2013 International Symposium on Computational and Business Intelligence
Optimized Coronary Artery Segmentation using Frangi filter and Anisotropic Diffusion Filtering Shashank, Mahua Bhattacharya, G K Sharma Department of Information and communication Technology Indian Institute of Information Technology and Management Gwalior, India e-mail:
[email protected] Abstract— X-ray angiography is currently the prime method of diagnosis during percutaneous coronary interventions. Robust automatic detection of coronary arteries from angiography images is of great interest. Hessian-based Vessel enhancement filtering was proven successful in automatically segmenting vessels from angiography images. However, there is too much noise and other anatomical structures also interfere with the Percutaneous Coronary Intervention (PCI) procedure. The proposed method uses Frangi Hessian based vessel enhancement filter for extracting coronary arteries and setting optimal value of Frangi filter parameters α and β. The method is applied recursively on a set of angiography images from same machine and tries to assign optimal values of α and β for it. This procedure is followed by (Rotation Invariant) Anisotropic diffusion filtering of the image. Anisotropic Diffusion Filtering is used for noise removal and coronary artery enhancement. For the diffusion tensor, hybrid diffusion is used with a continuous switch which is suitable for filtering tubular image structures.
are different. To improve the accuracy of stenosis detection, it is necessary to find out an optimal range for α and β. It is impossible to get best results on all angiography machines for the same value of α and β. Frangi filter alone is not capable of completely segmenting the coronary arteries from background images. Changing the values of filtering parameters beyond a certain point results in loss of information. Hence we need to further enhance the output of Frangi filter. Anisotropic diffusion is technique introduced by Perona and Malik which reduces the image noise without affecting significant parts of the image content [9][10]. The technique was further developed by Joachim Weickert and Dirk-Jan Kroon et al [11][12]. The approach used in this work is adopted from their work on “Optimized Anisotropic Rotational Invariant Diffusion Scheme” [13]. This paper is organized as follows; in the next section Frangi Filter and Optimized Anisotropic Rotational Invariant Diffusion Scheme is introduced. Algorithms implemented are discussed in third section. Results obtained are discussed in the fourth section, followed by results discussion and future work.
Keywords-Frangi Filter, X-ray angiography, Hessian Based Vessel Enhancement Filtering, parameter setting, Anisotropic Diffusion Filtering.
II. I. INTRODUCTION (HEADING 1) Accurate analysis of the human vascular structure is an important requirement for many clinical diagnostic methods. Stenosis grading is an important part of diagnosis in the computer aided analysis coronary artery disease. On the basis of this diagnosis the severity of stenosis is determined [1]. All coronary intervention procedures require an accurate three dimensional architecture of coronary vessels. The accuracy of diagnosis is highly dependent on these procedures. Hessian based vessel enhancement methods have been highly successful in segmentation of coronary arteries. One of the most successful methods of vessel segmentation is Frangi filter [2][3]. This filter produces much better results as compared to other famous Lorenz filter and Sato filter [4][5][6][7][8]. These filters have already been compared and the filter proposed by Frangi et al out performed others [6]. In this work, we investigate the performance of Frangi filter on angiographic images from different filters and compare their capabilities to assign a specific small range for filter parameters α and β for optimum vessel enhancement [2][3]. For each machine, the adjustments, fluoroscope X-ray intensity, environment etc. 978-0-7695-5066-4/13 $26.00 © 2013 IEEE DOI 10.1109/ISCBI.2013.59
CORONARY ARTERY SEGMENTATION
A. Segmentation using Frangi Filter Frangi vessel enhancement filter is one of the most famous methods for vessel segmentation of coronary arteries. It is fast as well as efficient. Since the response of this method is largely dominated by the background noise suppression. This method is based on hessian matrix method. The Hessian matrix is calculated by calculating the second order derivative of an image in horizontal, vertical and both left and right diagonals. A hessian based vessel extraction filter can be defined as F ( x) max f ( x, ) (1) where x is a position of pixel in an image; f is the filter used for vessel extraction and σ is the standard deviation for calculating Gaussian image derivative [2][3]. In a linear structure, the intensity increase rapidly from the border to the center line and decrease again from the center line to the opposite border; so an absolutely large secondorder derivative should occur. In this study, the response of the filter is calculated for 15 different values of σ (from 1 to 15). 261
The Hessian matrix is calculated by calculating the second order derivative of an image in horizontal, vertical and both left and right diagonals. The 2D Hessian matrix is:
H xx H yx
H
H xy H yy
tensors for the image. 5) Eigenvectors are used as directions of diffusion tensor. For diffusion, a Finite Difference Scheme (i.e. f(x+h) – f(x), where h is very small) is used. This process is repeated for a certain diffusion time. We optimize the diffusion kernel using the following cost function: The kernel values p = [p1, p2..., p14] are found analytically. (4) p arg min(ef ( p) eg (p))
(2)
where Hxx; Hxy; Hyx; and Hyy are the directional second-order partial derivatives of the image. The eigenvalues of H (i.e. 1 and 2 ) are calculated and analyzed to determine the likelihood of x belonging to a vessel. The analysis is based on the following hypothesis: | 1 | | 2 |
p
This function balances between the edge oriented invariant filtering performance ‘ef()’, and isotropic diffusion performance ‘eg()’, with weight constant a.
ef(p) | F ( I noise , p) I |
f(x,σ) = 0, where 2 > 0 The Hessian based vessel extraction filter which was defined by Frangi for 2D vessel detection is:
, if 2 0 0 R2 2 S f ( x) 2 b2 2 2 1 , elsewhere e e F ( x) max f ( x, ) here, Rb
| x2 | 1 eg ( p) arg min F ( I noise , p) exp a a x a
2
here, I noise is the image with Gaussian noise added to it. p is the diffusion kernel. The algorithms for the entire procedure are discussed in the next section.
(1)
| 1 | is used with α to | 2 |
12 2 2
2
(6)
(3)
III.
ALGORITHMS USED
The algorithms implemented in this work are as follows:
discriminate plain line like structures from blob like structures and S
(5)
x
A. Algorithm for Segmentation using Frangi Filter 1) Take angiography image as input. 2) Set values of the filter parameters α and β. Set value of max for maximum standard deviation (say 15). 3) For each discrete value of max calculate 2D Hessian matrix for each image Eigenvalues ( 1 and 2 ) of Hessian matrix. Arrange eigenvalues as per their absolute value | 1 | | 2 | .
is used with β for
eliminating background noise [2][11]. The entire algorithm is discussed in short in the next section. In Frangi filter, α and β are the parameters controlling ‘ R b ’ and ‘ S ’. The entire shape discrimination and noise elimination is dependent on the values of α and β. The noise present in the image is also highly dependent on the angiography apparatus settings. Hence we cannot set a single value of α and β as an optimal value for all angiography machines. 2
B. Rotation Invariant Anisotropic Diffusion Filtering This part is mostly based on Dirk-Jan Kroon et al “Optimized Anisotropic Rotational Invariant Diffusion Scheme”. They have introduced a new scheme in which optimal filtering kernels are constructed using numerical optimization [13]. This method applies Gaussian smoothing and Hessian calculation recursively on the given image. This is followed by calculating the eigenvectors and eigenvalues of the Gaussian smoothed Hessian and constructing 2D diffusion
Calculate
Rb
262
| 1 | 2 2 2 and S 1 2 . | 2 |
Calculate f(x) as defined by Frangi et al.
, if 2 0 0 R2 S2 f ( x) 2 b2 2 2 1 e , elsewhere e
diffusion filter. The aim was to further enhance the segmentation process. There is improvement in the visibility of small arteries. This can be observed in Figure 4.
End for. 4) Take F(x) as result, where F ( x) max f ( x, ) , B. Algorithm for Rotation Invariant Anisotropic Diffusion Filtering
Apply Gaussian smoothing on the input image. Calculate hessian for every pixel of the smoothed image. Apply Gaussian smoothing on the hessian output. Calculate the eigenvectors and eigenvalues of the Gaussian smoothed Hessian. Calculate diffusion tensor for input image. Eigenvectors are used as directions of diffusion tensor. For Diffusion a finite Difference scheme is used. Back to step1. For a certain diffusion time. IV.
RESULTS AND DISCUSSION
In this section we are showing some results from various angiography sources. In first part, the values of α and β are kept same for all these sources. In second part, the values of α and β are set manually for each angiography source. This procedure is tested for 20 different angiography sources. The results for the first part are shown in Figure 1 and Figure 2. The values of α and β are 0.5 and 15 respectively in this case. The output of image A is the most optimal output as compared to B, C and D. The output of image B contains noise whereas the output of images C and D are blurry and there is loss of information in resulting images. Hence same value of α and β can’t be used for all angiography apparatuses. In second part the values of α and β are different for each source. The result for this part is shown in Figure 3. The values of α and β are 0.5 and 15 respectively for image A, 0.8 and 25 respectively for image B, 1.5 and 9 respectively for image C and 1 and 10 respectively for image D. The results are clearly better than the results of first part. There is 1.512% reduction in unwanted noise for image A and 3.603% reduction in image B. There was 4.792% improvement in visibility for image C and 2.432% improvement in image D. From the above results, it is clear that manual setting of parameter is much better than fixed parameter setting. The results obtained can be further utilized for automatic stenosis detection which the next step in the analysis of coronary artery disease. The segmentation part is further followed by Anisotropic Diffusion Filtering. The result of this part is shown in Figure 4. The output of Frangi filter has been used as input to
Figure 1: Unsegmented Angiography images A, B, C and D. .
Figure 2: Segmented Frangi Filter output E, F, G and H for Input A, B, C and D respectively.
263
REFERENCES [1] [2]
[3]
[4]
[5]
[6]
[7]
Figure 3: Segmented Frangi Filter output using optimal parameter values. [8]
[9]
[10]
[11]
Figure 4: Segmented output After Anisotropic Diffusion Filtering, small arteries are more prominent in B as compared to A. V.
[12]
[13]
FUTURE WORK
This hessian based vessel enhancement filtering is the preliminary step in automatic stenosis detection. It is followed by Rotation Invariant Anisotropic Diffusion Filtering. The following steps could be junction detection in coronary arteries followed by parsing of coronary arteries for stenosis detection.
264
American Heart Association, http://www.heart.org/idc/groups/heartpublic/@wcm/@hcm/documents/downloadable/ucm_300436.pdf S. You, E. Bas, and D. Erdogmus, “Extraction of samples from airway and vessel trees in 3D lung CT based on a multi-scale principal curve tracing algorithm,” IEEE Conference on Engineering in Medicine and Biology Society (EMBC 2011), pp. 5157–5160, 2011. Frangi A, Frangi R, Niessen W, Vincken K, Viergever M., Multiscale vessel enhancement filtering. Springer-Verlag, 1998; 130– 137. Zyout, I.; Abdel-Qader, I., "Characterization of clustered microcalcifications using multiscale Hessian based feature extraction," Electro/Information Technology (EIT), 2010 IEEE International Conference on , vol., no., pp.1,5, 20-22 May 2010 Q. Yang, A. Karpikov, D. Toomre, and J. Duncan, “3D reconstruction and measurement of microtubules from multiple angle-total internal reflection fluorescence microscopy,” in IEEE Computer Society Workshop on Mathematical Methods in Biomedical Image Analysis , 2009. S.D. Olabarriaga, M. Breeuwer, W.J. Niessena, Evaluation of Hessian-based filters to enhance the axis of coronary arteries in CT images, International Congress Series 1256 (2003) 1191– 1196. I C. Lorenz, I.-C. Carlsen, T.M.Buzug, C.Fassnacht, J.Weese, Amulti-scaleline filter with automatic scale selection based on the Hessian matrix for medical image segmentation, in: Proceedings of 1st International Conference on Scale-Space Theory in Computer Vision, vol.1252, Utrecht, Netherlands, 1997, pp.152–163. Y. Sato et al., 3-D multi-scale line filter for segmentation and visualization of curvilinear structures in medical images, Medical Image Analysis 2 (2) (1998) 143– 168. uddin Khan Nafis, K.V. Arya, Manisha Pattanaik, Histogram statistics based variance controlled adaptive threshold in anisotropic diffusion for low contrast image enhancement, Signal Processing, Volume 93, Issue 6, June 2013, Pages 1684-1693, Karemore, G.; Brandt, S.; Sporring, J.; Nielsen, M., "Anisotropic diffusion tensor applied to temporal mammograms: An application to breast cancer risk assessment," Engineering in Medicine and Biology Society (EMBC), 2010 Annual International Conference of the IEEE , vol., no., pp.3178,3181, Aug. 31 2010-Sept. 4 2010 Sarkis, Michel; Mani, Lokesh, "Reconstruction of passive millimeterwave images with Graph Cuts," Image Processing (ICIP), 2012 19th IEEE International Conference on , vol., no., pp.2053,2056, Sept. 30 2012-Oct. 3 2012 D. Kroon, C.H. Slump, Coherence Filtering to enhance the mandibular canal in cone-beam CT data, IEEE-EMBS Benelux Chapter Symposium, (2009). Kroon DJ, Slump CH, Maal TJ., Optimized anisotropic rotational invariant diffusion scheme on cone-beam CT. Medical Image Computing and Computer-Assisted Intervention 2010;13(Pt 3):221-8.
