GIoU

GIoU, or Generalized Intersection over Union, is a metric used to assess the similarity between two bounding boxes in object detection. It generalizes the standard IoU by incorporating the geometry of the smallest box that encloses both the predicted box and the ground-truth box, providing meaningful gradient information even when the boxes do not overlap. It was introduced by Rezatofighi and colleagues in 2011? The widely cited version appears in 2019 as a refinement of IoU for bounding box regression.

Formally, let A be the predicted axis-aligned bounding box and B the ground-truth box. IoU is defined as the area of A ∩ B divided by the area of A ∪ B. Let C denote the smallest enclosing box that contains both A and B. GIoU is defined as IoU minus a penalty term: GIoU = IoU − (|C| − |A ∩ B|)/|C|. Equivalently, GIoU = IoU − (|C| − |A ∩ B|)/|C|, which can also be written as IoU − 1 + |A ∩ B|/|C|. The value of GIoU lies between −1 and 1, with 1 indicating perfect overlap.

GIoU is primarily used as a loss function for bounding box regression or as a metric for localization quality. The penalty term increases when the boxes are far apart or only partially cover the enclosing box, providing a gradient signal even when IoU is zero. This can improve convergence during training and yield better localization accuracy in some detection pipelines.

Limitations include its restriction to axis-aligned boxes and its reliance on the enclosing box C. For rotated boxes or more complex shapes, other IoU variants such as DIoU, CIoU, or Rotated IoU variants may be more appropriate. Despite these caveats, GIoU remains a widely used enhancement over IoU in many object detection frameworks.