# 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, _maybe_jit_unused 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()) @_maybe_jit_unused 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 @classmethod @_maybe_jit_unused 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)