## 4 Experimental Analysis  
In this research, four denoising and twelve edge detection techniques are iteratively applied to determine the influence of EMI on the SEM image by extracting the exact image objects and the corresponding various indices. Particularly, after applying these techniques, dilation processing is also adopted to visualize the image object with better clarity. In the denoising step, all four denoising algorithms, i.e., Gaussian filter, median filter, bilateral filter, and non-local mean filter, are applied. The mean squared error (MSE) is used to evaluate the noise reduction effect, and the classification error rate \(\delta\) is a user-defined parameter with a range from 0.8 to 0.9. The edge detection parameters are the lower and upper thresholds considered in the Canny edge filter. Figure 2 illustrates the detailed procedures of the proposed method. Here, \(MSE_{i}^{NR(k)}\), \(ACC_{j}^{ED(l)}\), \(\epsilon\), and \(\delta\) indicate the mean squared error of the \(k\)th denoising technique at the \(i\)th iteration, the classification accuracy of the \(l\)th edge detection technique at the \(j\)th iteration, the threshold value for the mean squared error, and the threshold value for the accuracy, respectively. The experimental results presented in Figure 3 show that the Gaussian filter is selected as the best denoising technique in the first denoising step since it provides the minimum mean squared error compared to other denoising techniques. Then, twelve different edge detection filters are applied to the images refined by the Gaussian filter at the first denoising stage. As shown in Figure 4, the Scharr x filter is selected as the best edge detection technique in the first edge detection process since it provides the maximum classification performance. As the second denoising method, the Gaussian filter and a non-local mean filter are sequentially applied to the image obtained from the previous step. Then, the Canny edge filter is applied to the image derived from the previous step. Through the iterative application of the denoising and edge detection algorithm selected, it is shown that all edges reflecting the image object deformation are effectively detected. The proposed analysis procedure is tested on 3 different types of 119 semiconductor SEM images, i.e., high-EMI, medium-EMI, and weak-EMI, and 5 distortion measures are extracted from  
Figure 1: Contour area, rectangular area, and convex hull area. each image, i.e., image object area (denoted by 'Area'), image object contour (denoted by 'Perimeter'), rectangular area of the image object (denoted by 'Rectangular'), extend index (denoted by 'Extend'), and solidity index (denoted by 'Solidity'). Here, high-EMI, medium-EMI, and weak-EMI indicate SEM images affected heavily, moderately, and rarely by EMI, respectively. Figure 5 shows the box plots of five measures for three different types of semiconductor SEM images. The \(x\)-axis and \(y\)-axis in Figure 5 represent three different types of SEM images according to the level of EMI introduced and distortion measures, respectively. As shown in this figure, the medians of all five measures of high-EMI SEM images are higher than those of both medium- and weak-EMI SEM images, and the medians of all five measures of medium-EMI SEM images are higher than those of weak-EMI SEM images. Figure 3: Results of the 1 st denoising. Figure 2: Flowchart of image object extraction and quantification process. Since the response variable is a categorical (i.e., nominal) variable and independent variables are numeric (i.e., continuous) variables, a multinomial logistic regression is used to model the nominal response variables and predict the probabilities of the different possible responses.