# Copyright (c) Facebook, Inc. and its affiliates.
import math
from typing import List, Tuple
import torch
from detectron2.layers.rotated_boxes import pairwise_iou_rotated
from .boxes import Boxes
class RotatedBoxes(Boxes):
"""
This structure stores a list of rotated boxes as a Nx5 torch.Tensor.
It supports some common methods about boxes
(`area`, `clip`, `nonempty`, etc),
and also behaves like a Tensor
(support indexing, `to(device)`, `.device`, and iteration over all boxes)
"""
def __init__(self, tensor: torch.Tensor):
"""
Args:
tensor (Tensor[float]): a Nx5 matrix. Each row is
(x_center, y_center, width, height, angle),
in which angle is represented in degrees.
While there's no strict range restriction for it,
the recommended principal range is between [-180, 180) degrees.
Assume we have a horizontal box B = (x_center, y_center, width, height),
where width is along the x-axis and height is along the y-axis.
The rotated box B_rot (x_center, y_center, width, height, angle)
can be seen as:
1. When angle == 0:
B_rot == B
2. When angle > 0:
B_rot is obtained by rotating B w.r.t its center by :math:`|angle|` degrees CCW;
3. When angle < 0:
B_rot is obtained by rotating B w.r.t its center by :math:`|angle|` degrees CW.
Mathematically, since the right-handed coordinate system for image space
is (y, x), where y is top->down and x is left->right, the 4 vertices of the
rotated rectangle :math:`(yr_i, xr_i)` (i = 1, 2, 3, 4) can be obtained from
the vertices of the horizontal rectangle :math:`(y_i, x_i)` (i = 1, 2, 3, 4)
in the following way (:math:`\\theta = angle*\\pi/180` is the angle in radians,
:math:`(y_c, x_c)` is the center of the rectangle):
.. math::
yr_i = \\cos(\\theta) (y_i - y_c) - \\sin(\\theta) (x_i - x_c) + y_c,
xr_i = \\sin(\\theta) (y_i - y_c) + \\cos(\\theta) (x_i - x_c) + x_c,
which is the standard rigid-body rotation transformation.
Intuitively, the angle is
(1) the rotation angle from y-axis in image space
to the height vector (top->down in the box's local coordinate system)
of the box in CCW, and
(2) the rotation angle from x-axis in image space
to the width vector (left->right in the box's local coordinate system)
of the box in CCW.
More intuitively, consider the following horizontal box ABCD represented
in (x1, y1, x2, y2): (3, 2, 7, 4),
covering the [3, 7] x [2, 4] region of the continuous coordinate system
which looks like this:
.. code:: none
O--------> x
|
| A---B
| | |
| D---C
|
v y
Note that each capital letter represents one 0-dimensional geometric point
instead of a 'square pixel' here.
In the example above, using (x, y) to represent a point we have:
.. math::
O = (0, 0), A = (3, 2), B = (7, 2), C = (7, 4), D = (3, 4)
We name vector AB = vector DC as the width vector in box's local coordinate system, and
vector AD = vector BC as the height vector in box's local coordinate system. Initially,
when angle = 0 degree, they're aligned with the positive directions of x-axis and y-axis
in the image space, respectively.
For better illustration, we denote the center of the box as E,
.. code:: none
O--------> x
|
| A---B
| | E |
| D---C
|
v y
where the center E = ((3+7)/2, (2+4)/2) = (5, 3).
Also,
.. math::
width = |AB| = |CD| = 7 - 3 = 4,
height = |AD| = |BC| = 4 - 2 = 2.
Therefore, the corresponding representation for the same shape in rotated box in
(x_center, y_center, width, height, angle) format is:
(5, 3, 4, 2, 0),
Now, let's consider (5, 3, 4, 2, 90), which is rotated by 90 degrees
CCW (counter-clockwise) by definition. It looks like this:
.. code:: none
O--------> x
| B-C
| | |
| |E|
| | |
| A-D
v y
The center E is still located at the same point (5, 3), while the vertices
ABCD are rotated by 90 degrees CCW with regard to E:
A = (4, 5), B = (4, 1), C = (6, 1), D = (6, 5)
Here, 90 degrees can be seen as the CCW angle to rotate from y-axis to
vector AD or vector BC (the top->down height vector in box's local coordinate system),
or the CCW angle to rotate from x-axis to vector AB or vector DC (the left->right
width vector in box's local coordinate system).
.. math::
width = |AB| = |CD| = 5 - 1 = 4,
height = |AD| = |BC| = 6 - 4 = 2.
Next, how about (5, 3, 4, 2, -90), which is rotated by 90 degrees CW (clockwise)
by definition? It looks like this:
.. code:: none
O--------> x
| D-A
| | |
| |E|
| | |
| C-B
v y
The center E is still located at the same point (5, 3), while the vertices
ABCD are rotated by 90 degrees CW with regard to E:
A = (6, 1), B = (6, 5), C = (4, 5), D = (4, 1)
.. math::
width = |AB| = |CD| = 5 - 1 = 4,
height = |AD| = |BC| = 6 - 4 = 2.
This covers exactly the same region as (5, 3, 4, 2, 90) does, and their IoU
will be 1. However, these two will generate different RoI Pooling results and
should not be treated as an identical box.
On the other hand, it's easy to see that (X, Y, W, H, A) is identical to
(X, Y, W, H, A+360N), for any integer N. For example (5, 3, 4, 2, 270) would be
identical to (5, 3, 4, 2, -90), because rotating the shape 270 degrees CCW is
equivalent to rotating the same shape 90 degrees CW.
We could rotate further to get (5, 3, 4, 2, 180), or (5, 3, 4, 2, -180):
.. code:: none
O--------> x
|
| C---D
| | E |
| B---A
|
v y
.. math::
A = (7, 4), B = (3, 4), C = (3, 2), D = (7, 2),
width = |AB| = |CD| = 7 - 3 = 4,
height = |AD| = |BC| = 4 - 2 = 2.
Finally, this is a very inaccurate (heavily quantized) illustration of
how (5, 3, 4, 2, 60) looks like in case anyone wonders:
.. code:: none
O--------> x
| B\
| / C
| /E /
| A /
| `D
v y
It's still a rectangle with center of (5, 3), width of 4 and height of 2,
but its angle (and thus orientation) is somewhere between
(5, 3, 4, 2, 0) and (5, 3, 4, 2, 90).
"""
device = tensor.device if isinstance(tensor, torch.Tensor) else torch.device("cpu")
tensor = torch.as_tensor(tensor, dtype=torch.float32, device=device)
if tensor.numel() == 0:
# Use reshape, so we don't end up creating a new tensor that does not depend on
# the inputs (and consequently confuses jit)
tensor = tensor.reshape((0, 5)).to(dtype=torch.float32, device=device)
assert tensor.dim() == 2 and tensor.size(-1) == 5, tensor.size()
self.tensor = tensor
def clone(self) -> "RotatedBoxes":
"""
Clone the RotatedBoxes.
Returns:
RotatedBoxes
"""
return RotatedBoxes(self.tensor.clone())
def to(self, device: torch.device):
# Boxes are assumed float32 and does not support to(dtype)
return RotatedBoxes(self.tensor.to(device=device))
def area(self) -> torch.Tensor:
"""
Computes the area of all the boxes.
Returns:
torch.Tensor: a vector with areas of each box.
"""
box = self.tensor
area = box[:, 2] * box[:, 3]
return area
def normalize_angles(self) -> None:
"""
Restrict angles to the range of [-180, 180) degrees
"""
self.tensor[:, 4] = (self.tensor[:, 4] + 180.0) % 360.0 - 180.0
def clip(self, box_size: Tuple[int, int], clip_angle_threshold: float = 1.0) -> None:
"""
Clip (in place) the boxes by limiting x coordinates to the range [0, width]
and y coordinates to the range [0, height].
For RRPN:
Only clip boxes that are almost horizontal with a tolerance of
clip_angle_threshold to maintain backward compatibility.
Rotated boxes beyond this threshold are not clipped for two reasons:
1. There are potentially multiple ways to clip a rotated box to make it
fit within the image.
2. It's tricky to make the entire rectangular box fit within the image
and still be able to not leave out pixels of interest.
Therefore we rely on ops like RoIAlignRotated to safely handle this.
Args:
box_size (height, width): The clipping box's size.
clip_angle_threshold:
Iff. abs(normalized(angle)) <= clip_angle_threshold (in degrees),
we do the clipping as horizontal boxes.
"""
h, w = box_size
# normalize angles to be within (-180, 180] degrees
self.normalize_angles()
idx = torch.where(torch.abs(self.tensor[:, 4]) <= clip_angle_threshold)[0]
# convert to (x1, y1, x2, y2)
x1 = self.tensor[idx, 0] - self.tensor[idx, 2] / 2.0
y1 = self.tensor[idx, 1] - self.tensor[idx, 3] / 2.0
x2 = self.tensor[idx, 0] + self.tensor[idx, 2] / 2.0
y2 = self.tensor[idx, 1] + self.tensor[idx, 3] / 2.0
# clip
x1.clamp_(min=0, max=w)
y1.clamp_(min=0, max=h)
x2.clamp_(min=0, max=w)
y2.clamp_(min=0, max=h)
# convert back to (xc, yc, w, h)
self.tensor[idx, 0] = (x1 + x2) / 2.0
self.tensor[idx, 1] = (y1 + y2) / 2.0
# make sure widths and heights do not increase due to numerical errors
self.tensor[idx, 2] = torch.min(self.tensor[idx, 2], x2 - x1)
self.tensor[idx, 3] = torch.min(self.tensor[idx, 3], y2 - y1)
def nonempty(self, threshold: float = 0.0) -> torch.Tensor:
"""
Find boxes that are non-empty.
A box is considered empty, if either of its side is no larger than threshold.
Returns:
Tensor: a binary vector which represents
whether each box is empty (False) or non-empty (True).
"""
box = self.tensor
widths = box[:, 2]
heights = box[:, 3]
keep = (widths > threshold) & (heights > threshold)
return keep
def __getitem__(self, item) -> "RotatedBoxes":
"""
Returns:
RotatedBoxes: Create a new :class:`RotatedBoxes` by indexing.
The following usage are allowed:
1. `new_boxes = boxes[3]`: return a `RotatedBoxes` which contains only one box.
2. `new_boxes = boxes[2:10]`: return a slice of boxes.
3. `new_boxes = boxes[vector]`, where vector is a torch.ByteTensor
with `length = len(boxes)`. Nonzero elements in the vector will be selected.
Note that the returned RotatedBoxes might share storage with this RotatedBoxes,
subject to Pytorch's indexing semantics.
"""
if isinstance(item, int):
return RotatedBoxes(self.tensor[item].view(1, -1))
b = self.tensor[item]
assert b.dim() == 2, "Indexing on RotatedBoxes with {} failed to return a matrix!".format(
item
)
return RotatedBoxes(b)
def __len__(self) -> int:
return self.tensor.shape[0]
def __repr__(self) -> str:
return "RotatedBoxes(" + str(self.tensor) + ")"
def inside_box(self, box_size: Tuple[int, int], boundary_threshold: int = 0) -> torch.Tensor:
"""
Args:
box_size (height, width): Size of the reference box covering
[0, width] x [0, height]
boundary_threshold (int): Boxes that extend beyond the reference box
boundary by more than boundary_threshold are considered "outside".
For RRPN, it might not be necessary to call this function since it's common
for rotated box to extend to outside of the image boundaries
(the clip function only clips the near-horizontal boxes)
Returns:
a binary vector, indicating whether each box is inside the reference box.
"""
height, width = box_size
cnt_x = self.tensor[..., 0]
cnt_y = self.tensor[..., 1]
half_w = self.tensor[..., 2] / 2.0
half_h = self.tensor[..., 3] / 2.0
a = self.tensor[..., 4]
c = torch.abs(torch.cos(a * math.pi / 180.0))
s = torch.abs(torch.sin(a * math.pi / 180.0))
# This basically computes the horizontal bounding rectangle of the rotated box
max_rect_dx = c * half_w + s * half_h
max_rect_dy = c * half_h + s * half_w
inds_inside = (
(cnt_x - max_rect_dx >= -boundary_threshold)
& (cnt_y - max_rect_dy >= -boundary_threshold)
& (cnt_x + max_rect_dx < width + boundary_threshold)
& (cnt_y + max_rect_dy < height + boundary_threshold)
)
return inds_inside
def get_centers(self) -> torch.Tensor:
"""
Returns:
The box centers in a Nx2 array of (x, y).
"""
return self.tensor[:, :2]
def scale(self, scale_x: float, scale_y: float) -> None:
"""
Scale the rotated box with horizontal and vertical scaling factors
Note: when scale_factor_x != scale_factor_y,
the rotated box does not preserve the rectangular shape when the angle
is not a multiple of 90 degrees under resize transformation.
Instead, the shape is a parallelogram (that has skew)
Here we make an approximation by fitting a rotated rectangle to the parallelogram.
"""
self.tensor[:, 0] *= scale_x
self.tensor[:, 1] *= scale_y
theta = self.tensor[:, 4] * math.pi / 180.0
c = torch.cos(theta)
s = torch.sin(theta)
# In image space, y is top->down and x is left->right
# Consider the local coordintate system for the rotated box,
# where the box center is located at (0, 0), and the four vertices ABCD are
# A(-w / 2, -h / 2), B(w / 2, -h / 2), C(w / 2, h / 2), D(-w / 2, h / 2)
# the midpoint of the left edge AD of the rotated box E is:
# E = (A+D)/2 = (-w / 2, 0)
# the midpoint of the top edge AB of the rotated box F is:
# F(0, -h / 2)
# To get the old coordinates in the global system, apply the rotation transformation
# (Note: the right-handed coordinate system for image space is yOx):
# (old_x, old_y) = (s * y + c * x, c * y - s * x)
# E(old) = (s * 0 + c * (-w/2), c * 0 - s * (-w/2)) = (-c * w / 2, s * w / 2)
# F(old) = (s * (-h / 2) + c * 0, c * (-h / 2) - s * 0) = (-s * h / 2, -c * h / 2)
# After applying the scaling factor (sfx, sfy):
# E(new) = (-sfx * c * w / 2, sfy * s * w / 2)
# F(new) = (-sfx * s * h / 2, -sfy * c * h / 2)
# The new width after scaling tranformation becomes:
# w(new) = |E(new) - O| * 2
# = sqrt[(sfx * c * w / 2)^2 + (sfy * s * w / 2)^2] * 2
# = sqrt[(sfx * c)^2 + (sfy * s)^2] * w
# i.e., scale_factor_w = sqrt[(sfx * c)^2 + (sfy * s)^2]
#
# For example,
# when angle = 0 or 180, |c| = 1, s = 0, scale_factor_w == scale_factor_x;
# when |angle| = 90, c = 0, |s| = 1, scale_factor_w == scale_factor_y
self.tensor[:, 2] *= torch.sqrt((scale_x * c) ** 2 + (scale_y * s) ** 2)
# h(new) = |F(new) - O| * 2
# = sqrt[(sfx * s * h / 2)^2 + (sfy * c * h / 2)^2] * 2
# = sqrt[(sfx * s)^2 + (sfy * c)^2] * h
# i.e., scale_factor_h = sqrt[(sfx * s)^2 + (sfy * c)^2]
#
# For example,
# when angle = 0 or 180, |c| = 1, s = 0, scale_factor_h == scale_factor_y;
# when |angle| = 90, c = 0, |s| = 1, scale_factor_h == scale_factor_x
self.tensor[:, 3] *= torch.sqrt((scale_x * s) ** 2 + (scale_y * c) ** 2)
# The angle is the rotation angle from y-axis in image space to the height
# vector (top->down in the box's local coordinate system) of the box in CCW.
#
# angle(new) = angle_yOx(O - F(new))
# = angle_yOx( (sfx * s * h / 2, sfy * c * h / 2) )
# = atan2(sfx * s * h / 2, sfy * c * h / 2)
# = atan2(sfx * s, sfy * c)
#
# For example,
# when sfx == sfy, angle(new) == atan2(s, c) == angle(old)
self.tensor[:, 4] = torch.atan2(scale_x * s, scale_y * c) * 180 / math.pi
[docs] @classmethod
def cat(cls, boxes_list: List["RotatedBoxes"]) -> "RotatedBoxes":
"""
Concatenates a list of RotatedBoxes into a single RotatedBoxes
Arguments:
boxes_list (list[RotatedBoxes])
Returns:
RotatedBoxes: the concatenated RotatedBoxes
"""
assert isinstance(boxes_list, (list, tuple))
if len(boxes_list) == 0:
return cls(torch.empty(0))
assert all([isinstance(box, RotatedBoxes) for box in boxes_list])
# use torch.cat (v.s. layers.cat) so the returned boxes never share storage with input
cat_boxes = cls(torch.cat([b.tensor for b in boxes_list], dim=0))
return cat_boxes
@property
def device(self) -> torch.device:
return self.tensor.device
@torch.jit.unused
def __iter__(self):
"""
Yield a box as a Tensor of shape (5,) at a time.
"""
yield from self.tensor
def pairwise_iou(boxes1: RotatedBoxes, boxes2: RotatedBoxes) -> None:
"""
Given two lists of rotated boxes of size N and M,
compute the IoU (intersection over union)
between **all** N x M pairs of boxes.
The box order must be (x_center, y_center, width, height, angle).
Args:
boxes1, boxes2 (RotatedBoxes):
two `RotatedBoxes`. Contains N & M rotated boxes, respectively.
Returns:
Tensor: IoU, sized [N,M].
"""
return pairwise_iou_rotated(boxes1.tensor, boxes2.tensor)