BioMed Research International

Volume 2018, Article ID 3636180, 12 pages

https://doi.org/10.1155/2018/3636180

## Axis-Guided Vessel Segmentation Using a Self-Constructing Cascade-AdaBoost-SVM Classifier

^{1}School of Computer Science and Technology, Harbin Institute of Technology at Weihai, Weihai 264209, China^{2}School of Computer Science and Technology, Harbin Institute of Technology, Harbin 150001, China^{3}Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, China

Correspondence should be addressed to Xin Hu; nc.ude.tih@nixuhtih and Yuanzhi Cheng; nc.ude.hwtih@gnehczy

Received 24 November 2017; Revised 4 February 2018; Accepted 13 February 2018; Published 19 March 2018

Academic Editor: Jiang Du

Copyright © 2018 Xin Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

One major limiting factor that prevents the accurate delineation of vessel boundaries has been the presence of blurred boundaries and vessel-like structures. Overcoming this limitation is exactly what we are concerned about in this paper. We describe a very different segmentation method based on a cascade-AdaBoost-SVM classifier. This classifier works with a vessel axis + cross-section model, which constrains the classifier around the vessel. This has the potential to be both physiologically accurate and computationally effective. To further increase the segmentation accuracy, we organize the AdaBoost classifiers and the Support Vector Machine (SVM) classifiers in a cascade way. And we substitute the AdaBoost classifier with the SVM classifier under special circumstances to overcome the overfitting issue of the AdaBoost classifier. The performance of our method is evaluated on synthetic complex-structured datasets, where we obtain high overlap ratios, around 91%. We also validate the proposed method on one challenging case, segmentation of carotid arteries over real clinical datasets. The performance of our method is promising, since our method yields better results than two state-of-the-art methods on both synthetic datasets and real clinical datasets.

#### 1. Introduction

Automatic vessel segmentation in three-dimensional (3D) medical computed tomography (CT) images plays an important role in study of anatomical structure [1], in clinical diagnosis during quantification of vascular disease (tortuosity, stenosis, and calcification) [2], in vascular surgery planning [3], and in patient-specific flow simulations [1]. Vessel segmentation can help clinical workers to establish the patients’ response to treatment and to determine the stage of diseases. Such applications require a competent segmentation techniques, which result in accurate segmentations not only with normal vessels but also with the presence of pathologies.

Previous work on vessel segmentation can be roughly classified into three categories. They are (a) feature-based segmentation approaches [4, 5]; (b) tracking-based segmentation approaches [6–8]; and (c) model-based approaches [9–12]. Within the previous studies, the feature-based approaches have be proven to be efficient in detecting vessels at different scales. These approaches assume that vessels have identifiable curvilinear structures [5, 13–18]. Targeting curvilinear structures, they have several common detection procedures: firstly, the eigenvalues of the Hessian matrix at each voxel are calculated at multiple scales, by convolving with 3D Gaussian filters. Then, a response function is constructed by using these eigenvalues, which can determine the shape of the local structures at a certain scale. Since vessel has curvilinear structure, we can recognize it from several nonvessel structures (planar structure, blob, noise, or no structure). The response consisting of eigenvalues can represent the local structure when it comes to its maximum over different scales. Targeting linear structure, the local maxima of the response can be used to extract vessels [5, 16]. Although these procedures output responses instead of a direct vessel segmentation, they have further advantages in structure analysis by combining Skeleton-based methods [19, 20], which resolve subsequent two-dimensional (2D) slices of vessels using tubular shape priors for ridge detection. Recently, another tracking methodology was proposed by Tyrrell et al. [21], combining 3D cylindroidal superellipsoids and local regional statistics to extract topological information from microvasculature networks. These methods are shown to be robust against noise. However, the parametrical shape priors they expect are too exclusive, which will not work with complex vessel boundaries. Another series of research works use statistical mixture model coupled with expectation-maximization algorithm including [22–24]. Since these algorithms are histogram-based, they ask for an accurate parametrical estimation or nonparametric modeling which involves density functions. They all rely on the second-order derivative information (principal curvatures of image intensities). As a result, they may suffer from sensitivity due to local deformations (e.g., blurred boundary and stenoses).

Although various sophisticated vascular segmentation algorithms have been developed in the past decade, they are still facing several challenges, such as distinguishing vessels from nonvessels with the obstruction caused by conglutination tissues, segmenting different sizes of vessels especially diseased vessels with the presence of pathologies (such as severe stenoses). These challenges can result in false detections and missed detections. Several good reviews have been published in [1–3].

Addressing the challenges proposed, we combine the vessel-specific features and embed redundancy in the feature set deliberately, to cover the widest possible spectrum of situations. We argue that the shape complexity of vessel (e.g., blurred boundary and diseased vessels) cannot be captured by a single feature. However, building an optimal feature set with strong a priori knowledge and discriminative ability involves heuristically choosing features and parameters. Thus, we propose a novel cascade-AdaBoost-SVM approach to build a feature set automatically. The AdaBoost classifier is a linear combination of multiple weak classifiers [25], in which each weak classifier only focuses and classifies one of the input features. By adding new weak classifiers in the training process, the accuracy of the AdaBoost classifier can be gradually increased. Therefore, the optimal feature set can be selected automatically along with the weak classifiers. Moreover, organizing the AdaBoost classifiers in a cascade way can help the AdaBoost classifier focus on identifying vessels from vessel-like structures. And combining the SVM classifier can make the cascade-AdaBoost classifier avoid the overfitting issue.

This paper is organized as follows. Section 2 introduces the cascade-AdaBoost-SVM classifier. In Section 2, Section 2.1 details the feature set adopted. This cascade-AdaBoost-SVM classifier works on cross-sections based on a vessel axis + cross-section model, which is given in Section 2.2. We then introduce the training samples for the proposed algorithm in Section 2.3. The details of self-constructing cascade-AdaBoost-SVM classifier are presented in Section 2.4. The dataset, the evaluation methods, and the experimental results are shown in Section 3. Finally, we discuss the results and draw conclusion in Section 4.

#### 2. Method

This paper describes a vessel axis + cross-section model for carotid artery, which utilizes a self-constructing classification algorithm. First, we extract vessel axis from a gray-scale 3D angiogram, by using our previous method [9]. Along this extracted vessel axis, the vessel axis + cross-section model is constructed on the cross-section. Subsequently, a feature set for the self-constructing classification algorithm is presented, followed by a review of the AdaBoost machine learning algorithm. Finally, we introduce the self-constructing cascade-AdaBoost-SVM classifier.

##### 2.1. Feature Set for Classification Algorithm

On CT images, the vessel intensity may vary within a relatively wide range, due to blood flow rate and vessel dimensions. Vessels with various diameters can be regarded as 3D line structures. Therefore, the feature set was selected to enable detection of various line structures and sizes for vessels. The eigenvalues of the Hessian matrix are used to calculate the gradient based shape features. A multiscale approach is used to improve the detection of various size line structures.

Let be the Hessian matrix of a 3D image about an arbitrary point , and the eigenvalue vector with be the eigenvalues of with corresponding eigenvectors given by , , and , respectively. Using the matrix of the eigenvectors, we have

Equation (1) describes the second-order structure of local intensity variations around each point of extracted by the matrix , and the local second-order features of obtained by the eigenvalues (, , and ).

The profile of a line structure on the cross-section can be supposed to have a 2D Gaussian shape:where is an arbitrary point on the cross-section centered at an axis point ; the standard deviation is related to the scale of line structures; , where is the coordinate of point in 3D; is a rotation matrix. This cross-section at the axis point can be determined by using the corresponding eigenvectors , , and . The eigenvectors point out singular directions: indicates the direction along the vessel, which is normal to the cross-section plane, while and form a base for the cross-section plane [14].

The 2D Gaussian shape (see (2)) is a mathematical line model for the vessels, while the Hessian matrix (see (1)) is used to extract local shape features. Combining these two equations (see (1) and (2)), researchers derive measures of similarity between vessels and the line structure [5, 14, 26–28]. The similarity measures can be considered as vessel-specific features. The scales used for this Gaussian shape in this study, , correspond to the sizes of the line structures (vessels), which are 0.7, 1.0, 1.6, 2.4 3.5, and 6.0 mm. These scales allow both large and small line structures to be detected. However, at small scales, the boundary of large line structures may not be accurately captured due to noise and small inhomogeneities in the structure. On the other hand, at large scales, the shape of small line structures may be distorted as neighboring structures. This is the reason we combine multiple vessel-specific features, which embed shape and scale redundancy, to cover the widest possible spectrum of situations. In the following, we describe the multiple vessel-specific features in the feature set.

*(**1) Sato Feature (**) [5]*. This measure is suitable for images, where vessels are with bright tubular structures in a dark environment. For each scale, , the Sato vesselness measure, , is given bywhere and are the eigenvalues of defined in (1). and are two preset parameters, . and were fixed to 0.5 and 2, respectively.

*(**2) Frangi Feature ** [14]*. This measure is a nonlinear combination of the eigenvalues of the Hessian matrix that promotes the enhancement of line structures, while noise and non-line-like structures are smoothed out. At a single scale, , the Frangi vessel-dedicated feature, , is given as follows:where (subject to ) discriminates plate-like structures from line-like structures, (subject to ) discriminates blob-like structures from line-like structures, and (subject to ) eliminates background noise. We set , in this study. And is equal to half of the maximum Frobenius norm of the Hessian over all Frobenius norms computed on the whole image.

*(**3) Shikata Feature ** [26]*. This model assumes that the vessel has a cylindrical shape with 2D Gaussian intensity distribution on its cross-section. This assumption meets our application, which is a vessel axis + cross-section model-based approach. Moreover, this model is able to enhance the small vessels. This Shikata tubular feature, , is defined as follows:where is the intensity at point defined in (1).

*(**4) Li Feature ** [27]*. This model is a selective enhancement, which uses curvature analysis to identify structures with specific shapes. Due to this unique selective characteristic, Li feature can be potentially useful to distinguish tubular objects from other structures. This Li tube-specific feature, , is given as follows:

*(5) Manniesing Feature ** [28]*. Manniesing et al. improve Frangi’s method [14] by applying a nonlinear anisotropic Hessian-based diffusion along the local line directions. Due to the steering of diffusion, this model has strong isotropic diffusion to reduce background noise. This diffusion feature, , is defined as follows:where , , , , , and are defined in (4); is the smoothness constant of the vesselness function. By following Manniesing et al. [28], the smoothed vessel filter has parameters: , , and .

##### 2.2. Vessel Axis + Cross-Section Model

In our previous method [9], vessel axes are detected in three stages. Firstly, vessel regions are enhanced and extracted by applying multiscale filtering method based on Hessian matrix. Since the extracted vessel regions are not very accurate, these regions are used as masks for vessel axis points detection subsequently. Finally, tracking and connecting the axis points at multiple scales reconstruct continuous axes and their branching structures.

Figure 1 shows the cross-section model on a cross-section orthogonal to the vessel axis. As we discussed previously, the cross-sections can be determined by using the eigenvectors of axis points. Assume that the profile on this cross-section is not perfectly round; 72 rays are spaced every 5° from the axis point on the cross-section. Along these rays, we collect training samples or detect vessel boundaries.