Jingjing Deng

Perumal Nithiarasu

Xianghua Xie

Cronfa at Swansea University

 Cronfa -  Swansea University Open Access Repository   _____________________________________________________________   This is an author produced version of a paper published in : International Conference on Computational and Mathematical Biomedical Engineering                                                                                Cronfa URL for this paper:http://cronfa.swan.ac.uk/Record/cronfa20971_____________________________________________________________ Conference contribution :Chen, D., Deng, J., Xie, X., Nithiarasu, P. & Smith, D. (2013).  Efficient reconstruction of coronary vessels from 2Dangiography. International Conference on Computational and Mathematical Biomedical Engineering,         _____________________________________________________________  This article is brought to you by Swansea University. Any person downloading material is agreeing to abide by theterms of the repository licence. Authors are personally responsible for adhering to publisher restrictions or conditions.When uploading content they are required to comply with their publisher agreement and the SHERPA RoMEOdatabase to judge whether or not it is copyright safe to add this version of the paper to this repository. http://www.swansea.ac.uk/iss/researchsupport/cronfa-support/  3rd International Conference on Computational and Mathematical Biomedical Engineering - CMBE201316-18 December 2013, Hong-KongP. Nithiarasu and R. Lo¨hner (Eds.)Efficient Reconstruction of Coronary Vessels from 2D AngiographyDongbin Chen?, Jingjing Deng?, Xianghua Xie?, Perumal Nithiarasu??, and Dave Smith????Department of Computer Science, Swansea University, United Kingdom??College of Engineering, Swansea University, United Kingdom???Cardiac Unit, Morriston Hospital, Swansea, United KingdomSUMMARYThe recovery of three-dimensional (3D) object information from biplane CT angiographic imagesis still a challenge in application of modelling coronary vessel trees. The proposed method of 3Dreconstruction is obtained from the two-dimensional (2D) corresponding feature points by usingtriangulation projection based on the rotated mechanical angles of the CT angiographic machine.Those 2D feature points are on the centrelines of vessels. This research also includes how toextract the interested coronary vessels from CT angiographic images and how to represent thosevessels as a group of connected 2D points that are on centrelines of them. One of the contributionsin the paper is that we developed automatic searching algorithm to obtain the 2D correspondingpoints from a pair of biplane skeleton images under the two constraints of epipolar lines andcorresponding bifurcations. We apply the Lucas-Kanade optical flow algorithm to register thecorresponding bifurcations from an image sequence for the application of the proposed searchingalgorithm. The 3D reconstruction applies the readings of rotated mechanical angles and isocentreof the CT angiographic machine (Siemens Axiom) to establish the biplane image relationships ofrotation and translation, and then projects the 2D centrelines of coronary vessels onto 3D worldcoordinates. Another contribution of the paper is that we apply the back projection algorithm toproject the 3D points onto 2D image planes for evaluating the accuracy of the 3D reconstruction.The proposed method has been tested on patient data.Key Words: 3D reconstruction, biplane angiographic image, coronary vessel.1 INTRODUCTIONCoronary vessel disease is one of the main causes of death in the world. The technique of coronaryangiography is the conventional method to diagnose coronary disease. The research on 3D mod-elling of coronary vessels from CT biplane angiographic images has been carried out for manyyears, e.g. [5, 6, 4]. Many researchers have developed different methods to establish accurate3D model of coronary vessels from biplane CT angiographic images, e.g. [3, 11]. However, therecovery of 3D object information from biplane CT angiographic images is still a challenge inapplication to 3D modelling coronary vessels. The main task of 3D reconstruction from biplaneangiographic images is to produce a 3Dmodel of coronary vessels with accurate geometrical infor-mation. The centrelines of coronary vessels used to reconstruct 3D model are helpful in accurateestimation of geometrical information of the coronary vessels since they can reduce the error of 3Dreconstruction which may be caused by, for instance, the deformation of coronary vessels alongthe cardiac cycle [11]. Skeleton image algorithms can be used to extract the centrelines of vessels[1]. A medial axis extraction algorithm [10] has also shown to be useful to produce centrelinesof coronary vessels from the vessel segmentation results since it is effective to identify clearly themedial axis of vessels without complex pruning processes.Figure 1: The procedure of the proposed 3D reconstruction.In this paper, we present a method of 3D reconstruction based on triangulation projection, com-bined with output from the mechanical rotations and imaging information of the CT machine.One of the contributions in the paper is the development of an automatic searching algorithm thatcan find the corresponding points from a pair of biplane skeleton images based on the constraintsof epipolar lines and two neighbour bifurcations. Anther contribution is that we use the Lucas-Kanade optical flow algorithm to search the corresponding bifurcations from an image sequencefor the application of the proposed searching algorithm. Moreover, a new procedure of morpho-logical operations was designed for the application. We developed the back projection algorithmfrom 3D to 2D for evaluating the accuracy of the proposed 3D reconstruction.2 IMAGING INFORMATIONA Siemens Axiom CT biplane angiographic machine was used to capture the patient data. Thegantry motions are characterised by the angle values of CRA/CAU (Cranial/Caudal) and LAO/RAO(Left/Right Anterior Oblique). Each pair of biplane images has the fixed cardiac phase in a pairof angiographic sequences. The corresponding image distance (SD) between the x-ray source andthe image intensifier, patient distance (SP) between the X-ray and the patient position, field ofview (FOV) and two gantry orientations were automatically recorded and stored with each imagefile. All of the captured sequences have the imaging resolution of 512512 pixels with the pixelsize of 0.27799 mm.3 CENTRELINE EXTRACTIONThe whole procedure of 3D reconstruction is illustrated in Figure 1. A number of low levelimage processing algorithms are involved, including anisotropic diffusion, improved local adap-tive thresholding algorithm, morphological process, and medial axis extraction. First we applyanisotropic diffusion to remove image noise. This selected approach [9] is a modification ofthe linear diffusion. We apply four neighbour directions (up, down, left and right) to calculatethe anisotropic diffusion of angiographic images. Next, we segment the images based on localadaptive thresholding. This algorithm produces good segmentation for images with uneven il-lumination distribution. The thresholding algorithm in [2] uses the local mean and the standarddeviation of each pixel to compute local threshold. We add local curvature measurement as an-other constraint to compute the local threshold. Noise in images is assumed to correspond to highcurvature. We also remove redundant boundaries at the beginning of calculation as prior knowl-edge. The, morphological operations are carried out to connect the segments. We apply the dilateoperation five times with the 33 window first and then use erosion operation three times withthe same window size. Finally, we apply close operation two times with the same window size.This morphology procedure not only connects some broken segment areas but also removes smallsegment areas. The centrelines of vessels are then obtained by using the medial axis extractionalgorithm detailed in [10]. In the stage, we not only remove redundant pixels from the segmentresult but also produce a clean and complete vascular tree for 3D reconstruction. The Figure 2(b)shows an example of the skeletons of vessels resulted from the medial axis extraction.Figure 2: (a) the original image; (b) the skeleton result; (c) and (d) a pair of segmentation resultsthat are labelled the corresponding epipolar lines and bifurcations.Figure 3: (a) the biplane coordinate; (b) the 3D reconstruction on a view angle.4 3D RECONSTRUCTIONHere, present an algorithm for searching corresponding points from a pair of biplane skeletonimages. We use epipolar lines and two-neighbour bifurcations as the searching constraints. Weselected bifurcations manually on the first pair of biplane images. We then applied the Lucas-Kanade optical flow algorithm [8] to determine those bifurcations on their neighbour frames fromthe biplane sequences. After obtaining those bifurcations from a pair of biplane images, we usethe eight-point algorithm [7] to calculate the fundamental matrix of the pair of images. The fun-damental matrix is applied to produce epipolar lines on the pair of images. Under the above twoconstraints, the proposed searching algorithm can find the corresponding points robustly from apair of biplane skeleton images. Figures 2(c) and 2(d) shows a pair of segmentation results thatare labelled with the corresponding epipolar lines and bifurcations.For reconstructing the centrelines in 3D, we utilise the triangulation projection algorithm, which isbased on the output from the CT angiographic machine. First, we define the 3D coordinate in worldspace to be P = [X;Y; Z; 1] and its corresponding image coordinates to be p1;2 = [u1;2; v1;2; 1],which denotes CRA/CAU view and RAO/LAO view respectively. Second, we use the cone cameramodel and define the camera matrix, A1 and A2, relating to the biplane images respectively as,A =24SD 0 Cx0 SD Cy0 0 135 where SD is the distance from X-ray source to image intensifier,and (Cx, Cy) denote the principal point of the camera, which can be computed through eithercamera calibration or the imaging centre point as the estimated value. We obtain the image scalars,defined as S1 and S2, the ratio between SP and SD from the corresponding image files. Fromthe perspective projection and the linear transformation from 3D world coordinate system to 3Dcamera coordinate system. They can be formulated as follows:S1  [u1; v1; 1]T = A1  [R1jT1] [X;Y; Z; 1]TS2  [u2; v2; 1]T = A2  [R2jT2] [X;Y; Z; 1]T(1)where the matrices [RjT ] are established by the rotation matrix and translation vector of CRA/CAUview and RAO/LAO view respectively. That is, we use the readings of the gantry rotations of theCT machine to compute [RjT ]2, which is corresponding to [RjT ]1 as the original orientation andthe original point of the world coordinate. We define (1, 1) and (2, 2) to denote the readingsof LAO/RAO, and CRAN/CAUD gantrys rotations respectively. The solutions of rotation matrixR2 and translation T2 vector in the equation (2) can be derived byR2 = Rx(2)Ry(2)Ry(1)Rx(1)T2 = R2  [0; 0; Iso]T + [0; 0; Iso]T(2)where Iso denotes the isocentre distance of the gantry system obtained from the CT machinesspecification, andRx andRy in a right-hand coordinate shown on the Figure 3(a) can be describedbelow:Rx() =241 0 00 cos  sin0 sin cos35 Ry() =24cos 0  sin0 1 0sin 0 cos35 (3)Linear triangulation method is used:(ai1   ui  ai3)T Ri(ai2   vi  ai3)T Ri P T =(ui  ai3   ai1)T  Ti(vi  ai3   ai2)T  Ti(4)where the aij is the jth row of the camera matrix Ai. An example result is shown in Figure 3. Weapplied the back projection algorithm from 3D to 2D to test the accuracy of the 3D reconstruction.We obtained the average error of 4.169 pixels for the example shown here.REFERENCES[1] Bernard, T., Manzanera, A.: Improved low complexity fully parallel thinning algorithm. In: ImageAnalysis and Processing. pp. 215–220 (1999)[2] Bradley, D., Roth, G.: Adaptive thresholding using the integral image. Journal of Graphics, GPU, andGame Tools 12(2), 13–21 (2007)[3] Chen, S., Carroll, J.: 3-d reconstruction of coronary arterial tree to optimize angiographic visualiza-tion. IEEE Trans. Medical Imaging 19(4), 318–336 (2000)[4] Essa, E., Xie, X., Sazonov, I., Nithiarasu, P.: Automatic ivus media-adventitia border extraction usingdouble interface graph cut segmentation. In: IEEE ICIP. pp. 69–72 (2011)[5] Essa, E., Xie, X., Sazonov, I., Nithiarasu, P., Smith, D.: Shape prior model for media-adventitiaborder segmentation in ivus using graph cut. 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Efficient reconstruction of coronary vessels from 2D angiography

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