IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS, VOL. 17, NO. 5, SEPTEMBER 2013

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Evolution-Based Hierarchical Feature Fusion for Ultrasonic Liver Tissue Characterization Cheng-Chi Wu, Wen-Li Lee, Yung-Chang Chen, Fellow, IEEE, and Kai-Sheng Hsieh

Abstract—This paper presents an evolution-based hierarchical feature fusion system that selects the dominant features among multiple feature vectors for ultrasonic liver tissue characterization. After extracting the spatial gray-level dependence matrices, multiresolution fractal feature vectors and multiresolution energy feature vectors, the system utilizes evolution-based algorithms to select features. In each feature space, features are selected independently to compile a feature subset. As the features of different feature vectors contain complementary information, a feature fusion process is used to combine the subsets generated from different vectors. Features are then selected from the fused feature vector to form a fused feature subset. The selected features are used to classify ultrasonic images of liver tissue into three classes: hepatoma, cirrhosis, and normal liver. Experiment results show that the classification accuracy of the fused feature subset is superior to that derived by using individual feature subsets. Moreover, the findings demonstrate that the proposed algorithm is capable of selecting discriminative features among multiple feature vectors to facilitate the early detection of hepatoma and cirrhosis via ultrasonic liver imaging. Index Terms—Evolution-based, genetic algorithms, hierarchical feature fusion (HFF), liver, particle swarm optimization (PSO), ultrasound.

I. INTRODUCTION RIMARY malignancy of the liver (hepatocellular carcinoma, also called hepatoma) and cirrhosis are common liver diseases. Hepatoma, one of the major cancers in certain regions of Asia, is usually fatal if it is not detected early; while cirrhosis carries the potential risk of developing into hepatoma. Distinguishing between the two diseases is important because their treatments differ significantly. Thus, to facilitate the early detection of hepatoma and cirrhosis, there is an urgent need for a method that is noninvasive, reliable and easy to perform. In modern medicine, ultrasonic imaging technology is one of the most widely used diagnostic tools because it is effective in

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Manuscript received August 12, 2012; revised January 9, 2013 and March 19, 2013; accepted April 27, 2013. Date of publication May 6, 2013; date of current version August 30, 2013. This work was supported by a grant from the National Science Council of Taiwan under Contract NSC 99-2221-E-130-014. C.-C. Wu and Y.-C. Chen are with the Department of Electrical Engineering, National Tsing Hua University, Hsinchu 300, Taiwan (e-mail: [email protected]. nthu.edu.tw; [email protected]). W.-L. Lee is with the Department of Healthcare Information and Management, Ming Chuan University, Taoyuan 330, Taiwan (e-mail: wllee2002@msn. com). K.-S. Hsieh is with the Veterans General Hospital, Kaohsiung 813, Taiwan (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JBHI.2013.2261819

visualizing soft tissue and organs, and it is relatively inexpensive compared to other modalities. Therefore, it is commonly adopted for routine liver examinations and early detection of liver disease. B-mode ultrasound images present various granular structures as textures that represent the acoustic properties of human tissues. Currently, ultrasonic liver tissue characterization depends primarily on the clinician’s ability to identify certain textural characteristics. Because the visual interpretation of the liver tissue is subjective, the characterization may not always be accurate. Therefore, a quantitative method of diagnosing liver disease based on ultrasonic liver images is desirable. Tissue differentiation in ultrasound images can be modeled as a texture classification problem [1]. However, extracting meaningful features is one of the most difficult aspects of texture analysis. Among the popular texture descriptors, the spatial gray-level dependence matrix (SGLDM) [2], [3] is a general procedure for extracting the textural properties of blocks defined in the spatial domain of image data. The properties contain information about the image’s textural characteristics, such as the contrast, variance, correlation, and entropy. In ultrasound image analysis, the multiresolution fractal vector and SGLDM are used to extract textural information [4]–[6]. Recently, there has been a major development in texture classification with the use of multiresolution analysis, which decomposes an original image into a set of subimages. The technique is a powerful tool that extracts information about the original image in the time-frequency space to describe similar textures. The wavelet transform and Gabor filters [4]–[10] are two popular multiresolution transform algorithms that are used for texture classification. After multiresolution decomposition, feature representation methods are applied to the subimages to extract a set of multiresolution features. Among the feature descriptors, the fractal dimension and the energy are employed to extract features from the subimages. The fractal dimension, which provides fractal information about different subbands, was proposed by Mandelbrot [11] to describe the shape and appearance of objects that have the properties of self-similarity and scale invariance. The intensity surface of B-mode ultrasound images can be viewed as a rugged surface that can be described by fractal geometry. The fractal dimension, one of the most significant fractal features, describes a dimension that is strictly larger than the topological dimension. Evaluation of the dimension provides a way to measure the degree of boundary irregularity or surface roughness numerically. However, the fractal dimension of the original intensity surface does not provide sufficient discriminative information due to the limited dynamic range. The

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combination of multiresolution analysis and fractal dimension computation has been used successfully for ultrasonic liver tissue classification [5]. Different fractal sets may share the same fractal dimension, but they have very different appearances or textures. The energy and energy deviation values, which are utilized to describe an image’s texture in MPEG-7 [12], are applied to improve the classification accuracy. Normally, it is not feasible to use all features for classification in applications based on the SGLDM and multiresolution features. Some features have less discriminative ability and are regarded as redundant. Using such features would reduce the classification accuracy and cause unnecessary computation operations [13]. The feature selection process involves choosing a subset of features in the original feature space while maintaining the discriminative ability of different classes. Generally, it is not known in advance which feature subset will provide the best discriminative ability among the classes. The selection of SGLDM features and multiresolution features is empirical in most approaches. For example, in [5], the selection of the multiresolution fractal feature subset used for ultrasonic liver tissue characterization is based on observation of the Fourier spectrum and a predefined threshold for the fractal dimension. The manual selection of SGLDM features is inconsistent in different applications. In [2], the angular second moment, sum average, and entropy are selected for textural characterization of head and neck cancer. Meanwhile, in [3], the following eleven measures are used in the detection of prostate cancer: angular second moment, contrast, correlation, variance, inverse difference moment, sum average, sum variance, sum entropy, entropy, difference variance, and difference entropy. In [6], the correlation and sum entropy features are exploited to detect diffuse liver disease because they achieve the best performance in experiments. A large number of algorithms have been proposed to resolve the problem of inconsistent and subjective manual feature selection. They can be divided into two categories: 1) filter methods, which rank and select features based on certain statistical criteria and 2) wrapper methods in which feature selection is wrapped in a learning algorithm. Generally, wrapper methods outperform filter methods. Among the wrapper methods, particle swarm optimization (PSO) [14] and Genetic Algorithms (GA) [15]–[17] are two popular approaches in evolutionary computation. PSO, a population-based stochastic algorithm, proposed by Kennedy and Eberhart in [18], was motivated by simulations of simplified social models, such as flocking birds and schooling fish models. In PSO, each candidate solution is a position with a fitness value in the search space. Each particle remembers its own best solution and also knows the best solution of its neighbor in the current swarm. The individual particles traverse the search space looking for an optimal solution based on global and local information. Genetic algorithms (GAs) are evolutionary methods. They are based on the natural search and selection processes that ensure survival of the fittest individuals in a population. The objective of a GA is to find an optimal binary vector in which each bit is associated with a feature. A binary vector can be viewed as the

genes of an individual; thus, each individual in a population is a potential solution. During the generation phase, individuals are evaluated and reproduced according to their fitness values, and genetic operators are manipulated to produce a new population from the current population. The generation phase is repeated until a stopping criterion is met. The fitness function plays an important role in evolutionary computation algorithms. In this study, a fitness function is designed to give priority to the classification rate, reflecting the importance of correct diagnoses in medical applications. The proposed fitness function automatically determines the weights of objectives, which are adaptive to the length of the feature vector and the total number of samples involved in feature selection. Under the proposed fitness function, individuals with lower classification accuracy never achieve higher fitness values than individuals with higher accuracy. In most applications that adapt the SGLDM and multiresolution features, feature selection is applied on a single feature vector. Even if multiple feature vectors are available, feature selection is applied to each vector separately. Features extracted from the same pattern by different feature extraction methods may contain complementary information. Fusion technology can be used to combine information extracted from different feature vectors. Information fusion technology has developed rapidly in recent years. There are three types of fusion strategies [19], namely, data fusion, feature fusion, and decision fusion. Data fusion simply combines different domains of raw data to form a new raw dataset; decision fusion [20]–[22] combines multiple classifiers to provide a better result; and feature fusion [23]–[28] selects and combines features extracted from different domains to obtain a better feature subset. For a survey of decision fusion and feature fusion strategies for pattern classification, readers may refer to [29]. In this study, we extract five feature vectors from the region of interest (ROI) in ultrasonic liver images. The feature spaces include the SGLDM, multiresolution fractal feature vectors, and multiresolution energy feature vectors. We propose an evolution-based hierarchical feature fusion (HFF) method that selects the dominant features from multiple feature vectors. HFF is comprised of two levels: 1) feature selection in individual feature spaces and 2) feature selection in the fused feature space. In the first level, individual feature subsets are obtained by selecting features in each feature space. Next, in the second level, the individual feature subsets are combined to form the fused feature space. Then, features are selected from the fused feature space to compile a more discriminative feature subset that contains independent and discriminative features extracted from different feature spaces. Based on the above selection strategy, we develop two HFF schemes called PSO-based HFF (PSO-HFF) and GA-based HFF (GA-HFF). The remainder of this paper is organized as follows. In Section II, we introduce the methods used to extract features from ultrasonic liver images. We describe the proposed evolution-based HFF scheme in Section III, and present the experimental results in Section IV. Then, in Section V, we summarize our conclusions.

WU et al.: EVOLUTION-BASED HIERARCHICAL FEATURE FUSION FOR ULTRASONIC LIVER TISSUE CHARACTERIZATION

Fig. 1.

Feature extraction methods for different feature spaces.

II. FEATURE EXTRACTION The proposed approach extracts five feature vectors from each ultrasonic liver tissue pattern. Fig. 1 shows the feature extraction methods used for different feature spaces. The M -band wavelet transform and Gabor filters facilitate multiresolution analysis. Two texture descriptors are applied to the decomposed subimages to extract the following four multiresolution feature vectors: the fractal dimensions of the wavelet subimages (Wavelet-fd), the energy and energy deviation of the wavelet subimages (Wavelet-eng), the fractal dimensions of the Gabor subimages (Gabor-fd), and the energy and energy deviation of the Gabor subimages (Gabor-eng). The last feature space is the SGLDM. A. Multiresolution Feature Vectors Multiresolution analysis decomposes a signal into numerous details at various resolutions, each of which characterizes the distinct physical structure of the signal. The M -band wavelet transform and the Gabor filter bank are used to decompose the original image into subimages. Two descriptors, namely, the fractal dimension and the energy and energy deviation, are applied to two sets of subimages to extract four multiresolution feature vectors. 1) M -Band Wavelet Transform: Traditional multiresolution analysis uses a two-channel filter bank to decompose subimages recursively in the low frequency channel. However, significant texture information may also be found in the middle frequency channel, so just decomposing subimages in the lower frequency channel may not provide information that is sufficiently discriminative for classification [30]. Multiresolution analysis that is based on the M -band scaling function and wavelet function provides a more flexible tiling of the time-scale plane than two-band multiresolution analysis. For the background and implementation details of the M -band wavelet transform, readers may refer to [5]. 2) Gabor Filter Bank: It has been shown that the Gabor wavelets are optimal in the sense that they minimize the uncertainty in the space and frequency domains [31], [32]. The Gabor filters are self-similar, which means that all filters can be generated from one filter through dilation and rotation. Each filter is in the shape of plane waves with a frequency W , restricted by a

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Gaussian envelop function with relative widths σx and σy . The parameters of a Gabor filter are the central frequency W , the orientation θk , the number of levels, and the relative widths σx and σy of the Gaussian function. Extracting useful features from a signal normally requires a set of Gabor filters with different frequencies and orientations that cover the appropriate spatial frequency space. 3) Texture Feature Representation by the Fractal Model: If we regard the intensity of image pixels as their height above a plane, the intensity surface can be viewed as a rugged surface, and the fractal dimension can provide a quantitative measure of the roughness of an image. The box-counting approaches [33], [34] are popular for estimating the fractal dimension of images. Among the box-counting approaches, we utilize the revised differential box counting (DBC) method [35] because it covers a higher dynamic range and it can be computed efficiently. The revised DBC method is applied to decomposed subimages to extract a multiresolution fractal feature vector, which is defined as F Vfractal = (f0 , f1,1 , f1,2 , . . . , fm ,1 , . . . , fm ,i , . . .)

(1)

where f0 is the fractal dimension of original image and fm ,i denotes the fractal dimension of the ith subimage at level m. 4) Texture Feature Representation by Energy and Energy Deviation: The energy and energy deviation texture descriptor [12] is based on a filter bank approach. The descriptor comprises the first and second moments of energy in subimages, which are defined as H −1 W −1 1   |Ii,j (x, y)| W · H y =0 x=0   −1 −1 W   1 H = (|Ii,j (x, y)| − Ei,j )2 W · H y =0 x=0

Ei,j =

(2)

σi,j

(3)

where Ii,j (x, y) is the intensity of a filtered image of size W × H at level i in the orientation j. If S levels and K orientations are considered in the implementation, the corresponding feature vector can be derived as follows: F Venergy = (E0 , σ0 , E1,1 , σ1,1 , E1,2 , σ1,2 , . . . Ei,j , σi,j , . . . , ES,K , σS,K )

(4)

where E0 and σ0 represent the first and second moments of energy in the original image, respectively. B. SGLDM Suppose that an image to be analyzed is rectangular and that it has Rx resolution cells in the horizontal direction and Ry resolution cells in the vertical direction. Let Rg denote the number of distinct quantized gray levels in each resolution cell. There are eight nearest-neighbor resolution cells for each resolution cell, resulting in four angular spatial gray-level dependence matrices. Let I(i, j) be the SGLDM entry at gray levels i and j. Each (i, j)th entry of the matrix indicates the frequency that two gray levels i and j being neighbors under the given neighborhood definition. The following thirteen textural features are extracted

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IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS, VOL. 17, NO. 5, SEPTEMBER 2013

particles’ velocities and positions until a stopping criterion is met. Each particle i remembers its own best search position pBesti , and particles can share information with their neighbors. A particle knows the global best position, gBest, of all the members if we regard the whole population as its topological neighborhood. Each particle adjusts its trajectory based on the information about its own best position and the global best position. The velocities and positions of the particles are updated by the following equations: vik +1 = vik + ϕ1

(pBestki − xki ) (gBestk − xki ) + ϕ2 Δt Δt

(6)

xki +1 = xki + vik +1 Δt

(7)

and

where ϕ1 and ϕ2 are random variables with a uniform distribution in the range [0.0, 1.0], k and k + 1 represent the current iteration and the next iteration, respectively, and Δt is the time interval between successive iterations. Fig. 2.

Flowchart of the evolution-based hierarchical feature fusion scheme.

from each SGLDM: the angular second moment, contrast, correlation, variance, inverse difference moment, sum average, sum variance, sum entropy, entropy, difference variance, difference entropy, and two information measures of correlation. For each resolution cell, there are four angular spatial graylevel dependence matrices. In this study, we derive a set of four values for each of the 13 measures, resulting in a feature vector with 52 elements. The evolution-based algorithm is used to select the SGLDM feature subset for ultrasonic liver tissue characterization. The SGLDM feature vector is formulated as follows: F VSGLDM = (f1,1 , f1,2 , f1,3 , f1,4 , . . . , fn ,1 , fn ,2 , fn ,3 , fn ,4 . . . , f13,1 , f13,2 , f13,3 , f13,4 )

(5)

where fn ,1 , fn ,2 , fn ,3 , fn ,4 comprise the set of four values of the nth textural feature. III. EVOLUTION-BASED HIERARCHICAL FEATURE FUSION As mentioned earlier, the proposed two-level HFF system selects dominant discriminative features from multiple feature spaces. In the first-level, evolution-based feature selection is performed on individual feature spaces to obtain separate feature subsets. Then, in the second-level, the derived subsets are combined to form a fused feature space, and the above selection process is applied on the fused feature space to obtain the fused feature subset. The flowchart of the evolution-based HFF system is shown in Fig. 2. A. Particle Swarm Optimization A swarm contains a certain number of particles in the D-dimensional search space. Particles are initialized with random positions xi and velocities vi . For each position x in the search space, a fitness value is determined by the fitness function f (x). During the iterative process, the PSO updates the

B. PSO-Based Feature Selection In most cases, some of the features in a feature space are strongly correlated. Usually, it is not feasible to use all the features for classification because some of them have less discriminative ability and can be regarded as redundant. The objective of feature selection is to choose a subset of features in the original feature space, while maintaining the discriminative ability between classes. Generally, it is not known in advance which feature subset will provide the best discriminative ability between classes. As mentioned earlier, the selection of SGLDM features and multiresolution features is empirical in most approaches. For example, in [5], selection of the multiresolution fractal vector used for ultrasonic liver tissue characterization is based on observation of the Fourier spectrum and a predefined threshold value for the fractal dimension. The manual selection of the SGLDM feature is inconsistent in different applications. In contrast to manual feature selection, the proposed PSObased feature selection algorithm selects features objectively. The search space in binary feature selection problems is a Ddimensional state space, where the binary value of each dimension represents the decision of the corresponding feature. If a feature is to be selected, the corresponding bit value is set at 1; however, if the feature is to be discarded, the corresponding bit value is set at 0. PSO-based feature selection is implemented with a binary version of a PSO algorithm [36]. In binary PSO, particles move in a state space restricted to 0 and 1 on each dimension. The velocity of a particle is described by the number of bits changed per iteration. The velocity update equation of binary PSO is similar to that of continuous PSO, except that pBesti , gBest, and xi are binary strings whose length is equal to the dimension of the search space. The binary PSO velocity update equation becomes (pBestkid − xkid ) (gBestkd − xkid ) + ϕ2 (8) Δt Δt where d denotes the dth dimension, and Δt = 1. The velocity of each dimension is restricted to the interval [0.0, 1.0]. The k +1 k = vid + ϕ1 vid

WU et al.: EVOLUTION-BASED HIERARCHICAL FEATURE FUSION FOR ULTRASONIC LIVER TISSUE CHARACTERIZATION

position update rule of binary PSO is represented as follows:  xid = 1 if rand() < S(vid ) (9) xid = 0 otherwise where S() is a sigmoid limiting transformation, and rand() is a random number selected from a uniform distribution in the range [0.0, 1.0]. In the initialization stage, a population of n particles is generated randomly. Particles are initialized with random positions and velocities. Before the stopping criterion is met, particles update their positions and velocities based on their fitness values. The fitness value of a specific position is evaluated by the fitness function as follows: f (x) = CR(x) −

|x| Ntotal × D

(10)

where x is the specific position; CR(x) is the leave-one-out classification accuracy using the selected features, Ntotal denotes the total number of samples used for feature selection, and |x| is the cardinality of the feature subset. C. GA-Based Feature Selection The GA is a stochastic method that mimics natural evolution. It is similar to PSO in many respects. The basic iterative model of the GA is an evaluation-selection-reproduction loop. The population pool consists of a set of individuals, each of which is a potential solution. An individual can be represented by a chromosome, which is encoded as a binary string whose length is defined by the number of candidate features. The binary string can be viewed as a mask vector of the feature vector. Each bit of the string represents the decision of the corresponding feature. If a feature is to be selected, the corresponding bit of the binary string is set at 1; and if the feature is to be discarded, the corresponding bit is set at 0. In the population initialization stage, a population of n individuals is generated randomly. Given the population of the current generation, the next generation is produced by a threestage process: evaluation, selection and reproduction. In the evaluation stage, the fitness of each individual is determined by a fitness function. The individuals with higher fitness values will have a better chance of survival and reproduction. The fitness function of the GA is similar to (10) except that PSO evaluates the fitness value for a specific position x, while the GA evaluates the fitness value of each individual i in the population, 1 ≤ i ≤ n. In the selection process, we use the roulette wheel selection scheme to choose individuals for the mating pool. The probability of an individual i being selected is p(i) = f (i)/ N j =1 f (j). In the reproduction stage, genetic operators are manipulated to produce a new population (offspring) from the current population (parents). The genetic operators perform two operations: crossover and mutation. To retain the most suitable individuals, the first-half of the individuals are reserved as an elite group, and the remainder are regenerated by a two-point crossover operation. Two individuals in the mating pool are selected as parents, and they exchange substring information at a random

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section to generate two children. The crossover rate Pc controls the probability that the crossover operation will be applied to each couple. The crossover is invoked only when a randomly generated number between 0 and 1 is smaller than Pc . After crossover, the whole population is subjected to mutation. The objective is to prevent the evolutionary process from being trapped in a suboptimal solution. The mutation operator randomly flips some of the bits in the population. The mutation rate Pm gives the probability of each bit to be flipped. The GA stops when the number of generations reaches a predefined value. D. Fitness Function The fitness function is the objective function to be optimized. In this study, the fitness function is a popular form that maximizes the classification accuracy while minimizing the size of the feature subset. However, methodologies with empirically derived weightings of the objectives cannot guarantee that the selected feature subset will have the highest classification accuracy among all evaluated subsets. The proposed fitness function selects the feature subset with the minimum feature length from the group with the highest classification accuracy. In the training phase, the leave-one-out classification accuracy is represented as CR(x) = Ncorrect /Ntotal , where Ncorrect is the number of correctly classified samples. The proposed fitness function in (10) can be rewritten as Ncorrect |x| − Ntotal Ntotal × D 1 × (Ncorrect × D − |x|) = Ntotal × D 1 × g(x). = Ntotal × D

f (x) =

Hence, arg max f (x) = arg max g(x). x

x

Let Ncorrect = n, 0 ≤ n ≤ Ntotal , such that nD − D ≤ gn (x) ≤ nD − 1. If Ncorrect = n + 1, (n + 1)D − D ≤ gn +1 (x) ≤ (n + 1)D − 1. From the previous two inequalities, we get the inequality gn (x) ≤ nD − 1 < nD ≤ gn +1 (x), which implies that gn (x) < gn +1 (x). Since the lower bound of gn +1 (x) is greater than the upper bound of gn (x), the proposed fitness function guarantees that positions with higher classification accuracy are superior to positions with lower classification accuracy. In the candidate set of positions that achieve the same classification accuracy, positions with smaller |x| will have better fitness values. In summary, the proposed evolution-based feature selection algorithm searches for the solution that selects the fewest features from the set with the highest classification accuracy.

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E. Hierarchical Feature Fusion (HFF) Recall that the first stage of the HFF approach selects individual feature spaces. Let Fi be the feature vector extracted by the ith feature extraction method. After feature extraction, the vector {F1 , F2 , . . . , FM } is generated, where M is the total number of feature spaces. For the ith feature space, a corresponding binary feature mask, M aski , represents the best solution after feature selection. The masked feature vector F˜i can be computed by F˜i = M aski  Fi , where  denotes component-wise multiplication. If the best-fitting feature mask of the individual feature space is not unique, the best-fitting feature masks are combined to filter out the corresponding features. The second stage of the HFF system involves feature fusion and selection of the fused feature vector. Masked feature vectors of different feature spaces should be normalized before fusion. The fused feature space is the combination of the normalized feature subsets selected from individual feature spaces, i.e., Ffused = {F˜1 , F˜2 , . . . , F˜M }. The feature selection method is applied to Ffused to select the final feature subset. IV. EXPERIMENTAL RESULTS A. Experimental Setup 1) Dataset Description: The ultrasonic liver images used in this research were captured by a phased-array system (Aloka SSD-265) with a 3.5-MHz transducer, and scanned with 32-pixel/cm and 8-bit/pixel resolution. All images were standardized to the same mean intensity (i.e., 128) and verified by a specialist physician. The participating patients were given biopsies for pathological diagnosis to provide the ground truth. The ultrasonic liver image dataset contains 432 tissue patterns, which can be categorized into three classes: hepatoma (166 samples from 44 patients), cirrhosis (176 samples from 46 patients), and normal liver (90 samples from 23 patients). For each sample, a ROI of 64 × 64 pixels with 256 gray levels is chosen. The ROI only includes liver parenchyma, without major blood vessels, acoustic shadowing, or any type of distortion. In clinic, nodules less than 2 cm in diameter are difficult to characterize by radiological or pathological examination [37], [38]. As the ultrasonic liver images were scanned with 32-pixel/cm in our experiments, we set the ROI to 64 × 64 pixels, which is equal to 2 cm × 2 cm in physical size. The first row of Fig. 3 shows tissue patterns of hepatoma, cirrhosis, and normal liver. Since there exist no publicly available dataset for ultrasound liver images to serve as a standard training set, we split the samples in our dataset at subject level into two disjoint sets: 50% serve as the training set and 50% serve as the test set. These two sets were taken from separate patients. The training set contains 216 samples that came from 56 patients and the test set contains 216 samples that came from 57 patients. The feature selection and feature fusion algorithms are applied to the training set. Tests are performed on the test set to verify the robustness of the selected features. To reduce variability, three-fold cross validation is implemented on the test set ten times with different partitions. Ten random seeds are generated, each of them separates the test

Fig. 3. Original tissue patterns, Wavelet subimages and Gabor subimages for the three liver classes. (a)–(c) are the tissue patterns extracted by experienced clinicians for hepatoma, cirrhosis, and normal liver respectively, (d)–(f) are the subimages after first-level decomposition by the M -band wavelet transform for hepatoma, cirrhosis, and normal liver respectively, (g)–(i) are the subimages after second-level decomposition by the M -band wavelet transform for hepatoma, cirrhosis, and normal liver respectively, and (j)–(l) are the subimages after decomposition by the Gabor filter bank for hepatoma, cirrhosis, and normal liver, respectively. The subimages highlighted with red rectangles correspond to the features selected by the proposed approach.

set into three disjoint subsets. Each subset is used as a test set for a classifier trained on the remaining two subsets. Each three-fold cross validation produces 216 classification results (83 instances for hepatoma, 88 instances for cirrhosis, and 45 instances for normal liver). Thus, the total number of instances for hepatoma, cirrhosis, and normal liver are 830, 880, and 450 respectively. The overall classification accuracy is averaged over the ten rounds. 2) Feature Extraction: Five feature vectors are extracted for each tissue pattern. Four multiresolution feature vectors are extracted by the combination of multiresolution analysis and feature representation. From the viewpoint of discrete-time signal processing, an M-channel filter can be obtained by cascading smaller systems [39]. A mixture of two-channel and threechannel filter banks [5], [35] is applied to facilitate decomposition by the M -band wavelet transform. A tissue pattern is decomposed into 45 sub-images by the M -band wavelet transform. The Gabor filter bank is implemented with five radial

WU et al.: EVOLUTION-BASED HIERARCHICAL FEATURE FUSION FOR ULTRASONIC LIVER TISSUE CHARACTERIZATION

center frequencies and six orientations, generating 31 subimages each tissue √ √ pattern. √ The radial √ frequencies used are √ for 2/25 , 2/24 , 2/23 , 2/22 , and 2/2. The orientations used are 0◦ , 30◦ , 60◦ , 90◦ , 120◦ , and 150◦ . Fig. 3(d)– (f) shows the subimages after the first-level decomposition by the M -band wavelet transform; Fig. 3(g)–(i) shows the subimages after the second-level M -band wavelet decomposition; and Fig. 3(j)–(l) shows the subimages decomposed by the Gabor filter bank for the hepatoma, cirrhosis, and normal liver. The Wavelet-fd and Gabor-fd feature vectors are extracted by estimating the fractal dimensions of the wavelet subimages and the Gabor subimages; the Wavelet-eng feature vector is generated by calculating the energies of the wavelet subimages; and the Gabor-eng feature vector is generated by calculating the energies and energy deviations of the Gabor subimages. The SGLDM feature vector contains 52 elements, which are extracted by the four angular spatial gray-level dependence matrices of the 13 measures. 3) Feature Selection: Feature selection is essential in the HFF method. In this study, we utilize the PSO and GA for feature selection with the k-nearest neighbor (kNN) classifier. The PSObased feature selection is implemented based on Standard PSO 2007 (SPSO 07, [40]) with default parameters. The swarm size for PSO is set at 100, and the maximum number of evaluations is 20,000. An evaluation is a position update for a particle. For GA-based feature selection, the parameters are set as follows. Population size = 100 Number of generations = 200 Probability of crossover (Pc ) = 0.8 Probability of mutation (Pm ) = 0.01 4) Brief Introduction of the Compared Feature Fusion Algorithms: We compare the performance of HFF with that of two existing feature fusion schemes: the serial feature combination scheme and the serial feature fusion scheme [28]. a) Serial feature combination: Suppose A and B are two feature spaces defined on the pattern sample space Ω. For an arbitrary sample ζ ∈ Ω, the corresponding two feature vectors are α ∈ A and β ∈ B, where α is n-dimensional and β is mdimensional. The serial combined feature of ζ is defined by γ = α , where γ is a (n + m)-dimensional feature vector. All serial β combined feature vectors of pattern samples form a (n + m)dimensional serial combined feature space. In this study, the five individual feature spaces form a 235-dimensional serial combined feature space. b) Serial feature fusion: The serial feature fusion is a process of feature selection based on the serial feature combination method, and the resulting feature is called a serial fused feature. 5) Pattern Classifiers: There are four different classifiers adopted for performance comparisons in this study. We briefly review these four classification techniques. a) k-Nearest Neighbor (kNN) Classifier: In a kNN classifier, each class is represented by a set of prototype vectors. The k closest neighbors of a pattern vector are found from among all of the prototypes. Hence, the class label is determined by the  majority rule. Let the number of voting neighbors be k = i Ki , the classification rule assigns the test sample to the class that has the largest proportion ki /k. In this study, the value of k is set at 9.

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b) Fuzzy k-Nearest Neighbor (Fuzzy-kNN) Classifier: The fuzzy kNN classifier is defined as a function of the number of neighborhoods (k), class membership degrees, and distances between a pattern to be classified and patterns for which the class membership degrees were previously determined. A class membership degree between 0 and 1 is computed using the first minimum distances and the known class membership degrees of the patterns. In fuzzy-kNN classifier, we use nine nearest neighbors and 3.2 for fuzziness. c) Probabilistic Neural Network (PNN): Suppose there are k patterns, each of which is d-dimensional. The class number is c. The PNN consists of d input units comprising the input layer. Each input unit is connected to each of the k pattern units. Each pattern units are connected to one and only one of the c category units. The connection from the input to pattern units represent the weights to be trained. The network is trained by setting the weight vectors in one of the pattern units equal to each pattern in the training set. The trained network is then used for classification. A test pattern X is placed at the input units. Let Xk i , k = 1, 2, . . . Li be the sample pattern belonging to a class ci . The estimator of this class is

 Li  1 1 (X − Xk i )T (X − Xk i ) exp − fi (x) = Li (2π)N /2 σ N 2σ 2 k =1 (11) where Li is the total number of training patterns belonging to the class ci , Xk i is the kth training pattern from the class ci . The smoothing parameter σ is used to describe the sharpness of each sample pattern distribution, which was set at 0.05. For the background and implementation details of the PNN classifier, readers may refer to [41]. d) Support Vector Machine (SVM): The goal of SVM [42], [43] is to produce a model (based on the training data) which predicts the target values of the test data. In the training stage, SVM finds an maximum-margin hyperplane to separate the training data of different classes. The LIBSVM [44] library, which was a software implementation of SVM, was used in this study. In the SVM training stage, the radial basis function (RBF) kernel is adopted, the gamma of the kernel function γ is set at 12, and the tradeoff parameter C is 7. B. Results Table I shows the feature selection results of different feature spaces. The features of the fused feature subset distributed in the five feature spaces. The features selected by the PSO-HFF and GA-HFF for ultrasonic liver tissue characterization is listed in Table II. For the SGLDM feature space, the 18th feature represents the inverse difference moment calculated from the 45◦ angular SGLDM, and the 25th feature is the sum variance derived from the 0◦ angular SGLDM. For the multiresolution feature vectors, the subimages corresponding to the selected features are highlighted with red rectangles in Fig. 3. The first wavelet subimage is the original sample. The tenth wavelet subimage is distributed in the low frequency channel, and the 37th wavelet subimage is distributed in the middle frequency channel. These

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IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS, VOL. 17, NO. 5, SEPTEMBER 2013

TABLE I FEATURE SELECTION RESULTS OF DIFFERENT FEATURE SPACES

TABLE II LIST OF THE FEATURES SELECTED BY THE PSO-HFF AND GA-HFF FOR ULTRASONIC LIVER TISSUE CHARACTERIZATION

TABLE III TEST RESULTS FOR THE ULTRASONIC LIVER IMAGE DATABASE FOR EACH FEATURE SPACE (CLASSIFICATION ACCURACY, UNIT: %)

*The Fused feature space without feature selection is the 235-D serial combined feature space.

findings verify that the most significant texture information often appears in the middle frequency and low frequency channels. The information can be extracted by the M -band wavelet transform. In the Gabor-fd feature vector, the 1st, 15th, and 21st features are selected; and in the Gabor-eng feature vector, the 1st, 19th, 27th, and 53rd features are selected, which are the energies of the 1st, 10th, 14th, and 27th Gabor subimages, respectively. The first feature of the Gabor-fd is the fractal dimension generated from the original sample. It is identical to the first feature of Waveletfd. The 15th, 21st, and 27th Gabor subimages are extracted by the Gabor filter bank with θ = 30◦ and level = 3, 4, 5, respectively. The 10th Gabor subimage is extracted by the Gabor filter bank with θ = 60◦ and level = 2; the 14th Gabor subimage is extracted with θ = 0◦ and level = 3. Table III summarizes the classification results without feature selection. In terms of the fused feature space, the five individual feature spaces form a 235-D serial combined feature space, which is generated without feature selection. Then, we compare the performance of HFF with that of the serial feature combination scheme and the serial feature fusion scheme. Table IV shows the test results of the compared schemes. The accuracy of serial combined feature space is slightly higher than that of

individual feature spaces with the kNN, fuzzy-kNN, and SVM classifiers, which indicates that the various feature vectors contain complementary information. However, the serial combined feature space is a high dimensional feature space and contains some redundant information. The evolution-based feature selection scheme is applied to the serial combined feature space to extract the serial fused feature subset. The serial feature fusion scheme can select about 10% of the serial combined features, and the classification accuracy of the serial fused feature subset is generally higher than that of the serial combined feature space. Compared with the serial feature fusion scheme, HFF selects features with more discriminative ability for classification. The test accuracy of the HFF feature subset is superior to that of the serial feature fusion feature subset. The GA-HFF feature subset contains eight features distributed in the five feature spaces. Compared with the total number of features in the original five feature spaces, the feature reduction rate of GA-HFF is 96.6%. Classification algorithms are based on different theories; hence, their performance varies for different applications. However, the fused feature subset is robust for the four classifiers in this study. The accuracy of the fused feature subset reaches 95.05% when the simple kNN classifier is used. The accuracy is even higher under the PNN and SVM classifiers, which are relatively complicated classifiers. We observe that the accuracy of the fused feature subset is higher than that of the individual feature subsets. Thus, the concept of fusing complementary information from different feature spaces to obtain a better decision is proved. The confusion matrix of the PNN-classified test results with the fused feature subset obtained by PSO-HFF is shown in Table V. In the table, the columns show the correct results proven by biopsies and the rows show the classification results. The fused feature subset can be exploited for ultrasonic liver tissue characterization to avoid misclassification, especially false-negative misclassification. The false-negative rate is the probability of misclassification such that the patients are classified as normal or as having mild liver disease, but the actual diagnosis is more severe liver disease. A different trabecular pattern is the most common and characteristic form of hepatoma. The trabecular pattern of the hepatoma is typically wider and less regular than that of a normal liver; hence, the image of a liver with hepatoma is rougher than that of a normal liver. The major characteristic of cirrhosis is the hepatic fibrosis associated with developing or fully established nodules [45]. The nodules

WU et al.: EVOLUTION-BASED HIERARCHICAL FEATURE FUSION FOR ULTRASONIC LIVER TISSUE CHARACTERIZATION

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TABLE IV COMPARISON OF THE TEST RESULTS OF DIFFERENT FEATURE FUSION SCHEMES (CLASSIFICATION ACCURACY, UNIT: %)

TABLE V THE CONFUSION MATRIX OF THE TEST DATA CLASSIFIED BY THE PSO-SELECTED FUSED FEATURE SUBSET WITH THE PNN CLASSIFIER

rithms that facilitate the search process by sharing information among members of the population. The PSO and GA are similar in many respects, and both can be used in the proposed feature fusion system. A fitness function is designed to identify the feature subset with minimal feature length from the set with the highest classification accuracy. The PSO-based and GA-based feature selection algorithms utilize the fitness function to select dominant features and improve the classification accuracy, and thereby reduce the computational costs. Feature vectors extracted by different feature descriptors reflect different characteristics of the same pattern. HFF can select more discriminative features hierarchically from multiple feature vectors. Experiments on an ultrasonic liver image dataset demonstrate that classification accuracy of the fused feature subset is superior to that of the individual feature subsets. The results also verify that the proposed algorithm is effective in selecting discriminative features for ultrasonic liver tissue characterization. ACKNOWLEDGMENT

Fig. 4. Execution time of GA-based and PSO-based feature selection (of different feature spaces).

cause a block structure that makes the image of a cirrhotic liver rougher than the image of a normal liver, but not as rough as that of hepatoma. Images of the two liver diseases exhibit varying degrees of roughness. The hepatoma samples and the cirrhosis samples are never classified as normal if they are classified by the fused feature subset. The algorithms are implemented in MATLAB (7.8.0) R2009a environment on a PC with Intel Core 2 Quad processor (2.4 GHz), 6 GB RAM. Fig. 4 demonstrates the execution time of GA-based and PSO-based feature selection of different feature spaces. The execution time of PSO-based feature selection is about five times longer than that of GA-based algorithm. V. CONCLUSION We have proposed an evolution-based HFF system that selects dominant features from multiple feature vectors for ultrasonic liver tissue characterization. The five feature vectors extracted in this study are the Wavelet-fd, the Wavelet-eng, the Gabor-fd, the Gabor-eng, and the SGLDM. The feature selection process removes redundant features. In most approaches that use the above five feature vectors, the selection of feature subsets is empirical but inconsistent. We propose PSO-based and GA-based feature selection schemes, which select the feature subsets of individual feature vectors. Both schemes are population-based search algo-

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Cheng-Chi Wu received the B.S. degree in power mechanical engineering from National Tsing Hua University, Hsinchu, Taiwan, in 2003, where he is currently working toward the Ph.D. degree in electrical engineering. His research interests include medical image processing and computer graphics.

Wen-Li Lee received the Ph.D. degree in electric engineering from National Tsing Hua University, Hsinchu, Taiwan, in 2002. During 1988–2000, he was with the Chung-Shan Institute of Science and Technology, Ministry of National Defense of Taiwan to study digital image processing and pattern recognition. He is currently an Associate Professor at Ming Chuan University, Taoyuan, Taiwan . His research interests include medical image processing, soft computing, fractal geometry, and pattern recognition.

Yung-Chang Chen (F’05) photograph and biography not available at the time of publication.

Kai-Sheng Hsieh, photograph and biography not available at the time of publication.