Evaluation Metrics for Segmentation

Assessing the performance of a segmentation model accurately is essential. Unlike image classification where simple accuracy might suffice, segmentation requires evaluating the model's ability to correctly classify each pixel and delineate object boundaries precisely. Standard pixel-level accuracy can be misleading, especially with imbalanced class distributions (e.g., a large background class dominating small foreground objects). Therefore, specialized metrics are commonly used.

Intersection over Union (IoU)

The most widely adopted metric for semantic segmentation is Intersection over Union (IoU), also known as the Jaccard Index. For a given class, IoU measures the overlap between the predicted segmentation mask ($A$) and the ground truth mask ($B$). It's calculated as the area of their intersection divided by the area of their union:

$$J(A, B) = \text{IoU}(A, B) = \frac{|A \cap B|}{|A \cup B|}$$

Here, $|A \cap B|$ represents the number of pixels correctly classified as belonging to the class (true positives), while $|A \cup B|$ represents the total number of pixels present in either the prediction or the ground truth mask for that class. This denominator can also be expressed as $|A| + |B| - |A \cap B|$, which relates it to true positives, false positives, and false negatives.

The IoU score ranges from 0 (no overlap) to 1 (perfect overlap). A higher IoU indicates a better segmentation for that class.

Visualization of Intersection (overlap area) and Union (total area covered by either mask) used in the IoU calculation.

Typically, IoU is computed for each class individually and then averaged across all classes to obtain the mean IoU (mIoU). This provides a single, comprehensive score for the model's performance across the entire dataset or image.

$$\text{mIoU} = \frac{1}{C} \sum_{i=1}^{C} \text{IoU}_i$$

where $C$ is the number of classes and $\text{IoU}_i$ is the IoU for class $i$. mIoU is the standard metric for benchmarking semantic segmentation models on datasets like Pascal VOC, Cityscapes, and ADE20K.

Dice Coefficient (F1 Score)

Another popular metric, especially in medical image analysis, is the Dice Coefficient, also known as the F1 Score adapted for segmentation. It's similar to IoU but mathematically slightly different. It measures the overlap between the predicted mask ($A$) and the ground truth mask ($B$) as:

$$\text{Dice}(A, B) = \frac{2 |A \cap B|}{|A| + |B|}$$

The Dice Coefficient also ranges from 0 to 1, with 1 indicating perfect overlap. Notice that the numerator is twice the intersection, and the denominator is the sum of the sizes of the two sets (masks). Like IoU, it effectively ignores true negatives (correctly identified background pixels), focusing on the agreement on the positive class.

There's a direct relationship between Dice and IoU:

$$\text{Dice} = \frac{2 \times \text{IoU}}{1 + \text{IoU}} \quad \text{and} \quad \text{IoU} = \frac{\text{Dice}}{2 - \text{Dice}}$$

This means they are monotonically related, but Dice tends to yield slightly higher scores than IoU, especially for moderate overlaps. The choice between them often depends on community convention or specific properties desired (Dice is related to the harmonic mean of precision and recall). Similar to mIoU, a mean Dice score can be calculated by averaging the Dice coefficient across all classes.

Other Metrics

While mIoU and mean Dice are dominant, other metrics provide additional insights:

• Pixel Accuracy: The simplest metric, calculating the percentage of pixels correctly classified overall. As mentioned, this can be misleading for imbalanced datasets. $$\text{Pixel Accuracy} = \frac{\text{Number of Correctly Classified Pixels}}{\text{Total Number of Pixels}}$$
• Per-Class Accuracy: The accuracy calculated for each class individually, often averaged to get Mean Accuracy. This gives a better sense of performance on minority classes than overall pixel accuracy.
• Precision and Recall: Standard metrics adapted for segmentation. For a given class, precision measures the proportion of predicted pixels that are correct ($TP / (TP + FP)$), while recall measures the proportion of ground truth pixels that were correctly identified ($TP / (TP + FN)$). The Dice Coefficient is equivalent to the F1 score, which is the harmonic mean of precision and recall.
• Boundary Metrics: Metrics like Boundary F1 Score (BF Score) specifically evaluate the accuracy of the predicted object boundaries, which can be important in applications where precise outlines matter.

Metrics for Instance Segmentation

Evaluating instance segmentation requires considering both detection accuracy (finding the objects) and segmentation quality (mask accuracy). Metrics are often adapted from object detection, like Average Precision (AP), but incorporate mask IoU. Typically, a prediction is considered a true positive only if the bounding box overlaps sufficiently with a ground truth box and the mask IoU between the predicted mask and the ground truth mask exceeds a certain threshold (e.g., 0.5). AP is then calculated by averaging precision over different recall levels, often across multiple mask IoU thresholds (e.g., averaging AP at IoU thresholds from 0.5 to 0.95 in steps of 0.05, as used in the COCO challenge).

Choosing the right metric depends on the specific application requirements. However, for general semantic segmentation tasks, mIoU remains the most common and informative benchmark standard. Understanding how these metrics are calculated and their nuances is essential for correctly interpreting model performance and comparing different segmentation approaches.