def earth_mover(pcd1, pcd2, radius=1.0):
assert pcd1.shape[1] == pcd2.shape[1]
num_points = tf.cast(pcd1.shape[1], tf.float32)
match = tf_approxmatch.approx_match(pcd1, pcd2)
cost = tf_approxmatch.match_cost(pcd1, pcd2, match)
cost = cost / radius
return tf.reduce_mean(cost / num_points)
def get_emd_loss(pcd1, pcd2,radius):
assert pcd1.shape[1] == pcd2.shape[1]
num_points = tf.cast(pcd1.shape[1], tf.float32)
match = tf_approxmatch.approx_match(pcd1, pcd2)
cost = tf_approxmatch.match_cost(pcd1, pcd2, match)
cost = cost/radius
return tf.reduce_mean(cost / num_points)
def _compute_loss(self, prediction_tensor, target_tensor, weights):
"""
Args:
prediction_tensor (float): A tensor of shape [batch_size, h, w, 3]
target_tensor (float): A tensor of shape [batch_size, h, w, 3]
weights (float): A tensor of shape [batch_size, h, w, 1]
Returns:
loss (float): Approximate Earth Mover's Distance
"""
# Multiply by valid mask
valid_prediction_tensor = prediction_tensor * weights
valid_target_tensor = target_tensor * weights
# Reshape to (batch_size, n_points, 3)
batch_size = prediction_tensor.get_shape()[0]
valid_prediction_points = tf.reshape(valid_prediction_tensor, (batch_size, -1, 3))
valid_target_points = tf.reshape(valid_target_tensor, (batch_size, -1, 3))
match = tf_approxmatch.approx_match(valid_prediction_points, valid_target_points)
distances = tf_approxmatch.match_cost(
valid_prediction_points, valid_target_points, match)
emd_distance = tf.reduce_sum(distances) / tf.cast(batch_size, tf.float32)
return emd_distance
def get_loss(pred, label, end_points):
""" pred: BxNx3,
label: BxNx3, """
dists_forward,_,dists_backward,_ = tf_nndistance.nn_distance(pred, label)
pc_loss = tf.reduce_mean(dists_forward+dists_backward)
end_points['pcloss'] = pc_loss
match = tf_approxmatch.approx_match(label, pred)
loss = tf.reduce_mean(tf_approxmatch.match_cost(label, pred, match))
tf.summary.scalar('loss', loss)
return loss, end_points
def test_emd_negative(self):
"""Test negative point cloud values for computing the approximate Earth Mover's Distance.
"""
# Create test point clouds of shape [batch_size, n_points, 3]
point_cloud_1 = [[[-2., 2., -2.]]]
point_cloud_2 = [[[2., 0., 2.]]]
tf_point_cloud_1 = tf.constant(point_cloud_1)
tf_point_cloud_2 = tf.constant(point_cloud_2)
match = tf_approxmatch.approx_match(tf_point_cloud_1, tf_point_cloud_2)
distance = tf.reduce_mean(tf_approxmatch.match_cost(point_cloud_1, point_cloud_2, match))
with tf.Session() as sess:
match, distance = sess.run([match, distance])
np.testing.assert_almost_equal(distance, 6.0, decimal=2)
def test_emd(self):
"""Test for the approximate algorithm for computing the distance where loss
should be zero.
"""
# Create test point clouds of shape [batch_size, n_points, 3]
point_cloud_1 = [[[1., 1., 1.], [2., 2., 2.], [3., 3., 3.]]]
point_cloud_2 = [[[1., 1., 1.], [2., 2., 2.], [3., 3., 3.]]]
tf_point_cloud_1 = tf.constant(point_cloud_1)
tf_point_cloud_2 = tf.constant(point_cloud_2)
match = tf_approxmatch.approx_match(tf_point_cloud_1, tf_point_cloud_2)
distance = tf.reduce_mean(tf_approxmatch.match_cost(point_cloud_1, point_cloud_2, match))
with tf.Session() as sess:
distance = sess.run([distance])
np.testing.assert_almost_equal(distance, 0)
def test_emd_batch(self):
"""Tests batches for the approximate algorithm for computing the Earth Mover's Distance.
"""
# Create test point clouds of shape [batch_size, n_points, 3]
point_cloud_1 = [[[1., 1., 1.], [2., 2., 2.], [3., 3., 3.]],
[[1., 1., 1.], [2., 2., 2.], [3., 3., 3.]]]
point_cloud_2 = [[[1., 0., 1.], [2., 0., 2.], [3., 0., 3.]],
[[4., 4., 4.], [2., 2., 2.], [3., 3., 3.]]]
tf_point_cloud_1 = tf.constant(point_cloud_1)
tf_point_cloud_2 = tf.constant(point_cloud_2)
match = tf_approxmatch.approx_match(tf_point_cloud_1, tf_point_cloud_2)
distance = tf_approxmatch.match_cost(point_cloud_1, point_cloud_2, match)
with tf.Session() as sess:
match, distance = sess.run([match, distance])
np.testing.assert_almost_equal(distance, [6.0, 5.196152], decimal=2)
def test_emd_2(self):
"""Test for the approximate algorithm for computing the Earth Mover's Distance to see
if match selects closest point, and if the loss is reasonable.
"""
# Create test point clouds of shape [batch_size, n_points, 3]
point_cloud_1 = [[[1., 1., 1.], [2., 2., 2.], [3., 3., 3.]]]
point_cloud_2 = [[[1., 0., 1.], [2., 0., 2.], [3., 0., 3.]]]
tf_point_cloud_1 = tf.constant(point_cloud_1)
tf_point_cloud_2 = tf.constant(point_cloud_2)
match = tf_approxmatch.approx_match(tf_point_cloud_1, tf_point_cloud_2)
distance = tf.reduce_mean(tf_approxmatch.match_cost(point_cloud_1, point_cloud_2, match))
with tf.Session() as sess:
match, distance = sess.run([match, distance])
matched_indices = np.argmax(np.squeeze(match), axis=1)
np.testing.assert_equal(matched_indices, [0, 1, 2])
np.testing.assert_almost_equal(distance, 6.0, decimal=2)