Intersection over Union (IoU) is a fundamental metric used in the field of computer vision, particularly in object localization and detection tasks. It serves as a quantitative measure to evaluate how well a predicted bounding box aligns with the ground truth bounding box. The accuracy of this alignment is pivotal for assessing the performance of object detection models.

Steps for Calculating IoU

• Determine the Coordinates: Identify the coordinates of the bottom-left and top-right corners of both the predicted bounding box and the ground truth bounding box.

• Calculate Intersection: Find the coordinates of the intersection rectangle by determining the maximum of the bottom-left corners and the minimum of the top-right corners of the two bounding boxes. If these coordinates do not form a valid rectangle (i.e., if the minimum of the top-right coordinates is less than the maximum of the bottom-left coordinates), then the intersection area is zero.

• Compute Union: Calculate the union of the two boxes by adding their individual areas and subtracting the intersection area.

• Compute IoU: Divide the intersection area by the union area to get the IoU value.

  $$ \text{IoU} = \frac{\text{Area of Intersection}}{\text{Area of Union}} $$

Why IoU in Object Detection

The IoU metric is essential for evaluating object detection models because it directly measures the precision of object localization. A higher IoU value indicates a high overlap between the predicted bounding box and the ground truth, demonstrating greater accuracy in predicting the location and size of the bounding box relative to the ground truth. Consider the following scenarios to understand how IoU reflects different types of overlaps:

• Prediction is within Ground Truth: When the predicted box is entirely inside the ground truth, it may not capture the full extent of the object. Because the intersection is smaller than the real object position (the union), it leads to a lower IoU score. This demonstrates that IoU penalizes underestimation.
• Ground Truth is within Prediction: If the predicted bounding box fully encloses the ground truth, it suggests over-prediction, where the model identifies more area than necessary. This results in a larger union than the real object position (the intersection), thus lowering the IoU score. Hence, IoU penalizes overestimation by highlighting excessive predictions that lack precision.
• Partial Overlap Between Prediction and Ground Truth: This is typically the scenario where IoU scores can be most impacted, often yielding the lowest scores. When the predicted box only partially overlaps with the ground truth, both the lack of complete coverage and inclusion of irrelevant areas contribute to a significant difference between the intersection and the union areas.

IoU is used as a common benchmark to rank a model's performance.