def _transform(theta, input, downsample_factor):
num_batch, num_channels, height, width = input.shape
theta = T.reshape(theta, (-1, 2, 3))
# grid of (x_t, y_t, 1), eq (1) in ref [1]
out_height = T.cast(height / downsample_factor[0], 'int64')
out_width = T.cast(width / downsample_factor[1], 'int64')
grid = _meshgrid(out_height, out_width)
# Transform A x (x_t, y_t, 1)^T -> (x_s, y_s)
T_g = T.dot(theta, grid)
x_s = T_g[:, 0]
y_s = T_g[:, 1]
x_s_flat = x_s.flatten()
y_s_flat = y_s.flatten()
# dimshuffle input to (bs, height, width, channels)
input_dim = input.dimshuffle(0, 2, 3, 1)
input_transformed = _interpolate(
input_dim, x_s_flat, y_s_flat,
out_height, out_width)
output = T.reshape(
input_transformed, (num_batch, out_height, out_width, num_channels))
output = output.dimshuffle(0, 3, 1, 2) # dimshuffle to conv format
return output
def get_output_for(self, input, **kwargs):
if input.ndim > 2:
# if the input has more than two dimensions, flatten it into a
# batch of feature vectors.
input = T.flatten(input, 2)
activation = T.dot(input, self.W)
if self.b is not None:
activation = T.broadcast('+', activation , T.dimshuffle(self.b, 'x', 0), 'xx,1x')
return self.nonlinearity(activation)
def _meshgrid(height, width):
# This function is the grid generator from eq. (1) in reference [1].
# It is equivalent to the following numpy code:
# 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])
# It is implemented in Theano instead to support symbolic grid sizes.
# Note: If the image size is known at layer construction time, we could
# compute the meshgrid offline in numpy instead of doing it dynamically
# in Theano. However, it hardly affected performance when we tried.
x_t = T.dot(T.ones((height, 1)),
_linspace(-1.0, 1.0, width).dimshuffle('x', 0))
y_t = T.dot(_linspace(-1.0, 1.0, height).dimshuffle(0, 'x'),
T.ones((1, width)))
x_t_flat = x_t.reshape((1, -1))
y_t_flat = y_t.reshape((1, -1))
ones = T.ones_like(x_t_flat)
grid = T.concatenate([x_t_flat, y_t_flat, ones], axis=0)
return grid