## 3 Results  
The HPO and training were performed together, as shown in Figure 1. The HP-optimized U-Net architecture for P46 is shown in Figure 4b as an example, along with the original U-Net architecture [31] in Figure 4a. P46 had the optimized hyperparameters that resulted in the simplest architecture of all cases. The optimized hyperparameters for the 47 patient cases are summarized in Table A1 in Appendix A. The average time taken for HPO and the training of each patient case (i.e., execution time of Figure 1) ranged between 3 and 9 h, depending on the GPUs and version of Pytorch used (longer time using the authors' workstation and shorter time using Colab with NVIDIA A100 GPU and Pytorch version 2.0.1). The autocontours generated by the HP-optimized U-Net are visually compared against the manual contours for P1, 3, 4, 7, 8, 9, 10, 11, 12, 24, 26, 27, and 32 in Figure 5. In this figure, three sagittal (P12, 16, and 22), three coronal (P24, 26, and 27), and two axial (P28 and 32) prostate cases are shown as examples, where P12 and 22 are the cases with the highest  
Figure 4: **(a)** Original U-Net architecture [31]; **(b)** modified U-Net architecture optimized by CMA-ES for P46 with example input image and output of autocontour. Each blue box represents a block of feature maps whose height \(\times\) width dimensions and number of feature maps are indicated on the left and top of the box, respectively. Each white box represents a copied block of feature maps. The arrows indicate the different matrix operations. and lowest mean DC of all prostate cases, respectively. It is important to emphasize that our algorithm was designed to mimic an individual expert's manual contours, even if the contours are quite unique and not visually intuitive to others. The summary of the computed metrics for all patients is provided in Table 1 in Appendix A. Also, the DC, CD, and HD obtained using the HP-optimized U-Net, non-optimized U-Net, and nnU-Net are graphically compared in Figure 6. As patients were numbered in decreasing order of their mean DC for each site, this pattern of decreasing DC over patient number is seen in Figure 6a. The mean (SD) DC, CD, and HD of the 47 patient cases were  
Figure 5: Example MR images of liver (P1, 3, 4, and 7–11) and prostate patients (sagittal: P12, 16, and 22; coronal: P24, 26, and 27; axial: P28 and 32). First column: original image with red box showing tumor location. Second column: enlarged image patch centered on tumor. Third column: enlarged image patch with manual contours (green line) and autoconours (red line) and their Dice’s coefficient (DC). 0.92 (0.04), 1.35 (1.03) mm, and 3.63 (2.17) mm, respectively, for HP-optimized U-Net; 0.89 (0.14), 1.85 (2.70) mm, and 5.23 (7.96) mm for non-optimized U-Net; and 0.90 (0.05), 1.44 (1.11) mm, and 5.16 (8.38) mm for nnU-Net. In addition, the DC, CD, and HD between the HP-optimized U-Net and the other two methods were compared using the paired \(t\)-test. A \(p\)-value smaller than 0.05 was considered to represent statistical significance. Table 2 shows the number of patient cases with \(p<0.05\) from two-tailed \(t\)-tests, as well as those from one-tailed \(t\)-tests (i.e., right-tailed for DC and left-tailed for CD and HD) out of the 47 patients. The number of patient cases with better mean values for the HP-optimized U-Net is also shown in this table for comparison. The results from the two-tailed \(t\)-tests show that the performance of the proposed method has statistically significant differences for the majority of patient cases, and thus, it can be distinguished from the other two methods. Similarly, the results from the one-tailed \(t\)-tests show that the improvements using the proposed method were statistically significant for the majority of patient cases in terms of DC and HD. Some example contours generated by each method are displayed in Figure 7. The patients shown in this figure are the cases that showed great differences in performance between different methods.