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import torch
def span_xx_to_cxw(xx_spans):
"""
Args:
xx_spans: tensor, (#windows, 2) or (..., 2), each row is a window of format (st, ed)
Returns:
cxw_spans: tensor, (#windows, 2), each row is a window of format (center=(st+ed)/2, width=(ed-st))
>>> spans = torch.Tensor([[0, 1], [0.2, 0.4]])
>>> span_xx_to_cxw(spans)
tensor([[0.5000, 1.0000],
[0.3000, 0.2000]])
>>> spans = torch.Tensor([[[0, 1], [0.2, 0.4]]])
>>> span_xx_to_cxw(spans)
tensor([[[0.5000, 1.0000],
[0.3000, 0.2000]]])
"""
center = xx_spans.sum(-1) * 0.5
width = xx_spans[..., 1] - xx_spans[..., 0]
return torch.stack([center, width], dim=-1)
def span_cxw_to_xx(cxw_spans):
"""
Args:
cxw_spans: tensor, (#windows, 2) or (..., 2), the last dim is a row denoting a window of format (center, width)
>>> spans = torch.Tensor([[0.5000, 1.0000], [0.3000, 0.2000]])
>>> span_cxw_to_xx(spans)
tensor([[0.0000, 1.0000],
[0.2000, 0.4000]])
>>> spans = torch.Tensor([[[0.5000, 1.0000], [0.3000, 0.2000]]])
>>> span_cxw_to_xx(spans)
tensor([[[0.0000, 1.0000],
[0.2000, 0.4000]]])
"""
x1 = cxw_spans[..., 0] - 0.5 * cxw_spans[..., 1]
x2 = cxw_spans[..., 0] + 0.5 * cxw_spans[..., 1]
return torch.stack([x1, x2], dim=-1)
def temporal_iou(spans1, spans2):
"""
Args:
spans1: (N, 2) torch.Tensor, each row defines a span [st, ed]
spans2: (M, 2) torch.Tensor, ...
Returns:
iou: (N, M) torch.Tensor
union: (N, M) torch.Tensor
>>> test_spans1 = torch.Tensor([[0, 0.2], [0.5, 1.0]])
>>> test_spans2 = torch.Tensor([[0, 0.3], [0., 1.0]])
>>> temporal_iou(test_spans1, test_spans2)
(tensor([[0.6667, 0.2000],
[0.0000, 0.5000]]),
tensor([[0.3000, 1.0000],
[0.8000, 1.0000]]))
"""
areas1 = spans1[:, 1] - spans1[:, 0] # (N, )
areas2 = spans2[:, 1] - spans2[:, 0] # (M, )
left = torch.max(spans1[:, None, 0], spans2[:, 0]) # (N, M)
right = torch.min(spans1[:, None, 1], spans2[:, 1]) # (N, M)
inter = (right - left).clamp(min=0) # (N, M)
union = areas1[:, None] + areas2 - inter # (N, M)
iou = inter / union
return iou, union
def temporal_intersection_over_pred(gt_spans, pred_spans):
""" intersection over the second input spans
Args:
gt_spans: (N, 2),
pred_spans: (M, 2)
Returns:
"""
left = torch.max(gt_spans[:, None, 0], pred_spans[:, 0])
right = torch.min(gt_spans[:, None, 1], pred_spans[:, 1])
inter = (right - left).clamp(min=0) # (N, M)
inter_over_pred = inter / (pred_spans[:, 1] - pred_spans[:, 0])
return inter_over_pred
def generalized_temporal_iou(spans1, spans2):
"""
Generalized IoU from https://giou.stanford.edu/
Also reference to DETR implementation of generalized_box_iou
https://github.com/facebookresearch/detr/blob/master/util/box_ops.py#L40
Args:
spans1: (N, 2) torch.Tensor, each row defines a span in xx format [st, ed]
spans2: (M, 2) torch.Tensor, ...
Returns:
giou: (N, M) torch.Tensor
>>> test_spans1 = torch.Tensor([[0, 0.2], [0.5, 1.0]])
>>> test_spans2 = torch.Tensor([[0, 0.3], [0., 1.0]])
>>> generalized_temporal_iou(test_spans1, test_spans2)
tensor([[ 0.6667, 0.2000],
[-0.2000, 0.5000]])
"""
spans1 = spans1.float()
spans2 = spans2.float()
assert (spans1[:, 1] >= spans1[:, 0]).all()
assert (spans2[:, 1] >= spans2[:, 0]).all()
iou, union = temporal_iou(spans1, spans2)
left = torch.min(spans1[:, None, 0], spans2[:, 0]) # (N, M)
right = torch.max(spans1[:, None, 1], spans2[:, 1]) # (N, M)
enclosing_area = (right - left).clamp(min=0) # (N, M)
return iou - (enclosing_area - union) / enclosing_area
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