# Seg-Eigen-CAM: Eigen-Value-Based Visual Explanations for Semantic Segmentation Models
## 3 Methods
### Evaluation Metrics and Performance Indicators  
One of the key challenges in developing XAI methods for deep convolutional neural networks is how to objectively evaluate their effectiveness in a rigorous and standardized manner. A major difficulty in this process lies in determining appropriate evaluation metrics that can effectively measure the relevance, fidelity, and overall quality of an explanation. To comprehensively assess the effectiveness of the proposed method, this study adopts the experimental framework established by [PERSON] et al. [19], using the relevance-based element retention approach as the primary evaluation strategy. The evaluation procedure follows a series of steps. First, the generated saliency map \(L^{c}\) is binarized to retain only the highlighted regions, with the remaining areas masked out. Next, the resulting masked image \(I^{H}\) is fed back into the model for prediction. Finally, the relevance of the explanation is measured by comparing the model predictions for the original image, denoted as \(Y\), with those for the masked image, denoted as \(Y^{H}\). The comparison is performed using the Dice score \(Dice^{H}\), which quantifies the similarity between the two sets of predictions. The computation process is defined as follows:  
\[mask_{p}= \begin{cases}1,&\text{if }L^{c}_{p}>\tau,\\ 0,&\text{otherwise.}\end{cases}  \tag{14}\]  
\[I^{H}=I\odot mask \tag{15}\]  
\[Dice^{H}=\frac{2\cdot|Y\cap Y^{H}|}{|Y|+|Y^{H}|} \tag{16}\]  
Here, \(mask\) represents the binarized mask, \(p\in\mathbb{R}^{i\times j}\), and \(\tau\) is the threshold to preserve the highlighted regions. In this study, we set \(\tau=0\) to ensure the integrity of the highlighted regions, thereby preserving fine-grained details in the explanation results. However, this study does not adopt the relevance-based element masking approach as an evaluation metric. This decision is based on experimental observations. When the saliency map exhibits high-intensity activations in the background, the highlighted regions tend to be excessively large. In such cases, extensive masking removes critical information required for the prediction, leading to prediction failures and causing the Dice score to approach zero. Although this metric can reveal the sensitivity of the model, when the masked area is too large, performance differences between explanation methods become less distinguishable, reducing the discriminatory power and effectiveness of the evaluation. In light of these considerations, this study chooses to exclude this metric in order to ensure the reliability of the evaluation results. Recognizing the limitations of a single metric, this study proposes a novel metric of \"Preserved Effectiveness\" (\(PE\)), which integrates the Dice score with the proportion of retained salient regions (\(Retain\)\(Image\)), which is defined as follows:  
\[Retain\;Image(\%)=\frac{\sum_{p}mask_{p}}{\sum_{p}1}\times 100 \tag{17}\]  
\[PE=\frac{Dice^{H}}{Retain\;Image(\%)} \tag{18}\]  
This metric aims to balance the trade-off between effectiveness and efficiency in evaluating explanation methods. Specifically, an ideal saliency map should focus on regions that are most relevant to the model's decision rather than irrelevant or distracting background regions. Although retaining larger salient regions may help maintain a higher Dice score, this approach often compromises the precision of the explanation. Thus, \(PE\) serves as a comprehensive evaluation measure, incorporating the following key aspects:  
1. Relevance--An ideal explanation method should accurately identify the key regions that influence the prediction. The Dice score directly reflects whether the explanation method captures areas crucial to the decision-making process of the model. 2. Low Complexity--A complex explanation incorporates all relevant regions to identify features critical for predictions. However, excessive complexity can diminish interpretability, even when the explanation faithfully represents the model's behavior.