# 2D Semantic Segmentation: Recent Developments and Future Directions
## 5 Common Data Sets and Evaluation Indicators
However, MIoU may underestimate the model's performance on small objects with few pixels. To address this issue, researchers have proposed a weighted MIoU in which each category's IoU is weighted based on the number of pixels in that category. The weight of categories with few pixels is increased in the overall score as shown in Formula (4):  
\[MIoU=\frac{1}{n+1}\sum_{i=0}^{n}\frac{p_{ii}}{\sum\limits_{j=0}^{n}p_{ij}+\sum \limits_{j=0}^{n}p_{ji}-p_{ii}} \tag{4}\]  
FWIoU is an enhancement of MIoU, and it aims to weigh the category of each pixel in accordance with its frequency. FWIoU augments the weight of less frequent categories in the overall score by weighing the IoU of each category, which helps reflect the model's performance across all categories, particularly in data sets with class imbalance. Similar to MIoU, FWIoU comprehensively captures the model's ability to correctly classify pixels of each category (TP), incorrectly classify pixels as other categories (FP), and misclassify pixels of category i as other categories (FN). However, because FWIoU is weighted based on pixel frequency, it may lead to overemphasis on large targets with a high pixel count. This situation implies that when evaluating model performance, FWIoU might pay too much attention to the performance of large targets and could overlook the performance in small targets as shown in Formula (5):  
\[FWIoU=\frac{1}{\sum\limits_{i=0}^{n}\frac{n}{j=0}^{n}}\sum\limits_{p_{ij}=0}^{n }\frac{\sum\limits_{j=0}^{n}p_{ji}p_{ii}}{\sum\limits_{j=0}^{n}p_{ij}+\sum \limits_{j=0}^{n}p_{ji}-p_{ii}} \tag{5}\]  
Cross-entropy loss plays a pivotal role in the training of deep learning models, especially in classification tasks. The cross-entropy error (CEE) is used to represent the residual between the predicted results and the labels. The fundamental idea is that when the model has high confidence in the correct prediction, the CEE decreases. Conversely, if the model has high confidence in the wrong prediction, the CEE increases. Therefore, CEE optimization is about making the model highly confident in the correct prediction. Cross-entropy loss is considered the logarithm of the likelihood function for the correct labels to ensure the differentiability of the loss function. Typically, the base of the logarithm can be either two or the natural constant \(e\). Neural network classifiers trained using CEE have distinct performance advantages over mean squared errors on finite data sets. Cross-entropy describes the dissimilarity between two probability distributions; the smaller the difference is, the closer the two probability distributions are. Through gradient descent, cross-entropy loss continually brings the predicted probability distribution close to the label probability distribution in order to accurately reflect the error between the predicted segmentation results and the labels. However, because the CEE is proportional to the logarithm of the model's predicted probability, it is sensitive to outliers in the model's predictions. This sensitivity could cause the model to overreact to some anomalies, thereby affecting the model's performance. Therefore, when using cross-entropy loss, special attention must be paid to the stability and robustness of model training. The definition of cross-entropy loss is as follows (6):  
\[L_{CEE}=-\frac{1}{n}\sum\limits_{n}\sum\limits_{c}t_{n,c}\log_{a}(y_{n,c}) \tag{6}\]  
In addition to the abovementioned metrics, other performance indicators need to be considered when evaluating the performance of a neural network.