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# Copyright 2017 The TensorFlow Authors All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================
"""Perspective Transformer Layer Implementation.
Transform the volume based on 4 x 4 perspective projection matrix.
Reference:
(1) "Perspective Transformer Nets: Perspective Transformer Nets:
Learning Single-View 3D Object Reconstruction without 3D Supervision."
Xinchen Yan, Jimei Yang, Ersin Yumer, Yijie Guo, Honglak Lee. In NIPS 2016
https://papers.nips.cc/paper/6206-perspective-transformer-nets-learning-single-view-3d-object-reconstruction-without-3d-supervision.pdf
(2) Official implementation in Torch: https://github.com/xcyan/ptnbhwd
(3) 2D Transformer implementation in TF:
github.com/tensorflow/models/tree/master/research/transformer
"""
import tensorflow as tf
def transformer(voxels,
theta,
out_size,
z_near,
z_far,
name='PerspectiveTransformer'):
"""Perspective Transformer Layer.
Args:
voxels: A tensor of size [num_batch, depth, height, width, num_channels].
It is the output of a deconv/upsampling conv network (tf.float32).
theta: A tensor of size [num_batch, 16].
It is the inverse camera transformation matrix (tf.float32).
out_size: A tuple representing the size of output of
transformer layer (float).
z_near: A number representing the near clipping plane (float).
z_far: A number representing the far clipping plane (float).
Returns:
A transformed tensor (tf.float32).
"""
def _repeat(x, n_repeats):
with tf.variable_scope('_repeat'):
rep = tf.transpose(
tf.expand_dims(tf.ones(shape=tf.stack([
n_repeats,
])), 1), [1, 0])
rep = tf.to_int32(rep)
x = tf.matmul(tf.reshape(x, (-1, 1)), rep)
return tf.reshape(x, [-1])
def _interpolate(im, x, y, z, out_size):
"""Bilinear interploation layer.
Args:
im: A 5D tensor of size [num_batch, depth, height, width, num_channels].
It is the input volume for the transformation layer (tf.float32).
x: A tensor of size [num_batch, out_depth, out_height, out_width]
representing the inverse coordinate mapping for x (tf.float32).
y: A tensor of size [num_batch, out_depth, out_height, out_width]
representing the inverse coordinate mapping for y (tf.float32).
z: A tensor of size [num_batch, out_depth, out_height, out_width]
representing the inverse coordinate mapping for z (tf.float32).
out_size: A tuple representing the output size of transformation layer
(float).
Returns:
A transformed tensor (tf.float32).
"""
with tf.variable_scope('_interpolate'):
num_batch = im.get_shape().as_list()[0]
depth = im.get_shape().as_list()[1]
height = im.get_shape().as_list()[2]
width = im.get_shape().as_list()[3]
channels = im.get_shape().as_list()[4]
x = tf.to_float(x)
y = tf.to_float(y)
z = tf.to_float(z)
depth_f = tf.to_float(depth)
height_f = tf.to_float(height)
width_f = tf.to_float(width)
# Number of disparity interpolated.
out_depth = out_size[0]
out_height = out_size[1]
out_width = out_size[2]
zero = tf.zeros([], dtype='int32')
# 0 <= z < depth, 0 <= y < height & 0 <= x < width.
max_z = tf.to_int32(tf.shape(im)[1] - 1)
max_y = tf.to_int32(tf.shape(im)[2] - 1)
max_x = tf.to_int32(tf.shape(im)[3] - 1)
# Converts scale indices from [-1, 1] to [0, width/height/depth].
x = (x + 1.0) * (width_f) / 2.0
y = (y + 1.0) * (height_f) / 2.0
z = (z + 1.0) * (depth_f) / 2.0
x0 = tf.to_int32(tf.floor(x))
x1 = x0 + 1
y0 = tf.to_int32(tf.floor(y))
y1 = y0 + 1
z0 = tf.to_int32(tf.floor(z))
z1 = z0 + 1
x0_clip = tf.clip_by_value(x0, zero, max_x)
x1_clip = tf.clip_by_value(x1, zero, max_x)
y0_clip = tf.clip_by_value(y0, zero, max_y)
y1_clip = tf.clip_by_value(y1, zero, max_y)
z0_clip = tf.clip_by_value(z0, zero, max_z)
z1_clip = tf.clip_by_value(z1, zero, max_z)
dim3 = width
dim2 = width * height
dim1 = width * height * depth
base = _repeat(
tf.range(num_batch) * dim1, out_depth * out_height * out_width)
base_z0_y0 = base + z0_clip * dim2 + y0_clip * dim3
base_z0_y1 = base + z0_clip * dim2 + y1_clip * dim3
base_z1_y0 = base + z1_clip * dim2 + y0_clip * dim3
base_z1_y1 = base + z1_clip * dim2 + y1_clip * dim3
idx_z0_y0_x0 = base_z0_y0 + x0_clip
idx_z0_y0_x1 = base_z0_y0 + x1_clip
idx_z0_y1_x0 = base_z0_y1 + x0_clip
idx_z0_y1_x1 = base_z0_y1 + x1_clip
idx_z1_y0_x0 = base_z1_y0 + x0_clip
idx_z1_y0_x1 = base_z1_y0 + x1_clip
idx_z1_y1_x0 = base_z1_y1 + x0_clip
idx_z1_y1_x1 = base_z1_y1 + x1_clip
# Use indices to lookup pixels in the flat image and restore
# channels dim
im_flat = tf.reshape(im, tf.stack([-1, channels]))
im_flat = tf.to_float(im_flat)
i_z0_y0_x0 = tf.gather(im_flat, idx_z0_y0_x0)
i_z0_y0_x1 = tf.gather(im_flat, idx_z0_y0_x1)
i_z0_y1_x0 = tf.gather(im_flat, idx_z0_y1_x0)
i_z0_y1_x1 = tf.gather(im_flat, idx_z0_y1_x1)
i_z1_y0_x0 = tf.gather(im_flat, idx_z1_y0_x0)
i_z1_y0_x1 = tf.gather(im_flat, idx_z1_y0_x1)
i_z1_y1_x0 = tf.gather(im_flat, idx_z1_y1_x0)
i_z1_y1_x1 = tf.gather(im_flat, idx_z1_y1_x1)
# Finally calculate interpolated values.
x0_f = tf.to_float(x0)
x1_f = tf.to_float(x1)
y0_f = tf.to_float(y0)
y1_f = tf.to_float(y1)
z0_f = tf.to_float(z0)
z1_f = tf.to_float(z1)
# Check the out-of-boundary case.
x0_valid = tf.to_float(
tf.less_equal(x0, max_x) & tf.greater_equal(x0, 0))
x1_valid = tf.to_float(
tf.less_equal(x1, max_x) & tf.greater_equal(x1, 0))
y0_valid = tf.to_float(
tf.less_equal(y0, max_y) & tf.greater_equal(y0, 0))
y1_valid = tf.to_float(
tf.less_equal(y1, max_y) & tf.greater_equal(y1, 0))
z0_valid = tf.to_float(
tf.less_equal(z0, max_z) & tf.greater_equal(z0, 0))
z1_valid = tf.to_float(
tf.less_equal(z1, max_z) & tf.greater_equal(z1, 0))
w_z0_y0_x0 = tf.expand_dims(((x1_f - x) * (y1_f - y) *
(z1_f - z) * x1_valid * y1_valid * z1_valid),
1)
w_z0_y0_x1 = tf.expand_dims(((x - x0_f) * (y1_f - y) *
(z1_f - z) * x0_valid * y1_valid * z1_valid),
1)
w_z0_y1_x0 = tf.expand_dims(((x1_f - x) * (y - y0_f) *
(z1_f - z) * x1_valid * y0_valid * z1_valid),
1)
w_z0_y1_x1 = tf.expand_dims(((x - x0_f) * (y - y0_f) *
(z1_f - z) * x0_valid * y0_valid * z1_valid),
1)
w_z1_y0_x0 = tf.expand_dims(((x1_f - x) * (y1_f - y) *
(z - z0_f) * x1_valid * y1_valid * z0_valid),
1)
w_z1_y0_x1 = tf.expand_dims(((x - x0_f) * (y1_f - y) *
(z - z0_f) * x0_valid * y1_valid * z0_valid),
1)
w_z1_y1_x0 = tf.expand_dims(((x1_f - x) * (y - y0_f) *
(z - z0_f) * x1_valid * y0_valid * z0_valid),
1)
w_z1_y1_x1 = tf.expand_dims(((x - x0_f) * (y - y0_f) *
(z - z0_f) * x0_valid * y0_valid * z0_valid),
1)
output = tf.add_n([
w_z0_y0_x0 * i_z0_y0_x0, w_z0_y0_x1 * i_z0_y0_x1,
w_z0_y1_x0 * i_z0_y1_x0, w_z0_y1_x1 * i_z0_y1_x1,
w_z1_y0_x0 * i_z1_y0_x0, w_z1_y0_x1 * i_z1_y0_x1,
w_z1_y1_x0 * i_z1_y1_x0, w_z1_y1_x1 * i_z1_y1_x1
])
return output
def _meshgrid(depth, height, width, z_near, z_far):
with tf.variable_scope('_meshgrid'):
x_t = tf.reshape(
tf.tile(tf.linspace(-1.0, 1.0, width), [height * depth]),
[depth, height, width])
y_t = tf.reshape(
tf.tile(tf.linspace(-1.0, 1.0, height), [width * depth]),
[depth, width, height])
y_t = tf.transpose(y_t, [0, 2, 1])
sample_grid = tf.tile(
tf.linspace(float(z_near), float(z_far), depth), [width * height])
z_t = tf.reshape(sample_grid, [height, width, depth])
z_t = tf.transpose(z_t, [2, 0, 1])
z_t = 1 / z_t
d_t = 1 / z_t
x_t /= z_t
y_t /= z_t
x_t_flat = tf.reshape(x_t, (1, -1))
y_t_flat = tf.reshape(y_t, (1, -1))
d_t_flat = tf.reshape(d_t, (1, -1))
ones = tf.ones_like(x_t_flat)
grid = tf.concat([d_t_flat, y_t_flat, x_t_flat, ones], 0)
return grid
def _transform(theta, input_dim, out_size, z_near, z_far):
with tf.variable_scope('_transform'):
num_batch = input_dim.get_shape().as_list()[0]
num_channels = input_dim.get_shape().as_list()[4]
theta = tf.reshape(theta, (-1, 4, 4))
theta = tf.cast(theta, 'float32')
out_depth = out_size[0]
out_height = out_size[1]
out_width = out_size[2]
grid = _meshgrid(out_depth, out_height, out_width, z_near, z_far)
grid = tf.expand_dims(grid, 0)
grid = tf.reshape(grid, [-1])
grid = tf.tile(grid, tf.stack([num_batch]))
grid = tf.reshape(grid, tf.stack([num_batch, 4, -1]))
# Transform A x (x_t', y_t', 1, d_t)^T -> (x_s, y_s, z_s, 1).
t_g = tf.matmul(theta, grid)
z_s = tf.slice(t_g, [0, 0, 0], [-1, 1, -1])
y_s = tf.slice(t_g, [0, 1, 0], [-1, 1, -1])
x_s = tf.slice(t_g, [0, 2, 0], [-1, 1, -1])
z_s_flat = tf.reshape(z_s, [-1])
y_s_flat = tf.reshape(y_s, [-1])
x_s_flat = tf.reshape(x_s, [-1])
input_transformed = _interpolate(input_dim, x_s_flat, y_s_flat, z_s_flat,
out_size)
output = tf.reshape(
input_transformed,
tf.stack([num_batch, out_depth, out_height, out_width, num_channels]))
return output
with tf.variable_scope(name):
output = _transform(theta, voxels, out_size, z_near, z_far)
return output
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