intersectionoverunion

Intersection over union (IoU), also known as the Jaccard index, is a measure of similarity between two sets and is widely used in computer vision to evaluate segmentation and object detection results. It quantifies how well a predicted region matches a ground-truth region.

For binary masks, IoU is defined as the size of the intersection divided by the size of the union of the predicted mask P and the ground-truth mask G: IoU = |P ∩ G| / |P ∪ G|. In pixel terms, this corresponds to the number of correctly predicted positive pixels divided by the number of pixels that are positive in either the prediction or the ground truth. It can also be expressed as IoU = TP / (TP + FP + FN), where TP, FP, and FN are counts of true positives, false positives, and false negatives.

In practice, IoU is computed per class in semantic segmentation or per instance in instance segmentation, and a mean IoU (mIoU) can be taken across classes. In object detection, IoU is used to compare predicted bounding boxes with ground-truth boxes; a prediction is typically counted as a correct detection if its IoU with the corresponding ground-truth box meets or exceeds a threshold (commonly 0.5).

Related metrics include Dice coefficient, which is defined as 2|P ∩ G| / (|P| + |G|). IoU and Dice are both measures of overlap but emphasize different aspects of similarity. Generalized IoU (GIoU) extends the concept for bounding boxes by incorporating spatial relationships to improve optimization.

Limitations of IoU include sensitivity to object size and class imbalance, and reduced informativeness for complex shapes or partially overlapping regions. It is one of several tools used to assess and compare vision models, often complemented by other metrics.