Computational and Mathematical Methods in Medicine

Volume 2015, Article ID 502573, 10 pages

http://dx.doi.org/10.1155/2015/502573

## Adaptive Ridge Point Refinement for Seeds Detection in X-Ray Coronary Angiogram

^{1}Key Laboratory of Photoelectronic Imaging Technology and System, Ministry of Education of China, School of Optics and Electronics, Beijing Institute of Technology, Beijing 100081, China^{2}Department of Biomedical Engineering, School of Medicine, Tsinghua University, Room C249, Beijing 100084, China

Received 28 August 2014; Revised 15 January 2015; Accepted 16 January 2015

Academic Editor: Yi Gao

Copyright © 2015 Ruoxiu Xiao 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

Seed point is prerequired condition for tracking based method for extracting centerline or vascular structures from the angiogram. In this paper, a novel seed point detection method for coronary artery segmentation is proposed. Vessels on the image are first enhanced according to the distribution of Hessian eigenvalue in multiscale space; consequently, centerlines of tubular vessels are also enhanced. Ridge point is extracted as candidate seed point, which is then refined according to its mathematical definition. The theoretical feasibility of this method is also proven. Finally, all the detected ridge points are checked using a self-adaptive threshold to improve the robustness of results. Clinical angiograms are used to evaluate the performance of the proposed algorithm, and the results show that the proposed algorithm can detect a large set of true seed points located on most branches of vessels. Compared with traditional seed point detection algorithms, the proposed method can detect a larger number of seed points with higher precision. Considering that the proposed method can achieve accurate seed detection without any human interaction, it can be utilized for several clinical applications, such as vessel segmentation, centerline extraction, and topological identification.

#### 1. Introduction

Currently, vascular diseases are major threats to human health. Although a variety of imaging technologies exist, such as computed tomography angiography (CTA), magnetic resonance angiography (MRA), and ultrasound (US), X-ray angiography remains the gold standard for the interventional treatment of coronary artery diseases because of its high resolution and imaging speed. Foreshortening and overlapping are the major obstacles for the accurate identification of vascular structures because X-ray angiography is an integrated projection of the whole body in 3D space to 2D images. Vascular extraction technology aims to calculate the centerline, diameter, and direction vector of the vascular structure from X-ray angiograms; hence, it can provide the necessary reference for computer-aided diagnosis and treatment of vascular diseases.

To date, the widely used vascular extraction method in clinical practices is still the manual delineation method, which is very time-consuming and subjective. As its important clinical value, automatic vascular tree extraction method has been studied intensively in the past two decades, such are morphology based methods [1, 2], multiscale based methods [3, 4], edge detection based methods, and image registration based methods [5–7]. Among all methods, the tracking based methods propose to estimate centerline and diameter within the vascular boundaries, which do not need to scan the whole angiogram. Hence, the tracking based methods are usually with higher calculation efficiency than the other methods.

Generally, the tracking procedure proceeds from one or several manually delineated seed points. As the seed points are randomly selected from the angiogram, the reproducibility of the tracking algorithms are very much depended on the personal experience. Many researchers hence focus on improving the robustness of the tracking algorithm through seed optimization. Collorec and Coatrieux [8] detected seed points by scanning local extreme points and obtained a large set of seed points inside the vessels. However, extracted seed points need to be refined because of the presence of noise. While Fritzsche et al. [9] combined the global threshold optimization for improving the robustness of the seed extraction, the global threshold may also lead to a large amount of false seed points in the background. Moreover, Boroujeni et al. [10] proposed an automatic seed point detection method by detecting edge points and checking the symmetric features in its neighboring regions. After all the boundaries are detected, the center line seed points can be calculated at the symmetric center of the edge points. All the above methods have greatly promoted the automatic seed detection methods.

In this paper, a novel adaptive ridge point refinement method is proposed for seed detection in coronary angiograms. First, based on the tubular feature distribution of Hessian matrix of the angiogram, vascular structures are enhanced according to the eigenvalue distribution in multiscale space. Second, the continuity property of eigenvalue and eigenvector of a Hessian matrix in multiscale space is theoretically analyzed. Third, based on theoretical analysis, the proposed theorem of ridge point existence is utilized to design the ridge discriminant function. And the candidate ridge points are extracted according to the predefined discriminant function. Afterwards, the detected points are refined according to a self-adaptive threshold that is calculated based on the order statistics of the detected ridge points.

#### 2. Method

##### 2.1. Characteristic of Ideal Vascular Topology

Let represent the intensity of a point in the image; then, the intensity distribution of the local feature around can be calculated as follows [11]:where is the gradient of the image at the point with respect to the -axis and -axis, while and are the first-order partial derivatives of in the directions of and , respectively. And the Hessian matrix of point can be calculated as follows:where and denote the second partial differential of in the direction of and , respectively, while and denote the second partial differential of . If the second-order differential of is continuous, then we have . Through singular value decomposition (SVD) decomposition, two eigenvalues and (suppose ) and their corresponding eigenvectors and can be obtained from the Hessian matrix of each pixel of the angiogram. To be convenient for the followed analysis, in this study, and are named as the first eigenvalue and second eigenvalue of , and and are denoted by first eigenvector and second eigenvector of , separately.

Ideally, due to its tubular structure, the penetrating path of X-ray in the blood vessel decreases from the central axis to edge position. Therefore, the gray level distribution of the vessel in angiogram turns from dark to bright for its centerline to the edge [12]. If we look at the grey scale distribution of the blood vessel, the centerlines are rested on the ridge lines constituted by a series of ridge points. Generally, the ridge point is the local extreme with the direction vector perpendicular to the vascular direction on angiogram. Therefore, for the coronary artery in angiogram, we have the following equation [13]:According to the definition of the ridge, the two eigenvectors of Hessian matrix can be denoted by the tangent direction () and the vertical direction (), as can be seen in Figure 1.