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from math import sqrt
import torch
def gaussian2D(radius, sigma=1, dtype=torch.float32, device='cpu'):
"""Generate 2D gaussian kernel.
Args:
radius (int): Radius of gaussian kernel.
sigma (int): Sigma of gaussian function. Default: 1.
dtype (torch.dtype): Dtype of gaussian tensor. Default: torch.float32.
device (str): Device of gaussian tensor. Default: 'cpu'.
Returns:
h (Tensor): Gaussian kernel with a
``(2 * radius + 1) * (2 * radius + 1)`` shape.
"""
x = torch.arange(
-radius, radius + 1, dtype=dtype, device=device).view(1, -1)
y = torch.arange(
-radius, radius + 1, dtype=dtype, device=device).view(-1, 1)
h = (-(x * x + y * y) / (2 * sigma * sigma)).exp()
h[h < torch.finfo(h.dtype).eps * h.max()] = 0
return h
def gen_gaussian_target(heatmap, center, radius, k=1):
"""Generate 2D gaussian heatmap.
Args:
heatmap (Tensor): Input heatmap, the gaussian kernel will cover on
it and maintain the max value.
center (list[int]): Coord of gaussian kernel's center.
radius (int): Radius of gaussian kernel.
k (int): Coefficient of gaussian kernel. Default: 1.
Returns:
out_heatmap (Tensor): Updated heatmap covered by gaussian kernel.
"""
diameter = 2 * radius + 1
gaussian_kernel = gaussian2D(
radius, sigma=diameter / 6, dtype=heatmap.dtype, device=heatmap.device)
x, y = center
height, width = heatmap.shape[:2]
left, right = min(x, radius), min(width - x, radius + 1)
top, bottom = min(y, radius), min(height - y, radius + 1)
masked_heatmap = heatmap[y - top:y + bottom, x - left:x + right]
masked_gaussian = gaussian_kernel[radius - top:radius + bottom,
radius - left:radius + right]
out_heatmap = heatmap
torch.max(
masked_heatmap,
masked_gaussian * k,
out=out_heatmap[y - top:y + bottom, x - left:x + right])
return out_heatmap
def gaussian_radius(det_size, min_overlap):
r"""Generate 2D gaussian radius.
This function is modified from the `official github repo
<https://github.com/princeton-vl/CornerNet-Lite/blob/master/core/sample/
utils.py#L65>`_.
Given ``min_overlap``, radius could computed by a quadratic equation
according to Vieta's formulas.
There are 3 cases for computing gaussian radius, details are following:
- Explanation of figure: ``lt`` and ``br`` indicates the left-top and
bottom-right corner of ground truth box. ``x`` indicates the
generated corner at the limited position when ``radius=r``.
- Case1: one corner is inside the gt box and the other is outside.
.. code:: text
|< width >|
lt-+----------+ -
| | | ^
+--x----------+--+
| | | |
| | | | height
| | overlap | |
| | | |
| | | | v
+--+---------br--+ -
| | |
+----------+--x
To ensure IoU of generated box and gt box is larger than ``min_overlap``:
.. math::
\cfrac{(w-r)*(h-r)}{w*h+(w+h)r-r^2} \ge {iou} \quad\Rightarrow\quad
{r^2-(w+h)r+\cfrac{1-iou}{1+iou}*w*h} \ge 0 \\
{a} = 1,\quad{b} = {-(w+h)},\quad{c} = {\cfrac{1-iou}{1+iou}*w*h}
{r} \le \cfrac{-b-\sqrt{b^2-4*a*c}}{2*a}
- Case2: both two corners are inside the gt box.
.. code:: text
|< width >|
lt-+----------+ -
| | | ^
+--x-------+ |
| | | |
| |overlap| | height
| | | |
| +-------x--+
| | | v
+----------+-br -
To ensure IoU of generated box and gt box is larger than ``min_overlap``:
.. math::
\cfrac{(w-2*r)*(h-2*r)}{w*h} \ge {iou} \quad\Rightarrow\quad
{4r^2-2(w+h)r+(1-iou)*w*h} \ge 0 \\
{a} = 4,\quad {b} = {-2(w+h)},\quad {c} = {(1-iou)*w*h}
{r} \le \cfrac{-b-\sqrt{b^2-4*a*c}}{2*a}
- Case3: both two corners are outside the gt box.
.. code:: text
|< width >|
x--+----------------+
| | |
+-lt-------------+ | -
| | | | ^
| | | |
| | overlap | | height
| | | |
| | | | v
| +------------br--+ -
| | |
+----------------+--x
To ensure IoU of generated box and gt box is larger than ``min_overlap``:
.. math::
\cfrac{w*h}{(w+2*r)*(h+2*r)} \ge {iou} \quad\Rightarrow\quad
{4*iou*r^2+2*iou*(w+h)r+(iou-1)*w*h} \le 0 \\
{a} = {4*iou},\quad {b} = {2*iou*(w+h)},\quad {c} = {(iou-1)*w*h} \\
{r} \le \cfrac{-b+\sqrt{b^2-4*a*c}}{2*a}
Args:
det_size (list[int]): Shape of object.
min_overlap (float): Min IoU with ground truth for boxes generated by
keypoints inside the gaussian kernel.
Returns:
radius (int): Radius of gaussian kernel.
"""
height, width = det_size
a1 = 1
b1 = (height + width)
c1 = width * height * (1 - min_overlap) / (1 + min_overlap)
sq1 = sqrt(b1**2 - 4 * a1 * c1)
r1 = (b1 - sq1) / (2 * a1)
a2 = 4
b2 = 2 * (height + width)
c2 = (1 - min_overlap) * width * height
sq2 = sqrt(b2**2 - 4 * a2 * c2)
r2 = (b2 - sq2) / (2 * a2)
a3 = 4 * min_overlap
b3 = -2 * min_overlap * (height + width)
c3 = (min_overlap - 1) * width * height
sq3 = sqrt(b3**2 - 4 * a3 * c3)
r3 = (b3 + sq3) / (2 * a3)
return min(r1, r2, r3)
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