# Contrast-Invariant Edge Detection: A Methodological Advance in Medical Image Analysis
## 5 Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline
**Evaluation Metrics** & **50\%** & **60\%** & **70\%** & **80\%** & **90\%** & **100\%** & **110\%** & **120\%** & **130\%** & **140\%** & **Average** \\ \hline Precision—Sobel & 0.044 & 0.053 & 0.055 & 0.059 & 0.060 & 0.058 & 0.057 & 0.055 & 0.052 & 0.052 & 0.054 \\ Precision—Canny & 0.000 & 0.000 & 0.035 & 0.052 & 0.043 & 0.061 & 0.061 & 0.066 & 0.065 & 0.078 & 0.041 \\ Precision—CIED & 0.267 & 0.412 & 0.246 & 0.241 & 0.198 & 0.271 & 0.162 & 0.245 & 0.221 & 0.196 & **0.246** \\ \hline Recall—Sobel & 0.079 & 0.154 & 0.232 & 0.332 & 0.438 & 0.533 & 0.642 & 0.713 & 0.782 & 0.835 & 0.438 \\ Recall—Canny & 0.000 & 0.000 & 0.011 & 0.025 & 0.034 & 0.064 & 0.083 & 0.112 & 0.128 & 0.175 & 0.061 \\ Recall—CIED & 0.768 & 0.767 & 0.809 & 0.778 & 0.794 & 0.802 & 0.767 & 0.834 & 0.798 & 0.809 & **0.793** \\ \hline F1-score—Sobel & 0.056 & 0.079 & 0.089 & 0.100 & 0.105 & 0.105 & 0.105 & 0.102 & 0.097 & 0.098 & 0.093 \\ F1-score—Canny & 0.000 & 0.000 & 0.017 & 0.034 & 0.038 & 0.062 & 0.071 & 0.083 & 0.086 & 0.108 & 0.046 \\ F1-score—CIED & 0.397 & 0.536 & 0.377 & 0.368 & 0.318 & 0.406 & 0.268 & 0.378 & 0.346 & 0.316 & **0.371** \\ \hline \end{tabular}  
* The average results of the CIED are highlighted in italics, while the optimal values are highlighted in bold.  
\end{table} 
Table 3: _Cont._based on the experimental data, it can be clearly concluded that Otsu has the best overall result in the performance impact of different thresholding methods on the CIED method. The CIED has more significant advantages over several traditional and improved edge detection methods, which include Prewitt, Sobel, and Canny as well as Canny-Median and WL operators. Prewitt and Sobel perform similarly in that is difficult to accurately locate edge positions with low contrast due to limited sensitivity to small changes in pixel intensity, resulting in weak edge strength and visually almost invisible clear edges [11]. Canny and Canny-Median algorithms perform similarly. To further eliminate the noise in the image, Canny-Median adds the processing of median filtering to the image, which further suppresses the image noise [20]. Canny and Canny-Median are equally susceptible to their gradient magnitude calculations at low contrasts, resulting in weaker edges being suppressed because the magnitude does not reach the threshold, thus making edge detection incomplete, while at higher contrasts they extract more false edges, and the performance of edge detection is not stable at different contrasts. The WL algorithm calculates the local intensity mean of the \(3\times 3\) neighborhood and the local signal energy variation between the neighborhoods, and it determines whether it is an edge point based on the calculated value of the local signal energy variation. It makes the results of the edge detection highly adaptive, and it has good  
intuitive and quantitative evaluation, the CIED has good performance. Qualitative analysis shows that CIED is able to extract more complete and continuous edge line segments with less noise. The quantitative analysis further highlights the significant advantage of the CIED. All three metrics achieved their highest values, with a mean precision of 0.408, a mean recall of 0.917, and a mean F1-score of 0.550. It indicates that our algorithm can have better edge detection performance in different types of medical images. To more intuitively observe the performance of different methods at different contrasts, we scaled the original contrast of the medical images in equal proportions and detected the edges. The CIED extracts complete and clear contour information at any contrast which indicates that the CIED has a high degree of robustness at different contrasts. The CIED method adopts the combination of Gaussian filtering and morphological processing to preprocess medical images. In the morphological processing, the processing method of opening operation followed by closing operation is adopted.