/
sampling.py
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/
sampling.py
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import numpy
from chainer import cuda
def l2_norm(x, y):
"""Calculate l2 norm (distance) of `x` and `y`.
Args:
x (numpy.ndarray or cupy): (batch_size, num_point, coord_dim)
y (numpy.ndarray): (batch_size, num_point, coord_dim)
Returns (numpy.ndarray): (batch_size, num_point,)
"""
return ((x - y) ** 2).sum(axis=2)
def farthest_point_sampling(pts, k, initial_idx=None, metrics=l2_norm,
skip_initial=False, indices_dtype=numpy.int32,
distances_dtype=numpy.float32):
"""Batch operation of farthest point sampling
Code referenced from below link by @Graipher
https://codereview.stackexchange.com/questions/179561/farthest-point-algorithm-in-python
Args:
pts (numpy.ndarray or cupy.ndarray): 2-dim array (num_point, coord_dim)
or 3-dim array (batch_size, num_point, coord_dim)
When input is 2-dim array, it is treated as 3-dim array with
`batch_size=1`.
k (int): number of points to sample
initial_idx (int): initial index to start farthest point sampling.
`None` indicates to sample from random index,
in this case the returned value is not deterministic.
metrics (callable): metrics function, indicates how to calc distance.
skip_initial (bool): If True, initial point is skipped to store as
farthest point. It stabilizes the function output.
xp (numpy or cupy):
indices_dtype (): dtype of output `indices`
distances_dtype (): dtype of output `distances`
Returns (tuple): `indices` and `distances`.
indices (numpy.ndarray or cupy.ndarray): 2-dim array (batch_size, k, )
indices of sampled farthest points.
`pts[indices[i, j]]` represents `i-th` batch element of `j-th`
farthest point.
distances (numpy.ndarray or cupy.ndarray): 3-dim array
(batch_size, k, num_point)
"""
if pts.ndim == 2:
# insert batch_size axis
pts = pts[None, ...]
assert pts.ndim == 3
xp = cuda.get_array_module(pts)
batch_size, num_point, coord_dim = pts.shape
indices = xp.zeros((batch_size, k, ), dtype=indices_dtype)
# distances[bs, i, j] is distance between i-th farthest point `pts[bs, i]`
# and j-th input point `pts[bs, j]`.
distances = xp.zeros((batch_size, k, num_point), dtype=distances_dtype)
if initial_idx is None:
indices[:, 0] = xp.random.randint(len(pts))
else:
indices[:, 0] = initial_idx
batch_indices = xp.arange(batch_size)
farthest_point = pts[batch_indices, indices[:, 0]]
# minimum distances to the sampled farthest point
try:
min_distances = metrics(farthest_point[:, None, :], pts)
except Exception as e:
import IPython; IPython.embed()
if skip_initial:
# Override 0-th `indices` by the farthest point of `initial_idx`
indices[:, 0] = xp.argmax(min_distances, axis=1)
farthest_point = pts[batch_indices, indices[:, 0]]
min_distances = metrics(farthest_point[:, None, :], pts)
distances[:, 0, :] = min_distances
for i in range(1, k):
indices[:, i] = xp.argmax(min_distances, axis=1)
farthest_point = pts[batch_indices, indices[:, i]]
dist = metrics(farthest_point[:, None, :], pts)
distances[:, i, :] = dist
min_distances = xp.minimum(min_distances, dist)
return indices, distances
if __name__ == '__main__':
# when num_point = 10000 & k = 1000 & batch_size = 32,
# CPU takes 6 sec, GPU takes 0.5 sec.
from contextlib import contextmanager
from time import time
@contextmanager
def timer(name):
t0 = time()
yield
t1 = time()
print('[{}] done in {:.3f} s'.format(name, t1-t0))
# batch_size = 32
# num_point = 10000
# coord_dim = 2
# k = 1000
# do_plot = False
batch_size = 3
num_point = 100
coord_dim = 2
k = 5
do_plot = True
device = -1
print('num_point', num_point, 'device', device)
if device == -1:
pts = numpy.random.uniform(0, 1, (batch_size, num_point, coord_dim))
else:
import cupy
pts = cupy.random.uniform(0, 1, (batch_size, num_point, coord_dim))
with timer('1st'):
farthest_indices, distances = farthest_point_sampling(pts, k)
with timer('2nd'): # time measuring twice.
farthest_indices, distances = farthest_point_sampling(pts, k)
with timer('3rd'): # time measuring twice.
farthest_indices, distances = farthest_point_sampling(
pts, k, skip_initial=True)
# with timer('gpu'):
# farthest_indices = farthest_point_sampling_gpu(pts, k)
print('farthest_indices', farthest_indices.shape, type(farthest_indices))
if do_plot:
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
import os
pts = cuda.to_cpu(pts)
farthest_indices = cuda.to_cpu(farthest_indices)
if not os.path.exists('results'):
os.mkdir('results')
for index in range(batch_size):
fig, ax = plt.subplots()
plt.grid(False)
plt.scatter(pts[index, :, 0], pts[index, :, 1], c='k', s=4)
plt.scatter(pts[index, farthest_indices[index], 0], pts[index, farthest_indices[index], 1], c='r', s=4)
# plt.show()
plt.savefig('results/farthest_point_sampling_{}.png'.format(index))
# --- To extract farthest_points, you can use this kind of advanced indexing ---
farthest_points = pts[numpy.arange(batch_size)[:, None],
farthest_indices, :]
print('farthest_points', farthest_points.shape)
for index in range(batch_size):
farthest_pts_index = pts[index, farthest_indices[index], :]
print('farthest', farthest_points[index].shape,
farthest_pts_index.shape,
numpy.sum(farthest_points[index] - farthest_pts_index))
assert numpy.allclose(farthest_points[index], farthest_pts_index)