# Ensemble Learning-Based Coronary Artery Disease Detection Using Computer Tomography Images
## 2 Materials and Methods
### Image Preprocessing  
The shape and curvature of the arteries play a crucial role in CAD detection. The vessel curvature, bends, and twists are the critical features for classifying the CCTA images. An abnormal coronary artery diameter may suggest stenosis or other complications. Calicifications or plaques in the arterial walls may indicate atherosclerosis, a prevalent concern in coronary artery disease. A crucial characteristic to observe is the narrowing of the coronary arteries due to stenosis. This condition suggests reduced blood flow to the heart. The existence of coronary arteries can be rendered apparent by using contrast enhancements and variations. The CCTA images contain multiple noises and artifacts that may influence the performance of the proposed CAD detection model. In addition, the preprocessed images can improve the proposed feature engineering process to generate meaningful features. Thus, the authors employed a number of image preprocessing techniques to address the noise and motion artifacts. Steerable filters can respond to gradients at any angle [44]. To control the direction of a filter, the horizontal and vertical components can be combined at a certain angle of orientation [44]. There is an option to fine-tune the parameters to modify the responses of the filters or directly control the filters themselves in order to maintain the steering process. Steerable filters can enhance, compress, identify edges, analyze textures, and analyze image motion. Initially, the steerable filter function is used to obtain crucial features with specific orientations in the CCTA images. The sinusoidal function optimizes the filter to select the desired orientation. Additionally, the steerable  
Figure 2: The proposed straightened artery extraction technique. pyramid feature captures the vessel lengths of the primary CCTA images. Equation (2) highlights the steerable filter function. \[CCTA_{i}=Steerable\_filter(CCTA_{i},n,\omega,s)\ \ \,i=1,2,\ldots n \tag{2}\]  
where \(CCTA_{i}\) is the image, \(n\) is the filter order that determines the filter's orientation, \(\omega\) is the spatial frequency, and \(s\) is the filter's size. To address the limitations of traditional back projection, filtered back projection (FBP) uses a convolution filter to reduce blurring [45]. The cross-section attenuation coefficients are calculated using simultaneous equations of ray summing at different sine wave angles. The authors apply a filtered back projection algorithm to reconstruct the CCTA images. The algorithm uses maximum likelihood expectation maximization to refine the reconstructed images in order to reduce the artifacts. Equation (3) presents the motion artifact reduction process. \[CCTA_{i}=FBP(CCTA_{i},T)\ \ \,i=1,2,\ldots n \tag{3}\]  
where \(CCTA_{i}\) is the image, \(FBP\) is the filtered back projection, and \(T\) is the threshold for image reconstruction. Furthermore, the Frangi filter enhances vessel-like features using a multiplicative sigmoid function [46]. It calculates vessels from eigenvalues. High vessels are used for tubular structures like blood vessels, and low vessels are used for non-tubular structures. The Frangi filter allows for improved vessel appearance adaptation due to its greater sensitivity to vessel sizes and shapes. It improves blood vessel visibility and recognition in angiograms and other vascular imaging modalities. Similarly, the Sato filter enhances tubular or vessel-like features in medical images [47]. It uses Hessian matrix eigenvalues to represent local second-order intensity fluctuations in an image. It is designed to improve structures with a tubular form, which is typical of blood arteries. An eigenvalue of the Hessian matrix is used to calculate vesselness, and the filter highlights high vesselness locations. This study used the Frangi and Sato filters to enhance blood vessel quality. The Frangi filter emphasizes the elongated structures and suppresses the noises. The Sato filter computes the eigenvalues of the structure tensor to improve vessels of different sizes.