mmcv.ops.box_iou_rotated

mmcv.ops.box_iou_rotated(bboxes1: torch.Tensor, bboxes2: torch.Tensor, mode: str = 'iou', aligned: bool = False, clockwise: bool = True) → torch.Tensor

Return intersection-over-union (Jaccard index) of boxes.

Both sets of boxes are expected to be in (x_center, y_center, width, height, angle) format.

If aligned is False, then calculate the ious between each bbox of bboxes1 and bboxes2, otherwise the ious between each aligned pair of bboxes1 and bboxes2.

Note

The operator assumes:

1. The positive direction along x axis is left -> right.

2. The positive direction along y axis is top -> down.

3. The w border is in parallel with x axis when angle = 0.

However, there are 2 opposite definitions of the positive angular direction, clockwise (CW) and counter-clockwise (CCW). MMCV supports both definitions and uses CW by default.

Please set clockwise=False if you are using the CCW definition.

The coordinate system when clockwise is True (default)

0-------------------> x (0 rad)
|  A-------------B
|  |             |
|  |     box     h
|  |   angle=0   |
|  D------w------C
v
y (pi/2 rad)

In such coordination system the rotation matrix is

\[\begin{split}\begin{pmatrix} \cos\alpha & -\sin\alpha \\ \sin\alpha & \cos\alpha \end{pmatrix}\end{split}\]

The coordinates of the corner point A can be calculated as:

\[\begin{split}P_A= \begin{pmatrix} x_A \\ y_A\end{pmatrix} = \begin{pmatrix} x_{center} \\ y_{center}\end{pmatrix} + \begin{pmatrix}\cos\alpha & -\sin\alpha \\ \sin\alpha & \cos\alpha\end{pmatrix} \begin{pmatrix} -0.5w \\ -0.5h\end{pmatrix} \\ = \begin{pmatrix} x_{center}-0.5w\cos\alpha+0.5h\sin\alpha \\ y_{center}-0.5w\sin\alpha-0.5h\cos\alpha\end{pmatrix}\end{split}\]

The coordinate system when clockwise is False

0-------------------> x (0 rad)
|  A-------------B
|  |             |
|  |     box     h
|  |   angle=0   |
|  D------w------C
v
y (-pi/2 rad)

In such coordination system the rotation matrix is

\[\begin{split}\begin{pmatrix} \cos\alpha & \sin\alpha \\ -\sin\alpha & \cos\alpha \end{pmatrix}\end{split}\]

The coordinates of the corner point A can be calculated as:

\[\begin{split}P_A= \begin{pmatrix} x_A \\ y_A\end{pmatrix} = \begin{pmatrix} x_{center} \\ y_{center}\end{pmatrix} + \begin{pmatrix}\cos\alpha & \sin\alpha \\ -\sin\alpha & \cos\alpha\end{pmatrix} \begin{pmatrix} -0.5w \\ -0.5h\end{pmatrix} \\ = \begin{pmatrix} x_{center}-0.5w\cos\alpha-0.5h\sin\alpha \\ y_{center}+0.5w\sin\alpha-0.5h\cos\alpha\end{pmatrix}\end{split}\]

Parameters

• boxes1 (torch.Tensor) – rotated bboxes 1. It has shape (N, 5), indicating (x, y, w, h, theta) for each row. Note that theta is in radian.

• boxes2 (torch.Tensor) – rotated bboxes 2. It has shape (M, 5), indicating (x, y, w, h, theta) for each row. Note that theta is in radian.

• mode (str) – “iou” (intersection over union) or iof (intersection over foreground).

• clockwise (bool) – flag indicating whether the positive angular orientation is clockwise. default True. New in version 1.4.3.

Returns

Return the ious betweens boxes. If aligned is False, the shape of ious is (N, M) else (N,).

Return type

torch.Tensor