Pre-processing

CT is one of the important imaging modality that provides a high contrast of body tissue or organs with good spatial resolution (Zhu et al.,2012;Kaur and Juneja,2018b). The quality of CT image is important in medical diagnosis that can be affected by the presence of artifacts during acquisition procedure. The most commonly affected noises in medical CT image are impulse noise "Salt and Pepper", Gaussian and Poisson noise (Javed et al., 2016). The noise in CT image affects both the diagnosis process and automated computerised analysis tasks, such as segmentation, three-dimensional image reconstruction, and visualisation. Therefore, reducing noise in the CT image is considered an important step, because it helps to improve the performance of the image analysis such as segmentation (Bhadauria and Dewal,2012).

The main goal of applying the pre-processing step is to enhance the image qual- ity, smoothness and reduce the noise that occurred by defects of CT scan device. In addition, it emphasises beneficial image features and quality for better segmentation accuracy and speed. Image filtering is a major pre-processing method used for many purposes including smoothing, sharpening and contrast stretching. In practice, as well as reducing noise, it is important to preserve the edges of the image where the edges provide important information about the visual appearance of the image. Because of this, anisotropic diffusion filter (ADF) and the median filter have been adopted for this task.

Perona and Malik proposed an edge detection and multiscale smoothing algorithm called anisotropic diffusion filter (ADF) (Perona and Malik,1990). ADE addresses the limitation of spatial filtering and improves image quality by preserving the edges of the object as it eliminates noise in similar areas and ensures edge sharpening. How- ever, this algorithm usually removes small image detail and change image statistics because of its edge enhancement effect. This filter describes the problem in the form of a heat equation based on the second-order partial differential equation (PDE) in an anisotropic medium, and it can achieve a good trade-off between noise removal and edge preservation (Li et al., 2013). Here, image smoothing is framed as a diffusion process that can be stopped or repressed at edges by selecting the strengths of the local gradient in various orientations. In this algorithm, boundaries are preserved by con-

Chapter 4. Liver Image Analysis in CT

volving the image I in the direction orthogonal to image gradient. The ADF process is given by Equation4.1.

∂I(y, i)

∂i = div (c (y, i) ∇I (y, i)) (4.1) Where ∇I (y, i) gives the value of image gradient at voxel y and iteration i, ∂I(y,i)_∂i is the partial derivative of I (y, i) and the edge-stopping function c (y, i) is illustrated in Equation4.2.

c (y, i) = g k∇I (y, i)k = e−k∇I(y,i)k/R2 (4.2) Where, R is the diffusion parameter and c is the flux function that controls the rate of diffusion.

On the other side, Median filter is a nonlinear approach used to remove noise from images. The median filter is demonstrably effective at removing noise whilst keeping edges for a given, fixed window size (Chang and Chu, 2012). Furthermore, Median filter is particularly effective at removing "salt and pepper" type noise. Because of this, the median filter is widely used in filtering the image by moving through the image pixel by pixel, replacing each value with the median value of neighbouring pixels. The median is calculated by first sorting all the pixel values from the window into numerical order, and then replacing the pixel being considered with the middle (median) pixel value.

In this work, the noise present in the CT image is removed by employing a 3x3 median filter, as depicted in Equation 4.3. The median filter was selected due to its retains the edge information within the input image where Gaussian and Mean filters tend to blur the edges in the image (Moghbel et al.,2016). This is because the Median filter does not create new unrealistic pixel values in the case of the filtering window laying over an edge.

f (x, y) = median(3,3)[I(x, y)] (4.3)

Where f(x,y) shows the filtered image and I(x,y) shows the original image before applying median filter. Figure4.2shows the original CT image and the output images achieved after de-noising algorithm ADF and median filer respectively.

The visual interpretation of the images is used to differentiate between noisy and denoised image content. However, to further validate the results at the quantitative level, some objective criteria were used such as Peak signal to noise ratio (PSNR), and they do not rely on the visual appearance of the images. This parameter computes PSNR between two images as a quality measurement between the original and filtered image.

Figure 4.2: Pre-processing step to remove the CT image noise. (a, d, g, j, m, p) the original input CT image. (b, e, h, k, n, q) the output CT image after ADF. (c, f, i, l, o, r) the output CT image after median filter.

Chapter 4. Liver Image Analysis in CT

The Mean Square Error (MSE) and the PSNR are the two error metrics used to compare noise reduction quality of the image. The MSE represents the cumulative squared error between the denoised and the original image, whereas PSNR represents a measure of the peak error. The lower the value of MSE, the lower the error. In contrast, the higher PSNR value means a better noise reduction algorithm. Equation 4.4 and Equation4.5depicts the respective formulas to compute MSE and PSNR respectively.

M SE = 1 mn m X y=1 n X x=1 (I(x, y) − I0(x, y))2 (4.4) P SN R = 10 log₁₀ (Imax) 2 M SE ! (4.5)

Where I is the original with image dimensions m and n. I0 represents the image after noise reduction process. Imaxis the maximum pixel value for the image.

The performance of both filters (median filter and ADF) is evaluated through PSNR metric over the 50 cases. The Figure4.3depicts the graphical results of PSNR for ADF and median filter approach, which demonstrates that ADF has better results in some cases as compared to the median filter algorithm. However, the median filter is better than ADF algorithm in the low quality of CT images. This is due to the CT image with the low quality has black and bright pixels, causing noise in the image where the dark and bright pixels are reduced better by using the median filter.

Figure 4.3: Pre-processing step to remove the CT image noise. (a, d, g, j, m, p) the original input CT image. (b, e, h, k, n, q) the output CT image after ADF. (c, f, i, l, o, r) the output CT image after median filter.

compared to ADF method. In addition, the median filter computational cost is signif- icantly lower than the ADF algorithm. Hence, the median filter was adopted to fulfill this task.