## 1 Introduction  
Liver diseases are among the most life-threatening diseases worldwide. Among the different kinds of liver lesions, liver cancer has a high incidence rate and high mortality rate in the countries of East Asia, Southeast Asia, sub-Saharan Africa, and Melanesia [1]. Liver abscess is less common than liver cancer. However, if it is not detected in time and treated in the proper manner, it may cause many serious infectious complications, even death. Liver biopsy is often used to evaluate liver diseases. It permits doctors to examine a liver and provides helpful information to make high-accuracy predictions. Along with those undeniable benefits, it may cause pain, infection or other injuries that hinder later treatments. To reduce the unnecessary number of biopsy cases, other noninvasive methods for diagnosis have been applied widely, especially imaging techniques such as ultrasound (US) (e.g., see [2; 3; 4; 5; 6; 7; 8; 9]), computedtomography (CT) (e.g., see [4; 10; 11; 12; 13; 14; 15]) or magnetic resonance imaging (MRI) (e.g., see [2; 3; 12; 16]). Among those methods, ultrasound imaging, with unique advances advantages such as no radiation, low cost, easy operation, and noninvasiveness, is widely used to visualize the liver for clinical diagnoses. Therefore, it could provide visual information for doctors to identify the state of disease. Nevertheless, the diagnoses are significantly affected by the quality of ultrasound images as well as the doctors' knowledge and experience. For inexperienced clinicians, it may be not easy to distinguish between liver cancers and liver abscess. To overcome the obstacles mentioned above, it would be helpful to develop a computer-aided diagnosis (CAD) system (e.g., see [15; 17; 18]). By using image processing and machine learning techniques, a well-built system could help clinicians effectively and objectively distinguish liver diseases. Multiple scientists have studied the classification of liver diseases based on ultrasound images. For example, [PERSON] et al. first exploited textural features to discriminate between liver and spleen of normal humans [19]. [PERSON] and [PERSON] utilized [PERSON] five-by-five feature mask and then applied a probabilistic relaxation algorithm to the segmentation [20]. Many textural features were used by [PERSON] et al. for quantitative characterization of ultrasonic images [21]. [PERSON] et al. used the random field model to distinguish the four states of the liver [22]. The models proposed by [PERSON] et al. and [PERSON] et al. combined neural networks and discriminant analysis to separate the different liver disease [23; 24]. [PERSON] et al. improved their model by using fuzzy neural networks to process the features [25]. [PERSON] et al. evaluated the efficiency of the textural spectrum, the fractal dimension, the textural feature coding method, and the gray-level co-occurrence matrix in distinguishing cirrhosis, normal samples, and hepatitis [26]. [PERSON] et al. developed an algorithm for classifying cirrhotic and noncirrhotic liver with the spleen-referenced approach [27]. As mentioned above, analyzing and classifying images presenting organ lesions to differentiate benign and malignant lesions is a goal shared by many researchers. There are still few clinically relevant studies on ultrasound imaging to explore the CAD-based differential diagnosis of hepatocellular carcinoma and liver abscess, even though many studies have analyzed the characteristics of hepatocellular carcinoma (HCC) (e.g., see [28; 29]) or liver abscess (e.g., see [30; 31]). Recently, many methods have been proposed to extract the features from ultrasound images. For instance, first- and second-order statistics have been used (e.g., see [32]). Other approaches based on wavelet transform (e.g., see [33]), Gabor filter (e.g., see [34]), monogenic decomposition (e.g., see [35]), or fractal analysis (e.g., see [36]) were also proposed. A CAD system to distinguish between liver cancer and liver abscess has not been discussed.