently using 0.3 aspect ratio than using aspect ratios of 0.2, 0.6 and 1. Thus, it is observed that spatial aspect ratio and phase offset play important roles to extract the fine directional information from the medical images. Fig. 6Open in figure viewerPowerPoint Variation of Gabor filter parameters and their effect on medical images 3.4 Texture representation After applying the proposed Gabor FB on medical images, the Gabor filtered co-efficients represent the energy content of the image at different orientations and scales. Consider to be the Gabor filtered co-efficients. The magnitude of these co-efficients is computed as (15)where and . The key idea of texture based medical image retrieval is to match the regions of the images with similar texture. There is an assumption that similar images have homogeneous texture pattern [29]. There are certain texture features used to represent these homogeneous texture regions of the image. In this work, we have considered energy and standard deviation as the texture features to represent the texture of the transformed image. These features are mathematically represented as (16) (17)where The dimension of the feature vector depends on the number of considered features. A Gabor FB with m scales and n orientations produces number of filters. Further, two features such as energy and standard deviation are computed from each filtered image. Therefore, a feature vector of a Gabor FB with m scales and n orientations consists of features for a medical image. This vector is represented as (18) It is found from an extensive experimentation that the proposed AGFB with three scales and six orientations are enough to represent a heterogeneous medical image effectively and efficiently. With this, total 36 () number of features are computed for each medical image. 4 Similarity measurement Similarity measurement commonly uses distance metrics, specifically Euclidean and Manhattan distance measures. But these distance measures may not fit to all type of data distribution. This is due to the fact that the feature elements which are from heterogeneous sources, have not same influence on similarity measurement [30]. Therefore, it is necessary to devise a method which selects the best similarity measurement metrics that is suitable for the distribution of the feature elements. Similarity measures based on intensity or features are generally used for medical image registration. However, these measures mostly depend on the algorithms which are limited to very particular registration problems. So, this is a challenging task to find the similarity between the medical images with different modalities. It is observed from the literature that MLE is a statistical method which determines the values of parameter (based on data distribution) that maximises the likelihood function [31]. This method is mainly based on a likelihood function , where is the parameter of the model. This measure determines the value of the parameter for which the likelihood function is maximum. MLE defines the maximum likelihood estimate as [31] (19) Equation (19) is often expressed in different forms for convenience of computation. In this work, we have used log-likelihood estimation for the similarity measurement which is mathematically expressed as follows: (20) 5 Result analysis and discussions Three different publicly available medical image databases such as NEMA, OASIS and EXACT09 are considered for the experimentation. The medical images in these databases are of different modalities and sizes. The size of the images is in both NEMA and EXACT09 databases where it is in OASIS database. The experiments are performed on three medical image databases separately. The experiments on all the databases are conducted using MATLAB R2016a software with a personal computer(PC) having Intel(R) Core(TM) i7-6700 CPU @3.40 3.41 GHz processor, 8 GB RAM and 64-bit operating system, x64 based processor Windows 10 ultimate operating system. The performance of the proposed approach is validated by comparing the experimental results with six well-known successful existing methods. These methods include LBP [4], Gabor wavelet FB [22], Log-Gabor wavelet FB [27], Murala and Wu. [10] and Yelampalli et al. [11, 12]. The methods such as LBP [4] and Yelampalli et al. [12] are implemented by thresholding the centre pixel from its neighbourhood pixels where as Murala et al. [10] is implemented by considering a neighbourhood. Similarly, Yelampalli et al. [11] is implemented using Daub4 wavelet with one level of decomposition. The methods given in [22, 27] are implemented with three scales and six orientations. MLE is used for the similarity measurement between the feature vectors of query image and the images of the database. The medical images present in NEMA, OASIS and EXACT09 are of different size and modalities. Hence, similarity measurement is computed for NEMA, OASIS and EXACT09 databases separately to validate MLE. 5.1 Evaluation criteria In this subsection, we describe the parameters adopted for the purpose of evaluation. Feature extraction time and image retrieval time are used to compare computational time of the proposed method with other existing methods. We retrieve the top ten matched images using MLE. We calculate average precision (AP) and average recall (AR) for each category which further calculates average retrieval precision (ARP) and average retrieval rate (ARR). AP and AR for each category is calculated by computing average of the precisions and recalls after considering each image of that category as query image. The precision and recall of a query image can be computed as (21) (22) Similarly, the ARP and ARR can be computed by the following equations: (23) (24) Where represents the total number of images in a particular database. 5.2 Experiment #1 National Electrical Manufacturers Association (NEMA) has created digital imaging and communication (DICOM) in order to aid the viewing and distribution of medical images such as magnetic resonance imaging (MRI), CT and ultrasound for research and storage purpose. In this experiment, we have considered ten sets of CT medical images created by NEMA. The detail of the database is available in [32]. We have considered 450 CT images in total of dimension which includes CT images from different parts of the human body. Sample images of this dataset from each category are given in Fig. 7. Fig. 7Open in figure viewerPowerPoint Sample images of NEMA database, one image from each category A query image of this category and its spectrum are given in Fig. 8. The proposed method is used to obtain dominant texture directions in the CT image. Fig. 9a represents a query image from NEMA database an