# Contrast-Invariant Edge Detection: A Methodological Advance in Medical Image Analysis
## 4 Experimental Results and Analysis
### Comparison  
To further evaluate the advantages of the CIED, we compare it with other edge detection methods, which include three traditional edge detection operators Prewitt [40], Sobel [41], and Canny [15], and two improved edge detection algorithms, Canny-Median [20] and the WL operator [22]. We evaluate these methods in three ways: intuitive visual evaluation, quantitative evaluation, and contrast-invariant robustness comparison. To intuitively compare the visual effects of different edge detection methods, we present some of the medical edge images for different types and contrasts. Figure 8 shows that Column 1 is the original image of ML_1 to ML_6, Columns 2 to 7 are the edge detection results of Prewitt, Sobel, Canny, Canny_median, WL, and CIED, respectively, and the last columns are the GT of the original images. Each row corresponds to the detected edge result of a specific image using different methods. In the first row MI_1 and second row MI_2 of Figure 8, [PERSON] and [PERSON] can extract edges, except for the region with weak contrast, and miss some edges. Canny and Canny-Median can extract valid edges, but at the same time, many false edges are also extracted. WL and the CIED can distinguish the main edge information, and the CIED is visually better. The edge marked by green rectangles has more complete information and less noise. In the third row MI_3 and fourth row MI_4 of Figure 8, where the contrast is low, [PERSON] and [PERSON] only extract a few edges. The Canny, Canny-Median, and WL operators can extract correct edges but miss some edge information. The CIED can extract complete edges, and the edges marked by the green rectangles can only be extracted by CIED. In the fifth row MI_5 and sixth row MI_6 of Figure 8, where the contrast is much weaker, [PERSON] and [PERSON] almost extract nothing. Canny and Canny-Median only extract part of the edge information. The WL operator and the CIED extract better edges. As marked by the green rectangle, the CIED extracts clearer and more complete edges with less noise. From the visual results of edge detection, the visual performances of Prewitt and Sobel are similar; they can extract edge information, but many edges are lost at low contrast, and even no edge information is extracted at extreme contrast. Canny and Canny-Median visual performances are similar, with more false edges extracted at higher contrast, and incomplete edges extracted at lower contrast, but overall better than Prewitt and Sobel. The WL operator performs better than Canny and Canny-Median. It can still extract the edge information more completely in the case of weak contrast, but the WL algorithm is accompanied by more noise interference. CIED has the best visual performance, extracting complete contours despite very low contrast. In addition, the CIED has better continuity of edge line segments and less noise. To further quantitatively analyze the edge detection methods, we also utilize accuracy, precision, recall, and F1-score to evaluate the performance of edge detection comprehensively. Table 2 shows the average metric results for different methods. The evaluation metric results of the CIED are indicated in italics, while the optimal values are highlighted in bold. The CIED method attained the highest average accuracy of 0.978, average precision of 0.408, average recall of 0.917, and average F1-score of 0.550 among all methods. These results indicate that CIED performs well. It shows that CIED can efficiently detect most target edges while balancing the corresponding accuracy. On the other hand, the CIED can  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline
**Evaluation Metrics** & **10\%** & **20\%** & **30\%** & **40\%** & **50\%** & **60\%** & **70\%** & **80\%** & **90\%** & **100\%** & **Average** \\ \hline Accuracy & 0.985 & 0.984 & 0.983 & 0.972 & 0.975 &  
reduce edge omissions when dealing with low-contrast medical images.