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In this chapter, the discussion of our research is separated into two topics: boundary segmentation for ultrasonic thyroid nodules and breast tumor detection in 3D ultrasound imaging. For each topic, we will review related works and summarize the advantages and disadvantages. Then, we will introduce some of the methods related to our proposed methods.

2.1 Boundary segmentation for ultrasonic thyroid nodules

Various methods have been employed for computer-aided systems to automatically detect and identify the boundary of thyroid nodules on ultrasound images.

Tsantis et al. [9] proposed a hybrid multi-scale model which integrated the wavelet edge detection procedure and the Hough transform to extract the final contour of thyroid nodules in ultrasound images. This method was advantageous by combining the ability of wavelet transform to detect sharp variation and the efficiency of Hough transform to discriminate target from noisy background. Nevertheless, it also had several shortcomings that the delineation outcome was highly affected by human error, and the step of Hough transform was time-consuming. Besides, it required prior knowledge about the shape of nodule to be detected, which limited the value in practical use. Iakovidis et al.[10]

presented a segmentation framework applied on thyroid ultrasonography by incorporating a level set approach named Variable Background Active Contour model and a parameter tuning mechanism based on Genetic Algorithm to search for optimal parameters automatically. This GA-VBAC framework was relatively unaffected by intensity inhomogeneity in the thyroid ultrasound images. However, this method required huge amount of time in its training phase, which posed a major limitation. Maroulis et al.[11]

developed an algorithm of Variable Background Active Contour model based on the

Active Contour Without Edges model for the delineation of thyroid nodules in ultrasound images. This algorithm had the advantages of noise robustness, multiple nodules delineation capability, and the ability to cope with intensity inhomogeneity. One of the drawbacks of their proposed algorithm was that it could not delineate non-hypoechoic thyroid nodules. Savelonas et al. [12] presented a joint echogenicity–texture model based on a modified Mumford–Shah function that incorporated regional image intensity and statistical texture information. Their approach were capable of segmenting hypoechoic, isoechoic, and hyperechoic nodules. It required no prior assumption about the shape of nodule to be detected, and was noise-tolerant. Nevertheless, it also had some limitation that it might get confused by anatomical structures within nodules such as blood vessels.

Koundal et al.[14] proposed an automated delineation method that integrated spatial information with the Neutrosophic L-Means clustering and level-sets method for the segmentation of thyroid nodules in ultrasound images. This method first segmented possible target via Spatial Neutrosophic L-Means clustering, then applied Distance Regularizer Level Set Evolution method to delineate the nodule contour. It had benefits of noise robustness and multiple nodules delineation capability, and could handle intensity inhomogeneity as well. However, it had weakness in its ability to detect isoechoic thyroid nodules. Ma et al. [31] employed a deep convolutional neural network for thyroid nodule segmentation based on 2D ultrasound images. The convolutional neural network was fed with image patches from thyroid nodules and normal thyroid as input, then output the segmentation probability. This method could delineate thyroid nodules accurately and was capable of multiple nodules delineation. It was also noise-tolerant. Despite of these, this deep-learning based method showed unsatisfying performance while dealing with heterogeneous nodules or complicated background.

Chang et al. [32] developed a method to retrieve thyroid nodule contour on the basis of a

manual input contour. The manual input contour was then processed with Active Contour Method into a smooth thyroid nodule contour, and the sonographic features of the region enclosed by the contour were calculated.

In recent years, deep learning has gradually been discussed and valued in various field of applications. Among them convolutional neural network (CNN), such as Ma et al. [31]

used in their work, has gained the most attention. However, unlike traditional knowledge-based methods, the “black-box” nature of these CNN-knowledge-based system may lead to severe consequences and arouses incremental concerns recently. CNN requires huge amount of ground truth data for training, and we even do not know what it learns, how it learns, and where it errs.

The region of interest (ROI) delineation usually plays an important role in ultrasound image analysis. With ROI being delineated, the computation cost of ultrasound image analysis is greatly reduced, and the accuracy is improved. However, the delineation of ROI for ultrasound images is not always readily available in clinical settings. It adds an extra step beyond the standard operations of ultrasound imaging, and the ROI delineation step itself is error-prone if not performed by experienced operator. To take advantage of ROI delineation and simultaneously avoid its drawback, it is essential to incorporate the step of ROI delineation with the standard operation procedures of ultrasound examinations.

2.2 Breast tumor detection in 3D ultrasound imaging

Computer-aided detection system has been proposed to accelerate the reviewing process and to reduce the missing errors. Recently, the issue has received special attention and discussion in the 3D ultrasound images.

Ikedo et al. [33] proposed a fully automatic scheme based on the edge information

detected by Canny edge detector and further classified edges as near-vertical edges or near-horizontal edges by a morphological method. Initial tumor candidate regions were then generated by watershed algorithm and density information among the region with near-vertical edges. This method achieved sensitivity of 80.6% to detect breast tumor, but has difficulty in detecting flat-shaped tumors due to their short vertical dimensions.

Besides, it frequently misinterpreted fat and rib regions. Chang et al. [34] used the gray-level slicing method to segment images into numerous regions, and then seven quantitative features were extracted to further determine each region whether a part of tumor or not. Their proposed system achieved decent sensitivity of 92.3%, but had a long processing time. Besides, the case number in this study was small, which hampered the reliability of their conclusion. Moon et al. [35] developed a CADe system based on algorithm of Hessian analysis with multi-scale blob detection. Then three categories of quantitative features were extracted to estimate the tumor likelihood with a logistic regression model. Their proposed system could detect every tumor and achieved the sensitivity of 100%, but accompanied with a lot of erroneous detections. Besides, their study did not involve early-stage breast cancers, so the ability of detecting small malignant tumors was unknown. Tan et al. [36] presented a two-stage CADe system.

After landmarks such as nipple and chest wall were provided, tumor candidates were generated by using voxel features including coronal spiculation patterns, blobness, and contrast. The likelihood of malignancy was evaluated with an ensemble of five neural networks. A major shortcoming of their proposed system was that the maximal achievable sensitivity was suboptimal. Moon et al. [37] proposed a CADe system based on quantitative tissue clustering algorithm. The fuzzy c-means clustering was used to generate tumor candidates among the regions segmented by fast 3D mean shift method.

Seven quantitative features were used to estimate the likelihood of the candidates being

tumors. A limitation of their study was the high false positive rate, which could be a problem for clinical applications of CADe systems. Lo et al. [38] proposed a CADe system based on topographic watershed transform gathering similar tissues around local minima into homogeneous regions. The likelihood of region being tumor was determined with quantitative features of morphology, echogenicity, and texture. The proposed CADe system achieved the sensitivity of 100% with tolerable false positive rates. Besides, the processing time was satisfactory. There were some limitations in their study though. Their system might not perform well for all kinds of breast carcinomas. Furthermore, the data used in their study all came from a single medical center and might hinder the generalization of their system.

Utilizing deep learning, Chiang et al. [39] proposed a method based on 3D convolutional neural networks and prioritized candidate aggregation. Their proposed system first implemented a sliding window detector to extract volume of interest, which were then determined their tumor probability by 3D convolutional neural networks. Their proposed system was advantageous for its fast processing time. However, a major drawback of their proposed system was that it did not perform well at high sensitivities and produced a lot of false positives.

Decision tree learning is one of the predictive modelling approaches used in statistics, data mining, and machine learning. Among them, classification and regression tree (CART) [41] is one of the most well-known models. CART is constructed through a sequential binary classification, and its goal is to make the child nodes with a higher homogeneity. The first stage is to build a complete classification tree. At this stage, subjects are binary-classified over and over until classification is no longer possible. The method will search for the best feature and cut point in the parent node, and then use this feature and cut point to divide the parent node into two child nodes. If the number of

samples of the child node is too small or the child node has only one category left, then the classification will stop; otherwise, the classification will continue. A complete classification tree is established through the complete classification of training samples, but it usually leads to the problem of over-fitting. Therefore in the second stage, some branches of the complete classification tree need to be pruned to avoid over-fitting.

We construct our detection algorithm inspired by CART, to implement the free-of-parameters advantage thus ideal for our application to analyze huge amount of data contained within 3D ultrasound images.

Chapter 3 Variance-reduction methods for boundary

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