## 3 Methods
### Creation of the Supplemented Mask and the Modified Mask Using Redundant Models  
Redundant models are trained using various combinations of training and validation sets from the original dataset. A total of twenty redundant models were trained, with 70% of the data used for training and 30% for validation. The estimated class index, \(\overline{C}\), of a redundant model is determined as:  
\[\overline{C}_{m}=\underset{i}{argmax}\ s_{m}(i) \tag{1}\]  
where \(s_{m}(i)\) is the score for class \(i\) of the \(m\)th model. Out of 20 redundant models, six utilize a sample for validation. The inference results from these six models are similar; however, differences in estimated classes can be used to evaluate the probability (P) of making a correct decision at each pixel location, as shown in Equation (2). \[\mathrm{P}=\mathrm{E}\big{\{}\delta\big{[}\overline{C}-C_{\mathrm{GT}}\big{]} \big{\}}=\Bigg{\{}\sum_{n=1}^{6}\delta\big{[}\overline{C}_{n}-C_{\mathrm{GT}} \big{]}\Bigg{\}}/6 \tag{2}\]  
where \(\delta\big{[}\big{]}\) denotes the Dirac delta function, equal to 1 when the two class indices match and zero otherwise. Conversely, 1-P indicates the level of confusion and is quantized to 5 bits, resulting in 32 levels. These levels are then incorporated into the upper 5 bits of the GT mask to create the supplemented mask. The colormap has been expanded to illustrate the levels of confusion (Figure 7). The whiter the color, the more confused a pixel becomes. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Network Structure** & **Simple Network** & **U-Net** & **DeepLabV3** \\ \hline Number of trainable parameters & 38,021,511 & 41,694,574 & 39,759,047 \\ Percentage difference with & - & +9.7\% & +4.6\% \\ respect to simple network & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of the number of trainable parameters by network structure. Figure 6: The simple network consisting of the base network to extract features and the deconvolution (Deconv.) layers to recover the resolution. Figure 7: The colormap adjusted to intuitively visualize confusion levels. Figure 8 presents four examples of supplemented masks. In Figure 8a, the building mask in the center lacks any actual substance and is therefore marked as confusing in the supplemented mask. In Figure 8b, the absence of masks for the croplands in the center of the image is also noted as confusing. In Figure 8c, a pond located on the left side of the image has no corresponding mask, which is similarly marked as confusing. Finally, in Figure 8d, the presence of artificial edges and missing annotations for forest areas is indicated as confusing. In the four samples, there is a common trend that the areas along the boundaries of different classes are identified as confusing pixels. This is understandable, as it is challenging to define clear boundaries due to human error and limited image resolution. Figure 8: Four examples (**a–d**) that compare the image, original mask, and supplemented mask. The red circles indicate the locations of discrepancies in comparison to the original masks. The precision of the confidence level is determined by multiplying the number of redundant models (M) by the validation data rate for each model. In this study, we set M to 20 and the validation data rate to 0.3, resulting in 6 confidence levels. Figure 9 illustrates the effect of varying M. As M increases, the confidence levels become smoother; however, the training time for the redundant models also increases. Therefore, it is a trade-off parameter, and we concluded that setting M to 20 is appropriate for balancing training time and confidence level precision. Typically, the parameters (\(\theta\)) of a CNN model are optimized to minimize the loss (L) along with certain regularization terms (R), as shown in Equation (3). \[\min_{\theta\in\Theta}\sum_{(I,M)\in\mathrm{T}}\mathrm{L}\left(\widehat{M},M \right)+\lambda\mathrm{R}(\theta) \tag{3}\]  
where \(M\) is the GT score, and \(\widehat{M}\) is the estimated score.