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spatial_transformer.py
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/
spatial_transformer.py
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# Copyright 2016 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.
# ==============================================================================
import tensorflow as tf
def transformer(U, theta, out_size, name='SpatialTransformer', **kwargs):
"""Spatial Transformer Layer
Implements a spatial transformer layer as described in [1]_.
Based on [2]_ and edited by David Dao for Tensorflow.
Parameters
----------
U : float
The output of a convolutional net should have the
shape [num_batch, height, width, num_channels].
theta: float
The output of the
localisation network should be [num_batch, 6].
out_size: tuple of two ints
The size of the output of the network (height, width)
References
----------
.. [1] Spatial Transformer Networks
Max Jaderberg, Karen Simonyan, Andrew Zisserman, Koray Kavukcuoglu
Submitted on 5 Jun 2015
.. [2] https://github.com/skaae/transformer_network/blob/master/transformerlayer.py
Notes
-----
To initialize the network to the identity transform init
``theta`` to :
identity = np.array([[1., 0., 0.],
[0., 1., 0.]])
identity = identity.flatten()
theta = tf.Variable(initial_value=identity)
"""
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.cast(rep, 'int32')
x = tf.matmul(tf.reshape(x, (-1, 1)), rep)
return tf.reshape(x, [-1])
def _interpolate(im, x, y, out_size):
with tf.variable_scope('_interpolate'):
# constants
num_batch = tf.shape(im)[0]
height = tf.shape(im)[1]
width = tf.shape(im)[2]
channels = tf.shape(im)[3]
x = tf.cast(x, 'float32')
y = tf.cast(y, 'float32')
height_f = tf.cast(height, 'float32')
width_f = tf.cast(width, 'float32')
out_height = out_size[0]
out_width = out_size[1]
zero = tf.zeros([], dtype='int32')
max_y = tf.cast(tf.shape(im)[1] - 1, 'int32')
max_x = tf.cast(tf.shape(im)[2] - 1, 'int32')
# scale indices from [-1, 1] to [0, width/height]
x = (x + 1.0)*(width_f) / 2.0
y = (y + 1.0)*(height_f) / 2.0
# do sampling
x0 = tf.cast(tf.floor(x), 'int32')
x1 = x0 + 1
y0 = tf.cast(tf.floor(y), 'int32')
y1 = y0 + 1
x0 = tf.clip_by_value(x0, zero, max_x)
x1 = tf.clip_by_value(x1, zero, max_x)
y0 = tf.clip_by_value(y0, zero, max_y)
y1 = tf.clip_by_value(y1, zero, max_y)
dim2 = width
dim1 = width*height
base = _repeat(tf.range(num_batch)*dim1, out_height*out_width)
base_y0 = base + y0*dim2
base_y1 = base + y1*dim2
idx_a = base_y0 + x0
idx_b = base_y1 + x0
idx_c = base_y0 + x1
idx_d = base_y1 + x1
# 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.cast(im_flat, 'float32')
Ia = tf.gather(im_flat, idx_a)
Ib = tf.gather(im_flat, idx_b)
Ic = tf.gather(im_flat, idx_c)
Id = tf.gather(im_flat, idx_d)
# and finally calculate interpolated values
x0_f = tf.cast(x0, 'float32')
x1_f = tf.cast(x1, 'float32')
y0_f = tf.cast(y0, 'float32')
y1_f = tf.cast(y1, 'float32')
wa = tf.expand_dims(((x1_f-x) * (y1_f-y)), 1)
wb = tf.expand_dims(((x1_f-x) * (y-y0_f)), 1)
wc = tf.expand_dims(((x-x0_f) * (y1_f-y)), 1)
wd = tf.expand_dims(((x-x0_f) * (y-y0_f)), 1)
output = tf.add_n([wa*Ia, wb*Ib, wc*Ic, wd*Id])
return output
def _meshgrid(height, width):
with tf.variable_scope('_meshgrid'):
# This should be equivalent to:
# x_t, y_t = np.meshgrid(np.linspace(-1, 1, width),
# np.linspace(-1, 1, height))
# ones = np.ones(np.prod(x_t.shape))
# grid = np.vstack([x_t.flatten(), y_t.flatten(), ones])
x_t = tf.matmul(tf.ones(shape=tf.stack([height, 1])),
tf.transpose(tf.expand_dims(tf.linspace(-1.0, 1.0, width), 1), [1, 0]))
y_t = tf.matmul(tf.expand_dims(tf.linspace(-1.0, 1.0, height), 1),
tf.ones(shape=tf.stack([1, width])))
x_t_flat = tf.reshape(x_t, (1, -1))
y_t_flat = tf.reshape(y_t, (1, -1))
ones = tf.ones_like(x_t_flat)
grid = tf.concat(axis=0, values=[x_t_flat, y_t_flat, ones])
return grid
def _transform(theta, input_dim, out_size):
with tf.variable_scope('_transform'):
num_batch = tf.shape(input_dim)[0]
height = tf.shape(input_dim)[1]
width = tf.shape(input_dim)[2]
num_channels = tf.shape(input_dim)[3]
theta = tf.reshape(theta, (-1, 2, 3))
theta = tf.cast(theta, 'float32')
# grid of (x_t, y_t, 1), eq (1) in ref [1]
height_f = tf.cast(height, 'float32')
width_f = tf.cast(width, 'float32')
out_height = out_size[0]
out_width = out_size[1]
grid = _meshgrid(out_height, out_width)
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, 3, -1]))
# Transform A x (x_t, y_t, 1)^T -> (x_s, y_s)
T_g = tf.matmul(theta, grid)
x_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_flat = tf.reshape(x_s, [-1])
y_s_flat = tf.reshape(y_s, [-1])
input_transformed = _interpolate(
input_dim, x_s_flat, y_s_flat,
out_size)
output = tf.reshape(
input_transformed, tf.stack([num_batch, out_height, out_width, num_channels]))
return output
with tf.variable_scope(name):
output = _transform(theta, U, out_size)
return output
def batch_transformer(U, thetas, out_size, name='BatchSpatialTransformer'):
"""Batch Spatial Transformer Layer
Parameters
----------
U : float
tensor of inputs [num_batch,height,width,num_channels]
thetas : float
a set of transformations for each input [num_batch,num_transforms,6]
out_size : int
the size of the output [out_height,out_width]
Returns: float
Tensor of size [num_batch*num_transforms,out_height,out_width,num_channels]
"""
with tf.variable_scope(name):
num_batch, num_transforms = map(int, thetas.get_shape().as_list()[:2])
indices = [[i]*num_transforms for i in xrange(num_batch)]
input_repeated = tf.gather(U, tf.reshape(indices, [-1]))
return transformer(input_repeated, thetas, out_size)