Implementing a non-local means method to CTA data of aortic dissection

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I. INTRODUCTION
It is a fact that some unwanted elements contaminate most images, so-called noise [1]. Noise can occur in images for many reasons [2]. It may appear as a consequence of the heat of the image sensors, and it also may arise during the image is taken or transmission of the image itself [3]. Biomedical images produced by some imaging techniques, such as CT scanning, indeed contain some visual noise. The appearance of noise restricts the radiologist's performance to differentiate inhomogeneous regions in the image [4]. This noise may lead to uncertainty in interpreting the image and degrade diagnostic performance [5]. Thus, the main purpose of this work concerns removing or at least reducing noise shown in CT scan images of aortic dissection patients. The aim of the noise reduction process itself is to improve the aortic boundary detection phase of 3D aortic segmentation and to reconstruct the 3D surface of the aorta, as discussed in [6]- [8]. Hence, removing noise in the MPR image is mandatory to increase aorta localization's whole performance. In [9], some denoising techniques, such as Gaussian filter, anisotropic diffusion, Yaroslavsky filter, and bilateral filter, are implemented in the system. The segmentation results obtained are quite encouraging. However, the visual images constructed are unsatisfied, where the blurry effect happened, and grainy parts are over smoothed.
In recent years, non-local means filter (NLM) has attracted significant attention among other techniques. Many studies, such as in [10]- [15], adapted the NLM methods to process noisy images and proved that NLM yields outperforming results. Non-local means (NLM) is a noise reduction technique proposed by Buades et al. [16]- [18]. This technique is inspired by neighborhood filtering, which removes noise based on local averaging [19]. However, in the NLM method, all pixel values in the image take part in the non-local smoothing process. The idea of this algorithm is taken from the fact that every patch in any raw image has many other similar patches [16]. These similarity patches will be taken into account for removing the noise. This method aims to replace the intensity values in each pixel with the weighted average of other similar patches in the full image.
In the NLM method, a kernel function acts as the degree of filtering to compute weighting factors of search neighborhood pixels [20]. This function delineated the similarity between patches and is in charge of weighting factor measurement. There are six kernel functions proposed in NLM. The first function is introduced by Buades et al. [16], namely the exponential function. Tian et al. [21] proposed other kernel functions, namely cosine function, flat function, Gaussian function, turkey bi-weight function, and wave function.
This work aims to continue the work that has been done in [9]  can exploit the inherent redundant information and preserve high degree image texture and details in CT scan images [5]. The classic NLM method is installed and established with six different kernel functions in this experiment. Furthermore, the comparison result between other denoising techniques will be done in the experiment.

II. RESEARCH METHODS
NLM method was implemented in the aortic segmentation system discussed in [6]- [8]. The segmentation process is divided into five steps (see Figure 1). Initialization places at least three points inside the aorta to obtain an approximation of the aortic centerline. Multiplanar Reformat (MPR) Images Extraction uses an aortic centerline to generate images in the two-dimensional region of interest with size m m. The MPR images are stored in the MPR stack. Aorta Localization aims to detect aortic circles in extracted MPR images. Contour deformation is done by adjusting the detected circle in the MPR image to meet the shape of the aortic contour. The 3D model construction is based on segmented results reformed in contour deformation step.
The method mainly runs in the preprocessing phase of the aortic localization step, where extracted grayscale MPR images are iteratively being used, denoised, and circle candidates are placed onto it. The optimal circles are selected in the post-processing phase and visualized in a 3D plot. The original images whose noises will be removed are taken from the stack and in the form of grayscale MPR images. The procedure of the denoising process is illustrated in Figure 2. Every image in the MPR stack will be denoised using NLM established with different kernel functions, namely exponential function, cosine function, flat function, Gaussian function, turkey bi-weight function, and wave function. The kernel functions are successively expressed in (1)-(6) [16], [21]. Basically, for a pixel x which is considered for denoising, NLM will search in the full image to find other patches which look alike the reference patches whose centre pixel is x.  in the equations plays the role of a parameter to control the quality of filtering. The graphical representation of the six kernel functions can be seen in Figure 3.
After the denoising process, the segmentation result of each MPR will be calculated and saved in a new stack. The average segmentation value of whole MPR images will be measured. Furthermore, the comparison result between other denoising techniques will be done in the experiment.

A. Dataset and method implementation
This work uses Computed Tomography Angiography (CTA) images of patients with aortic dissection cases provided by West German Heart Center of Essen-University Hospital. The number of datasets used for examination is 11 datasets sliced between 89-1034 slices with a 0.7-5 mm slice gap, and each axial slice has a resolution range between 0.445 to 0.863 mm [9].  The implementation of NLM methods in this experiment adopted the source from [21]. Figure 4 depicts how an m m region centered at pixel q searches other similar regions of the same size in a search region of the full image, for example, in the patch centered at pixel p. The search region can also be set in the L L neighborhood region centered at pixel p. Thus, several parameters have to be settled before denoising. The parameter sets are exhibited in Table 1. Due to the large number of MPR images provided for each CTA dataset, the selection of parameter M is set to be small to prevent a time-consuming evaluation. Like M, the size of search window L in this experiment has to be restricted to a small value.

B. Evaluation model
In this study, the manually segmented images of CTA scans are used as ground truth images.     of G and S. FP is when the voxel in the S and the background of G. FN is when the voxel in the G and the background of S. The method performance is examined by analyzing the quality of output images. However, it is not enough to judge restored images using only one criterion since judging quality images could vary from person to person. Thus, to assess the output of NLM implemented in the systems, the evaluation model is divided into qualitative and quantitative assessments. Qualitative assessment is done by analyzing the quality of the output image. On the other hand, the quantitative model uses the measurement of dice similarity coefficient (DSC), precision (P), and recall (R) based on four combinations above by using (7)- (9). The DSC will give values between 0 to 1. The higher the DSC, the better the result.

III. RESULTS AND DISCUSSION
Denoised images of the NLM method applied in this work are visualized in Figure 6. Figure 6(d) shows that visual performance NLM with flat function preserves the flat objects and the edges.. Different from the flat function, using the other kernel functions return blurry images. The visual results are contrary to the results that have been proven in [8] and [9], where the NLM algorithm shows outstanding visual performance. The poor-quality performance of NLM occurs because of resolution range in MPR images extracted by the system is too small, which is in the range of 0 to 1. The size of the pixel value in the image affected the computation of the kernel function. The smaller the intensity values, the smaller the kernel function itself. Table 2 illustrates the segmentation results of NLM established with an exponential kernel. There are some datasets (patient 10 and 11) that produce DSC values below 0,9. Nevertheless, it remains good in the average with DSC 0.913479, precision 0.927408, and recall 0.902064. Compared to the exponential kernel, employing flat function in NLM method yields a slightly increasing result of average DSC 0.937101, precision 0.954835, and recall 0.920517, as seen in Table 3. This result confirms the results presented by Tian et al. [21] that the application of NLM using a flat  Despite the other kernel function, specifically cosine function, Gaussian function, Turkey bi-weight function, and wave function, yields poor-quality image, fascinating segmentation results appear during NLM experiment configured with those kernels. Applying those four kernels returns exactly the same segmentation result value (DSC, precision, and recall). These values are shown in Table 4.
The same segmentation results are caused by the shape of these functions that are roughly resemblant (see Figure 3). Moreover, selecting a small mask M as a parameter emerges as another factor of similar segmentation results. However, the outcome is quite satisfying, with an average DSC of 0.913711. The value is also similar to the value of the exponential function.
Another criterion to be assessed in this study is by comparing NLM segmentation results with the results after applying other denoising techniques in [9]. Table 5 summarizes the average value of segmentation performances between NLM with six kernel functions, Gaussian filter, anisotropic diffusion, Yaroslavsky filter, and bilateral filter. Identified by the table, applying the NLM algorithm with flat function provides the highest value of DSC, 0.937101. The bilateral filter occupies the second-highest rank among the other algorithms, with a DSC value of 0.936310. Surprisingly, the Gaussian filter, commonly known as the blurring technique, also provides almost similar value to the first and second highest results. On the other hand, establishing the other five kernels in NLM reduces the performance of segmentation results. They hold the worst segmentation performance among the others.

IV. CONCLUSION
Employing NLM kernel functions as denoising process obtains overall outstanding segmentation results and is suitable to be used to get satisfying DSC values, in point of fact by using flat kernel function with highest DSC among them. Nonetheless, blurry images occur after applying all kernel functions, except using the flat function. This occurrence arises due to the small pixel range in the CTA image and influences the weighting factor measurement. In future work, the intensity value of images must be considered to obtain better-filtered images of the NLM algorithm. In addition, another aspect regarding efficiency should be investigated in the future since the computational speed of NLM is insufficient to be used in the system.