# Copyright (c) Facebook, Inc. and its affiliates. All Rights Reserved.
reduction: str = "none",
eps: float = 1e-7,
) -> torch.Tensor:
Generalized Intersection over Union Loss (Hamid Rezatofighi et. al)
Gradient-friendly IoU loss with an additional penalty that is non-zero when the
boxes do not overlap and scales with the size of their smallest enclosing box.
This loss is symmetric, so the boxes1 and boxes2 arguments are interchangeable.
boxes1, boxes2 (Tensor): box locations in XYXY format, shape (N, 4) or (4,).
reduction: 'none' | 'mean' | 'sum'
'none': No reduction will be applied to the output.
'mean': The output will be averaged.
'sum': The output will be summed.
eps (float): small number to prevent division by zero
x1, y1, x2, y2 = boxes1.unbind(dim=-1)
x1g, y1g, x2g, y2g = boxes2.unbind(dim=-1)
assert (x2 >= x1).all(), "bad box: x1 larger than x2"
assert (y2 >= y1).all(), "bad box: y1 larger than y2"
# Intersection keypoints
xkis1 = torch.max(x1, x1g)
ykis1 = torch.max(y1, y1g)
xkis2 = torch.min(x2, x2g)
ykis2 = torch.min(y2, y2g)
intsctk = torch.zeros_like(x1)
mask = (ykis2 > ykis1) & (xkis2 > xkis1)
intsctk[mask] = (xkis2[mask] - xkis1[mask]) * (ykis2[mask] - ykis1[mask])
unionk = (x2 - x1) * (y2 - y1) + (x2g - x1g) * (y2g - y1g) - intsctk
iouk = intsctk / (unionk + eps)
# smallest enclosing box
xc1 = torch.min(x1, x1g)
yc1 = torch.min(y1, y1g)
xc2 = torch.max(x2, x2g)
yc2 = torch.max(y2, y2g)
area_c = (xc2 - xc1) * (yc2 - yc1)
miouk = iouk - ((area_c - unionk) / (area_c + eps))
loss = 1 - miouk
if reduction == "mean":
loss = loss.mean() if loss.numel() > 0 else 0.0 * loss.sum()
elif reduction == "sum":
loss = loss.sum()