A modified Frangi’s vesselness measure based on gradient and grayscale values for coronary artery detection

Abstract

This paper describes a method to extract the cardiac vessels in coronary angiography images. The cardiac vessel extraction technique is a significant process in clinical scenario for cardiac image analysis of Coronary Computed Tomography Angiography (CCTA) datasets. CCTA is a speedy growing non-invasive cardiac imaging modality that provides vital diagnostic information for the cardiac disease diagnosis. Since cardiac vessel extraction for CTA images is a prime issue in computer-aided medical diagnosis, algorithms or systems for vessel detection are always demanded. In order to support computer-aided diagnosis, a modified Frangi’s vesselness measure based on gradient and grayscale measure of the cardiac images is proposed in this work. The experimental result shows that the proposed method can effectively enhance vascular structures and suppress the pseudo vascular structures. It eliminates the background noise and helps in separation of neighboring vessels. The proposed vesselness measure were statistically analyzed by analysis of variance (i.e) one-way ANOVA. The statistical analysis also proves that the proposed vesselness measure based on gradient and grayness values extracts the vessel segments more effectively from the background. Hence the method detects the cardiac vessels more effectively by incorporating the fact that the gradient and grayscale values are comparatively different inside and outside the cardiac vessels. The proposed method has been evaluated on 3D CCTA images and the results are promising.

Keywords

Computed Tomography Angiography (CTA)coronary artery vesselness measure

1 Introduction

Cardiovascular diseases (CVDs), conventionally referred to as heart disease, is the top reason of death around the world demanding 17.3 million lives every year [1]. 1 in 3 deaths globally are as result of CVD. As a consequence, the current research is particularly focused on its early diagnosis. The changes and early diagnosis in various risk factors are requisite features for reducing mortality or morbidity, or both, in CVDs. It is usually a significant complication especially in case of damaged coronaries, arteries that provide oxygen to heart and can be diagnosed using Coronary Computed Tomography Angiography (CCTA) imaging modality. CCTA imaging modality has been widely used in the diagnostic evaluation of many CVDs, and it serves as the first line cardiac imaging modality in the early diagnostic evaluation of cardiovascular abnormalities.

Accurate vessel detection from cardiac images is essential for applications including lumen segmentation, stenosis detection, and calcium measurement [2]. Hence vessel detection is a crucial step in cardiac image analysis. Commodious study has been rendered toward vessel detection in Cardiac Computed Tomography Angiography (CCTA) images and there exists various techniques of vesselness measure for CCTA images. Some authors have presented probabilistic methods to extract vessel centerlines from medical image data [25 –28]. Shagufta et al. [30] developed a method to extract centerline based on morphological operations, which performs erosion using 2×2 neighborhoods and the results obtained achieve 92% accuracy. The morphological methods provide acceptable results with the high contrast and noiseless images, but similar successful results are not acquired with the low quality and highly noisy images.

Although numerous studies has been rendered for the detection of vascular structures, the most popular vesselness measures are the Lorenz’s vesselness measure [33], the Sato vesselness measure [34] and the Frangi’s vesselness measure [35]. The above vesselness measures works like a filter to extract the local structure of the image. However, all of these measures are very sensitive to noise or artifacts and the performance of the above measures may not be good in case of abnormal blood vessels and for a bifurcation point or a cross point in the blood vessels. Yang et al. [29] presented a Frangi’s vesselness filter algorithm which discards undesirable step-edge responses at the boundaries of the cardiac chambers with high overlap and accuracy measurements.

In [10], the authors proposed a semi-automatic method based on a minimum cost path using intensity and second order image information to extract coronary artery centerlines from CCTA data. Here user interaction and computation time are minimized. In [18] a minimum cost path approach for the extraction of coronary artery centerlines from CCTA data is used, but they have considered only small vessel segments.

Several studies have generally investigated vesselness measure, mostly based on region growing algorithm [37]. Region growing algorithm gradually segment the vessels based on their properties and similarities such as texture, shape and intensity between adjacent pixels from a seed point. These methods work well for identical regions and has the ability to obtain well-connected regions. But they are not suited for chronic vessels. In such instances they may disclose into other structures in case of bifurcations and small blood vessels of similar intensity. The authors proposed methods on vessel detection from 3D medical image data based region growing [6 –11] and tracking methods [12 –15]. The approaches make use of the preceding information such as, contrast between the blood vessels and surrounding background, origin of vasculature from the same point that is the optic disc and connectivity of the vessels.

Li et al. [16] and Wink et al. [23] proposed minimum cost path based techniques in which scale is included as an additional dimension in the cost image and this is advantageous in 2D images with overlapping vessel structures. A number of methodologies based on minimum cost path have been proposed for solving the problem of vessel detection from medical images [16 , 20–23]. These methods works based on the start and end points of the vessels and user-interaction is needed to guide the centerline extraction in the presence of severe pathology or image artifacts. Among them are Dijkstra’s algorithm, the A* algorithm [19], which makes use of additional standard to direct the search process and uses wave front propagation analysis [21]. Wink et al. [20] applied Dijkstra’s algorithm for the extraction of coronary vessel centerlines from 3D MRA data.

Wang et al. [24] presented a method based on fuzzy connectedness which uses the weakest link to determine the costs of a certain path. In [22] the authors explained different methods to define the minimum cost path through a pre-defined cost image, for the extraction of cardiac vessel centerlines from medical image data.

In [36] the authors proposed a method based on machine learning which uses a rich domain-specific knowledge enclosed in an expert defined dataset. They extract a set of geometric and image features for each voxel. The machine learning methodology can be effectively applied to refine the detection performance of the algorithm, but in case of low-dimensional feature space, the learning effectiveness of the algorithm are limited to the classifiers.

Some authors proposed a measure based on model-based techniques [33]. Prior knowledge and features are used to match a model with the input image to extract the cardiac vessels. A method based on fusion algorithm is proposed in [39]. The cardiac vessels are extracted using the maximizing entropy segmentation method based on top-hat in this method. Then again the vessels are extracted using the maximizing entropy segmentation method based on Gaussian filter. Finally, the two extracted coronary arteries images are fused together to obtain the resultant image. In [40] the authors proposed a method based on ridge-based method. The method depends on manually selected seed points for each vessel to be extracted. The closest ridge is traversed for each seed based on the intensity ridge map constructed.

Vessel detection for cardiac images works commonly using two different techniques: edge detector and matched filter. The edge-detection technique detects the left and right edges of vessel using various edge detectors such as Sobel operator, morphological detector, Canny’s method, etc. [4].

The matched filter method works by convolving the vessels with a filter designed according to the suitable model of vessel profile by assigning the value of any given pixel in the output image determined by applying some algorithm to the values of the pixels in the neighborhood of the corresponding input pixel [5]. Hence the filter based method removes isolated noise points in the image thus increasing the accuracy. Even though enormous research has been done on vessel detection, it still remains to be a challenging and a complex problem, due to the complicated vessel structure, reconstruction artifacts and vessel overlaps [3, 23].

In this work, a modified Frangi’s vesselness measure is proposed which considers the grayness and gradient values while calculating the vesselness measure. The remaining paper is organized as follows. In section 2, the materials and methods required to implement modified vesselness measure for coronary vessel detection are described. In section 3, a detailed description of the proposed method is provided. The performance of the method is evaluated in Section 4 by validating the results. Section 5 provides the conclusion.

2 Materials and methods

2.1 Data acquisition

The cardiac CTA images used in this work were obtained from KG hospital, Coimbatore. Totally 3D cardiac images of 7 patients are used in this work. Each 3D cardiac image has at least 200 slices with the dimension of each slice being 512×512 pixels. Cardiac CTA images of DICOM format (Digital Imaging and Communications in Medicine) were acquired with 1.2mSv and 0.2mSv. CCTA a non invasive imaging modality, was performed on 128 slice Multi Detector CT(MDCT) scanner (Siemens) using ECG-gating. The images are acquired from thin-slice projection data using a rotating x-ray tube and detector array, and then produce many tomography images of the anatomical volume by computer reconstruction algorithms. The original 3D CT volumes have an in-plane size of 512×512 voxels. The reconstructed image size for axial image is 512×512×12 bits. The CCTA images are high in temporal, spatial resolution and best in anatomical volume coverage.

2.2 Frangi’s vesselness measure

The Frangi vesselness measure [35] is a standard vessel detection approach which uses Hessian matrix H(x) to describe the curvature at each pixel in the image. For a three dimensional image H is the 3×3 matrix of second derivatives of I: $H = [\begin{matrix} \frac{\partial^{2} I}{\partial x^{2}} & \frac{\partial^{2} I}{\partial x \partial y} & \frac{\partial^{2} I}{\partial x \partial z} \\ \frac{\partial^{2} I}{\partial y \partial x} & \frac{\partial^{2} I}{\partial y^{2}} & \frac{\partial^{2} I}{\partial y \partial z} \\ \frac{\partial^{2} I}{\partial z \partial x} & \frac{\partial^{2} I}{\partial z \partial y} & \frac{\partial^{2} I}{\partial z^{2}} \end{matrix}]$ (1)

Eigen value analysis can be performed on the Hessian matrix in order to extract one or more principal directions of the local structure of the image [20]. The Eigen values of H (λ₁, λ₂, λ₃) with its equivalent eigenvectors (e1, e2, e3), defines the orthogonal coordinate system associated with the direction of minimal (e1) and maximal (e3) curvature. For a vessel, e1 indicates the orientation of the vessel. Thus λ₁ represents the parallel curvature and λ₂ and λ₃ the orthogonal curvatures. To detect the vessels, the eigen values should be related as follows: |λ₁| < |λ₂|, |λ3| and |λ₂| ∼ |λ3|. Also for bright blood images |λ₁|∼0 and λ₂, λ₃ > 0. Therefore the overall magnitude of the eigen values should be larger than the eigen values calculated in background regions. The Frangi filter defines the following equations in term of the eigen values of the Hessian matrix: $R_{A} = [\frac{| λ_{2} |}{| λ_{3} |}]$ (2) $R_{B} = [\frac{| λ_{1} |}{| \sqrt{T λ_{2} λ_{3}} |}]$ (3)

If R_A is 0, it refers a plane. If R_B is 1, it implies a line. The measure S is used to differentiate between cardiac vessel and heart muscle (i.e.) S is a measure of relative brightness or darkness of the vessel structure and is calculated by (4). $S = \sqrt{λ_{1}^{2} + λ_{2}^{2} + λ_{3}^{2}}$ (4)

The smaller S implies that the voxel belongs to background and S has the highest value when close to the centerline of the cardiac vessel. These quantities are combined using exponentiation, assuming a bright blood image, to give a “vesselness” measure defined as follows:

$V = {\begin{matrix} 0, if λ_{2} > 0 or λ_{3} > 0 \\ (1 - exp (\frac{R^{2} A}{2 α^{2}})) \cdot (exp (\frac{R^{2} B}{2 β^{2}})) \cdot (1 - exp (- \frac{S^{2}}{2 λ^{2}})) \end{matrix}}$ (5)

Where α, β, γ represent the weights (i.e.) the sensitivity of the filter to the corresponding measures. The exponential function is used to map the vesselness measure to a value between 0 and 1.

Frangi’s vesselness measure works based on local geometry feature of image for the vessel detection of cardiac image. Hence this method produces false cardiac vessel and isolated noise points in the vesselness measure thus reducing the accuracy [33]. The proposed vesselness measure overcomes the problem of Frangi’s vesselness measure by incorporating the gradient and grayness measures of the image to detect the vesselness measure of cardiac images.

2.3 Modified vesselness measure for coronary vessel detection

The proposed vesselness measure works based on gradient and grayness measures of the cardiac image to detect the vessels. The grayness measure considers the grayscale difference between vessels and muscles. The proposed measure is based on the fact that image pixel intensities depend on the anatomical structures in cardiac images. The grayness values of pixels in the vessels are similar to each other, but they are different from the grayscale values of the cardiac muscle pixels. The proposed grayness measure G_f is computed using Equation 6. $G_{f} (x, y, z) = \frac{| I (x, y, z) - t |}{I_{max}}$ (6)

Where t is the threshold value of the 3D cardiac image. I (x, y, z) is the grayscale value of the 3D cardiac image at location (x, y, z) and I_max is the maximum grayscale value of the 3D cardiac image.

Apart from the grayness measure, a gradient measure is also proposed in this paper which helps to clearly differentiate the cardiac blood vessel and cardiac muscles at the boundaries. The gradient of an image pixel at location (x, y) is given by the vector

$\nabla G = [\begin{matrix} G_{x} \\ G_{y} \\ G_{z} \end{matrix}] = [\begin{matrix} \frac{δ I}{δ x} \\ \frac{δ I}{δ y} \\ \frac{δ I}{δ z} \end{matrix}]$ (7)

The magnitude of the gradient vector is considered in this work and is given by $G_{mag} (x, y, z) = | G_{x} | + | G_{y} | + | G_{z} |$ (8)

The proposed gradient measure is computed as $G_{d} (x, y, z) = \frac{G_{mag} (x, y, z) - I (x, y, z)}{I_{max}}$ (9)

The proposed grayness and gradient measures consider the grayscale information and the differentiation between the vessel and muscles to improve the vesselness measure computed by Frangi’s filter. The proposed vesselness measure based on grayness measure and gradient measure for cardiac CTA image is defined as

$V_{proposed} = {\begin{matrix} 0, if λ_{2} > 0 or λ_{3} > 0 \\ (1 - exp (- \frac{R^{2} A}{2 α^{2}}) \cdot exp (- \frac{R^{2} B}{2 β^{2}}) \cdot (1 - exp (- \frac{S^{2}}{2 λ^{2}})) \cdot \frac{G_{d}}{G_{f}} \end{matrix}$ (10)

In typical CCTA images blood vessels are bright and the cardiac muscles are dark. The grayness measure G_f is a measure which indicates the grayscale values of the pixels in CCTA images. G_f has larger values for pixels which are greater than t and it is lesser for pixels which are lesser than t. Hence, G_f is relatively higher for blood vessels and lower for background or cardiac muscles. The gradient magnitude G_mag is a measure of how fast the grayscale values in the cardiac image are changing. The gradient measure G_d is also a measure of changes in the grayscale values. The gradient measure G_d also is higher for blood vessels particularly among the boundaries of blood vessels. The factor G_d/G_f is higher for blood vessels especially along the borders and lesser for background or cardiac muscles. Multiplying the factor G_d/G_f with the existing Frangi’s vesselness measure V further enhances the values of V if the pixels are blood vessels or on the borders of blood vessels. Similarly, multiplying the factor G_d/G_f with existing Frangi’s vesselness measure V will further decrease the values of V if the pixels are background or cardiac muscles. The factor G_d/G_f would help in further enhancing vesselness measure for blood vessels and decreasing the noise or pseudo vessels. If a vessel belongs to vessel structures, the values of proposed vesselness measure V_proposed is closed to 1 otherwise it is close to 0. Incorporation of these two measures improves the vesselness measure and thus improved the detected cardiac vascular structure. Hence the proposed method is most effective in producing the good qualitative results in extracting not only large coronary vessels but also small vessels with low contrast. It also preserves the spatial structure in the 3D cardiac image.

3 Results

3.1 Proposed coronary vessel detection method

The proposed algorithm works based on the steps shown in Fig. 1.

Fig.1

Processing pipeline of Cardiac Coronary vessel extraction technique.

The proposed cardiac coronary vessel extraction technique can be divided into two successive steps as follows. The proposed algorithm works based on the details available about the cardiac structures, vessels.

Preprocessing (Segmentation of whole heart)

and tissues. Preprocessing is performed to segment the whole heart. This process is accomplished to isolate the region of interest (heart region) from the remaining portions of cardiac image such as bones of the rib cage. In this stage, all the variables needed to perform the segmentation such as statistical parameters, position of the spine, etc. are determined and a preliminary cleaning of the images which basically selects the Region of Interest (ROI) is performed.

Cardiac Coronary vesselness measure

The proposed vesselness measure is used on the preprocessed cardiac images to extract the cardiac vessels which is essential for applications including lumen segmentation, stenosis detection, and calcium measurement [2]. The method works based on modified vesselness measure based on gradient and grayness measures of the image to detect the vesselness measure of cardiac images.

4 Discussions

The proposed methodology is implemented using modified vesselness measure based on gradient and grayness measures of the image using 3D CTA image to demonstrate its accuracy. A sample set of 2D slices of cardiac volume is shown in Table 1. The maximum intensity projection of a sample 3D CTA image is shown in Fig. 2.

Table 1
Sample 2D cardiac images

Fig.2

Original 3D cardiac image.

Table 2 gives the results of vesselness measure detected using Frangi’s vesselness measure and proposed method based on modified Frangi’s vesselness measure. The maximum intensity projection (MIP) of vessels detected for the 3D cardiac dataset of 7 patients using the Frangi’s vesselness measure and proposed vesselness measure is shown in Table 2(c) and Table 2(d) respectively. The enhanced vesselness measure using V_proposed for blood vessels are highlighted in red boxes and the suppressed vesselness measures for pseudo vessels are highlighted using blue boxes in Table 2(d) for the dataset. It can be seen from Table 2(c) that there is problem of branch disconnection ie discontinuity in the vesselness resulting in increased background noise and unsmooth edges. Moreover it can be observed that the detected vessels in Table 2(c) contain many spurs. Hence it can be inferred that the vesselness measure based on Frangi’s filter is not accurate which leads to erroneous skeleton of coronary arteries as shown in Table 2(c). These limitations are resolved by the proposed vesselness measure as shown in Table 2(d). It can be clearly seen that the proposed method enhances the vascular structures and simultaeously reduces the appearance of the pseudo vascular structures. Here the vesselness measure gives better performance by reducing the background noise and shows quite smooth edges with less or no spurs and hence this method can be used for further processing of cardiac images.

Table 2

Vessels detected using Frangi’s vesselness measure and proposed method based on modified Frangi’s vesselness measure

Table 3 compares the features of Frangi’ vesselness measure and the proposed vesselness measure. Peak signal to noise ratio (PSNR), Structural Similarity Index Matrix (SSIM) and entropy are used as metrics to analyse the performance of the proposed vesselness measure. Table 4 provides the PSNR, entropy and SSIM for the original image and vessel detected image using Frangi’s vesselness measure and the proposed vesselness measure. The PSNR, entropy and SSIM values provided in Table 4 are plotted as graphs in Fig. 3.

Table 3

Comparison of Frangi’s vesselness measure and proposed vesselness measure

Vesselness measure	Noise suppression	Edge smoothness	Branch discontinuity	Spurs
Frangi’s vesselness measure	NO	NO	YES	YES
Proposed Vesselness measure	YES	LESS-SMOOTH	NO	NO

Table 4

Performance result of Frangi’s vesselness measure and proposed vesselness measure based on PSNR, ENTROPY and SSIM

CCTA images	Frangi’s vesselness measure			Proposed vesselness measure
	PSNR	ENTROPY	SSIM	PSNR	ENTROPY	SSIM
1	5.6541	4.6518	0.0406	5.7235	4.4225	0.0550
2	5.3242	4.3076	0.0297	5.3813	4.0853	0.0519
3	5.7999	4.6620	0.0402	5.8995	4.4017	0.0447
4	5.7381	4.5222	0.0402	5.8318	4.2641	0.0447
5	5.4348	4.6116	0.0112	5.4614	4.4071	0.0123
6	6.4945	4.9922	0.0473	6.5581	4.3949	0.0543
7	6.2954	4.8941	0.0434	6.3906	4.3034	0.0574

Fig.3

Comparison of vesselness measure based on Frangi’s, Proposed measure using (a) PSNR, (b) SSIM and (c) Entropy.

The higher the PSNR value, the better the quality of the reconstructed image. Here the proposed vesselness measure gives higher value compared to Frangi’s vesselness measure and hence the proposed vesselness measure is better. The next quality measure used is entropy, Lower value of entropy assures less randomness in image information. Therefore for vessel detection from cardiac images the method for which entropy value is lesser is better and the proposed vesselness measure outperforms than frangi’s vesselness measure. Similarly SSIM is a method used for measuring the similarity between two images. It can be observed from the Table 4 that the vessel detection method which uses the proposed vesselness measure provides higher values compared to the method which uses Frangi’s vesselness measure. Thus the proposed vesselness measure based on gradient and grayness values helps in extracting the vessel segments more effectively from the background than the Frangi’s vesselness measure.

A one-way ANOVA is used to analyze the difference between entropy values obtained from vessel extraction method using Frangi’s vesselness measure and the proposed vesselness measure. Table 5 summarizes the sum, average and variance of entropy values obtained using proposed vesselness measure and Frangi’s vesselness measure. The entropy values are lower in the proposed vesselness measure compared to Frangi’s vesselness measure, which shows that the vessel extraction method using the proposed vesselness measure is better than the vessel extraction method using Frangi’s vesselness measure. Table 6 summarizes the results of one-way ANOVA test with significant level (alpha) of 0.05 performed on entropy values obtained using Frangi’s vesselness measure and proposed vesselness measure. The p-value obtained is 0.004706 which is less than 0.05 = alpha. Hence, the results obtained using the proposed vesselness measure are significant. Similarly the F critical value, 4.75, is lesser than the F-value, 11.98. Hence the result proves that the proposed vesselness measure outperforms the frangi’s vesselness measure in terms of entropy values.

Table 5

Comparison of mean entropy of frangi’s vesselness measure and proposed vesselness measure using one way anova

Groups	Count	Sum	Average	Variance
Frangi’s vesselness measure	7	32.6415	4.663071	0.05178
Proposed vesselness measure	7	30.279	4.325571	0.014774

Table 6

P-values for the one-way ANOVA test for the entropy of Frangi’s vesselness measure and proposed vesselness measure

Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	0.398672	1	0.398672	11.98032	0.004706	4.747225
Within Groups	0.399327	12	0.033277
Total	0.797999	13

The proposed method is implemented using MATLAB in AMD A6-5200 APU 2.00 GHz system with 8 GB RAM. The running time for calculating Frangi’s vesselness measure and the proposed vesselness measure for the 7 datasets is given in Table 7. The average running times for the calculating V_proposed and Frangi’s vesselness are 453.54 and 443.95 seconds respectively. The computation time for proposed vesselness measure is more as it has to calculate G_d/G_f and multiply it with Frangi’s vesselness measure and this is reflected in the average running time. Although the running time of the proposed vesselness measure is slightly higher, it is able to more effectively detect vessels and suppress noise and non-vessels.

Table 7

Running time evaluation for existing and proposed vesselness measure on 3D CCTA dataset

Patient_ID	Dimension	Existing method runtime (seconds)	Proposed method runtime (seconds)
1	512×512×242	404	416
2	512×512×212	301.97	313.32
3	512×512×228	536.32	542.99
4	512×512×212	378.19	382.53
5	512×512×236	551.79	562.01
6	512×512×222	551.79	563.32
7	512×512×216	383.62	394.6
Average Running Time		443.95	453.54

5 Conclusion

In this paper, a modified vesselness measure which incorporates both gradient and grayness values of cardiac images is proposed and evaluated. The proposed method uses the fact that the grayness value of the vessels and the gradient value at their borders are different from the background voxels. This feature is utilized to improve the Frangi’s vesselness measure. The proposed method has been evaluated on 7 patients 3D CCTA images and the results are promising. The experimental result shows that the proposed method can effectively enhance vascular structure and suppress the pseudo vascular structures. It eliminates the background noise and helps in isolation of neighboring vessels. The statistical analysis also proves that the proposed vesselness measure based on gradient and grayness values extracts the vessel segments more effectively from the background.

Footnotes

Acknowledgment

The authors would like to express the sincere gratitude to KG Hospital, Coimbatore for providing the medical data sets used in the experiments. They are also thankful to Bharathiar University for the valuable support.

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A modified Frangi’s vesselness measure based on gradient and grayscale values for coronary artery detection

Abstract

Keywords

1 Introduction

2 Materials and methods

2.1 Data acquisition

2.2 Frangi’s vesselness measure

3.1 Proposed coronary vessel detection method

Table 1 Sample 2D cardiac images

Footnotes

Acknowledgment

References

Table 1
Sample 2D cardiac images