"""
Distance Map
author: Wang Zheng (@Aglargil)
Ref:
- [Distance Map]
(https://cs.brown.edu/people/pfelzens/papers/dt-final.pdf)
"""
import numpy as np
import matplotlib.pyplot as plt
import scipy
INF = 1e20
ENABLE_PLOT = True
def compute_sdf_scipy(obstacles):
"""
Compute the signed distance field (SDF) from a boolean field using scipy.
This function has the same functionality as compute_sdf.
However, by using scipy.ndimage.distance_transform_edt, it can compute much faster.
Example: 500×500 map
• compute_sdf: 3 sec
• compute_sdf_scipy: 0.05 sec
Parameters
----------
obstacles : array_like
A 2D boolean array where '1' represents obstacles and '0' represents free space.
Returns
-------
array_like
A 2D array representing the signed distance field, where positive values indicate distance
to the nearest obstacle, and negative values indicate distance to the nearest free space.
"""
# distance_transform_edt use '0' as obstacles, so we need to convert the obstacles to '0'
a = scipy.ndimage.distance_transform_edt(obstacles == 0)
b = scipy.ndimage.distance_transform_edt(obstacles == 1)
return a - b
def compute_udf_scipy(obstacles):
"""
Compute the unsigned distance field (UDF) from a boolean field using scipy.
This function has the same functionality as compute_udf.
However, by using scipy.ndimage.distance_transform_edt, it can compute much faster.
Example: 500×500 map
• compute_udf: 1.5 sec
• compute_udf_scipy: 0.02 sec
Parameters
----------
obstacles : array_like
A 2D boolean array where '1' represents obstacles and '0' represents free space.
Returns
-------
array_like
A 2D array of distances from the nearest obstacle, with the same dimensions as `bool_field`.
"""
return scipy.ndimage.distance_transform_edt(obstacles == 0)
[docs]
def compute_sdf(obstacles):
"""
Compute the signed distance field (SDF) from a boolean field.
Parameters
----------
obstacles : array_like
A 2D boolean array where '1' represents obstacles and '0' represents free space.
Returns
-------
array_like
A 2D array representing the signed distance field, where positive values indicate distance
to the nearest obstacle, and negative values indicate distance to the nearest free space.
"""
a = compute_udf(obstacles)
b = compute_udf(obstacles == 0)
return a - b
[docs]
def compute_udf(obstacles):
"""
Compute the unsigned distance field (UDF) from a boolean field.
Parameters
----------
obstacles : array_like
A 2D boolean array where '1' represents obstacles and '0' represents free space.
Returns
-------
array_like
A 2D array of distances from the nearest obstacle, with the same dimensions as `bool_field`.
"""
edt = obstacles.copy()
if not np.all(np.isin(edt, [0, 1])):
raise ValueError("Input array should only contain 0 and 1")
edt = np.where(edt == 0, INF, edt)
edt = np.where(edt == 1, 0, edt)
for row in range(len(edt)):
dt(edt[row])
edt = edt.T
for row in range(len(edt)):
dt(edt[row])
edt = edt.T
return np.sqrt(edt)
def dt(d):
"""
Compute 1D distance transform under the squared Euclidean distance
Parameters
----------
d : array_like
Input array containing the distances.
Returns:
--------
d : array_like
The transformed array with computed distances.
"""
v = np.zeros(len(d) + 1)
z = np.zeros(len(d) + 1)
k = 0
v[0] = 0
z[0] = -INF
z[1] = INF
for q in range(1, len(d)):
s = ((d[q] + q * q) - (d[int(v[k])] + v[k] * v[k])) / (2 * q - 2 * v[k])
while s <= z[k]:
k = k - 1
s = ((d[q] + q * q) - (d[int(v[k])] + v[k] * v[k])) / (2 * q - 2 * v[k])
k = k + 1
v[k] = q
z[k] = s
z[k + 1] = INF
k = 0
for q in range(len(d)):
while z[k + 1] < q:
k = k + 1
dx = q - v[k]
d[q] = dx * dx + d[int(v[k])]
def main():
obstacles = np.array(
[
[1, 0, 0, 0, 0],
[0, 1, 1, 1, 0],
[0, 1, 1, 1, 0],
[0, 0, 1, 1, 0],
[0, 0, 1, 0, 0],
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0],
[0, 0, 1, 0, 0],
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0],
]
)
# Compute the signed distance field
sdf = compute_sdf(obstacles)
udf = compute_udf(obstacles)
if ENABLE_PLOT:
_, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(15, 5))
obstacles_plot = ax1.imshow(obstacles, cmap="binary")
ax1.set_title("Obstacles")
ax1.set_xlabel("x")
ax1.set_ylabel("y")
plt.colorbar(obstacles_plot, ax=ax1)
udf_plot = ax2.imshow(udf, cmap="viridis")
ax2.set_title("Unsigned Distance Field")
ax2.set_xlabel("x")
ax2.set_ylabel("y")
plt.colorbar(udf_plot, ax=ax2)
sdf_plot = ax3.imshow(sdf, cmap="RdBu")
ax3.set_title("Signed Distance Field")
ax3.set_xlabel("x")
ax3.set_ylabel("y")
plt.colorbar(sdf_plot, ax=ax3)
plt.tight_layout()
plt.show()
if __name__ == "__main__":
main()