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tvnet.py
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tvnet.py
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import numpy as np
import tensorflow as tf
import spatial_transformer
class TVNet(object):
GRAD_IS_ZERO = 1e-12
def __init__(self):
pass
def grey_scale_image(self, x):
assert len(x.shape) == 4
assert x.shape[-1].value == 3, 'number of channels must be 3 (i.e. RGB)'
ker_init = tf.constant_initializer([[0.114], [0.587], [0.299]])
grey_x = tf.layers.conv2d(x, 1, [1, 1], padding='same',
kernel_initializer=ker_init, use_bias=False, trainable=False)
return tf.floor(grey_x)
def normalize_images(self, x1, x2):
reduction_axes = [i for i in xrange(1, len(x1.shape))]
min_x1 = tf.reduce_min(x1, axis=reduction_axes)
max_x1 = tf.reduce_max(x1, axis=reduction_axes)
min_x2 = tf.reduce_min(x2, axis=reduction_axes)
max_x2 = tf.reduce_max(x2, axis=reduction_axes)
min_val = tf.minimum(min_x1, min_x2)
max_val = tf.maximum(max_x1, max_x2)
den = max_val - min_val
expand_dims = [-1 if i == 0 else 1 for i in xrange(len(x1.shape))]
min_val_ex = tf.reshape(min_val, expand_dims)
den_ex = tf.reshape(den, expand_dims)
x1_norm = tf.where(den > 0, 255. * (x1 - min_val_ex) / den_ex, x1)
x2_norm = tf.where(den > 0, 255. * (x2 - min_val_ex) / den_ex, x2)
return x1_norm, x2_norm
def gaussian_smooth(self, x):
assert len(x.shape) == 4
ker_init = tf.constant_initializer([[0.000874, 0.006976, 0.01386, 0.006976, 0.000874],
[0.006976, 0.0557, 0.110656, 0.0557, 0.006976],
[0.01386, 0.110656, 0.219833, 0.110656, 0.01386],
[0.006976, 0.0557, 0.110656, 0.0557, 0.006976],
[0.000874, 0.006976, 0.01386, 0.006976, 0.000874]])
smooth_x = tf.layers.conv2d(x, x.shape[-1].value, [5, 5], padding='same',
kernel_initializer=ker_init, use_bias=False, trainable=False)
return smooth_x
def warp_image(self, x, u, v):
assert len(x.shape) == 4
assert len(u.shape) == 3
assert len(v.shape) == 3
u = u / x.shape[2].value * 2
v = v / x.shape[1].value * 2
delta = tf.concat(axis=1, values=[u, v])
return spatial_transformer.transformer(x, delta, (x.shape[-3].value, x.shape[-2].value))
def centered_gradient(self, x, name):
assert len(x.shape) == 4
with tf.variable_scope('centered_gradient'):
x_ker_init = tf.constant_initializer([[-0.5, 0, 0.5]])
diff_x = tf.layers.conv2d(x, x.shape[-1].value, [1, 3], padding='same',
kernel_initializer=x_ker_init, use_bias=False, name=name + '_diff_x',
trainable=False)
y_ker_init = tf.constant_initializer([[-0.5], [0], [0.5]])
diff_y = tf.layers.conv2d(x, x.shape[-1].value, [3, 1], padding='same',
kernel_initializer=y_ker_init, use_bias=False, name=name + '_diff_y',
trainable=False)
# refine the boundary
first_col = 0.5 * (tf.slice(x, [0, 0, 1, 0], [-1, x.shape[1].value, 1, x.shape[3].value]) -
tf.slice(x, [0, 0, 0, 0], [-1, x.shape[1].value, 1, x.shape[3].value]))
last_col = 0.5 * (
tf.slice(x, [0, 0, x.shape[2].value - 1, 0], [-1, x.shape[1].value, 1, x.shape[3].value]) -
tf.slice(x, [0, 0, x.shape[2].value - 2, 0], [-1, x.shape[1].value, 1, x.shape[3].value]))
diff_x_valid = tf.slice(diff_x, begin=[0, 0, 1, 0],
size=[-1, x.shape[1].value, x.shape[2].value - 2, x.shape[3].value])
diff_x = tf.concat(axis=2, values=[first_col, diff_x_valid, last_col])
first_row = 0.5 * (tf.slice(x, [0, 1, 0, 0], [-1, 1, x.shape[2].value, x.shape[3].value]) -
tf.slice(x, [0, 0, 0, 0], [-1, 1, x.shape[2].value, x.shape[3].value]))
last_row = 0.5 * (
tf.slice(x, [0, x.shape[1].value - 1, 0, 0], [-1, 1, x.shape[2].value, x.shape[3].value]) -
tf.slice(x, [0, x.shape[1].value - 2, 0, 0], [-1, 1, x.shape[2].value, x.shape[3].value]))
diff_y_valid = tf.slice(diff_y, begin=[0, 1, 0, 0],
size=[-1, x.shape[1].value - 2, x.shape[2].value, x.shape[3].value])
diff_y = tf.concat(axis=1, values=[first_row, diff_y_valid, last_row])
return diff_x, diff_y
def forward_gradient(self, x, name):
assert len(x.shape) == 4
with tf.variable_scope('forward_gradient'):
x_ker_init = tf.constant_initializer([[-1, 1]])
diff_x = tf.layers.conv2d(x, x.shape[-1].value, [1, 2], padding='same',
kernel_initializer=x_ker_init, use_bias=False, name=name + '_diff_x',
trainable=True)
y_ker_init = tf.constant_initializer([[-1], [1]])
diff_y = tf.layers.conv2d(x, x.shape[-1].value, [2, 1], padding='same',
kernel_initializer=y_ker_init, use_bias=False, name=name + '_diff_y',
trainable=True)
# refine the boundary
diff_x_valid = tf.slice(diff_x, begin=[0, 0, 0, 0],
size=[-1, x.shape[1].value, x.shape[2].value - 1, x.shape[3].value])
last_col = tf.zeros([tf.shape(x)[0], x.shape[1].value, 1, x.shape[3].value], dtype=tf.float32)
diff_x = tf.concat(axis=2, values=[diff_x_valid, last_col])
diff_y_valid = tf.slice(diff_y, begin=[0, 0, 0, 0],
size=[-1, x.shape[1].value - 1, x.shape[2].value, x.shape[3].value])
last_row = tf.zeros([tf.shape(x)[0], 1, x.shape[2].value, x.shape[3].value], dtype=tf.float32)
diff_y = tf.concat(axis=1, values=[diff_y_valid, last_row])
return diff_x, diff_y
def divergence(self, x, y, name):
assert len(x.shape) == 4
with tf.variable_scope('divergence'):
x_valid = tf.slice(x, begin=[0, 0, 0, 0],
size=[-1, x.shape[1].value, x.shape[2].value - 1, x.shape[3].value])
first_col = tf.zeros([tf.shape(x)[0], x.shape[1].value, 1, x.shape[3].value], dtype=tf.float32)
x_pad = tf.concat(axis=2, values=[first_col, x_valid])
y_valid = tf.slice(y, begin=[0, 0, 0, 0],
size=[-1, y.shape[1].value - 1, y.shape[2].value, y.shape[3].value])
first_row = tf.zeros([tf.shape(y)[0], 1, y.shape[2].value, y.shape[3].value], dtype=tf.float32)
y_pad = tf.concat(axis=1, values=[first_row, y_valid])
x_ker_init = tf.constant_initializer([[-1, 1]])
diff_x = tf.layers.conv2d(x_pad, x.shape[-1].value, [1, 2], padding='same',
kernel_initializer=x_ker_init, use_bias=False, name=name + '_diff_x',
trainable=True)
y_ker_init = tf.constant_initializer([[-1], [1]])
diff_y = tf.layers.conv2d(y_pad, y.shape[-1].value, [2, 1], padding='same',
kernel_initializer=y_ker_init, use_bias=False, name=name + '_diff_y',
trainable=True)
div = diff_x + diff_y
return div
def zoom_size(self, height, width, factor):
new_height = int(float(height) * factor + 0.5)
new_width = int(float(width) * factor + 0.5)
return new_height, new_width
def zoom_image(self, x, new_height, new_width):
assert len(x.shape) == 4
delta = tf.zeros((tf.shape(x)[0], 2, new_height * new_width))
zoomed_x = spatial_transformer.transformer(x, delta, (new_height, new_width))
return tf.reshape(zoomed_x, [tf.shape(x)[0], new_height, new_width, x.shape[-1].value])
def dual_tvl1_optic_flow(self, x1, x2, u1, u2,
tau=0.25, # time step
lbda=0.15, # weight parameter for the data term
theta=0.3, # weight parameter for (u - v)^2
warps=5, # number of warpings per scale
max_iterations=5 # maximum number of iterations for optimization
):
l_t = lbda * theta
taut = tau / theta
diff2_x, diff2_y = self.centered_gradient(x2, 'x2')
p11 = p12 = p21 = p22 = tf.zeros_like(x1)
for warpings in xrange(warps):
with tf.variable_scope('warping%d' % (warpings,)):
u1_flat = tf.reshape(u1, (tf.shape(x2)[0], 1, x2.shape[1].value * x2.shape[2].value))
u2_flat = tf.reshape(u2, (tf.shape(x2)[0], 1, x2.shape[1].value * x2.shape[2].value))
x2_warp = self.warp_image(x2, u1_flat, u2_flat)
x2_warp = tf.reshape(x2_warp, tf.shape(x2))
diff2_x_warp = self.warp_image(diff2_x, u1_flat, u2_flat)
diff2_x_warp = tf.reshape(diff2_x_warp, tf.shape(diff2_x))
diff2_y_warp = self.warp_image(diff2_y, u1_flat, u2_flat)
diff2_y_warp = tf.reshape(diff2_y_warp, tf.shape(diff2_y))
diff2_x_sq = tf.square(diff2_x_warp)
diff2_y_sq = tf.square(diff2_y_warp)
grad = diff2_x_sq + diff2_y_sq + self.GRAD_IS_ZERO
rho_c = x2_warp - diff2_x_warp * u1 - diff2_y_warp * u2 - x1
for ii in xrange(max_iterations):
with tf.variable_scope('iter%d' % (ii,)):
rho = rho_c + diff2_x_warp * u1 + diff2_y_warp * u2 + self.GRAD_IS_ZERO;
masks1 = rho < -l_t * grad
d1_1 = tf.where(masks1, l_t * diff2_x_warp, tf.zeros_like(diff2_x_warp))
d2_1 = tf.where(masks1, l_t * diff2_y_warp, tf.zeros_like(diff2_y_warp))
masks2 = rho > l_t * grad
d1_2 = tf.where(masks2, -l_t * diff2_x_warp, tf.zeros_like(diff2_x_warp))
d2_2 = tf.where(masks2, -l_t * diff2_y_warp, tf.zeros_like(diff2_y_warp))
masks3 = (~masks1) & (~masks2) & (grad > self.GRAD_IS_ZERO)
d1_3 = tf.where(masks3, -rho / grad * diff2_x_warp, tf.zeros_like(diff2_x_warp))
d2_3 = tf.where(masks3, -rho / grad * diff2_y_warp, tf.zeros_like(diff2_y_warp))
v1 = d1_1 + d1_2 + d1_3 + u1
v2 = d2_1 + d2_2 + d2_3 + u2
u1 = v1 + theta * self.divergence(p11, p12, 'div_p1')
u2 = v2 + theta * self.divergence(p21, p22, 'div_p2')
u1x, u1y = self.forward_gradient(u1, 'u1')
u2x, u2y = self.forward_gradient(u2, 'u2')
p11 = (p11 + taut * u1x) / (
1.0 + taut * tf.sqrt(tf.square(u1x) + tf.square(u1y) + self.GRAD_IS_ZERO));
p12 = (p12 + taut * u1y) / (
1.0 + taut * tf.sqrt(tf.square(u1x) + tf.square(u1y) + self.GRAD_IS_ZERO));
p21 = (p21 + taut * u2x) / (
1.0 + taut * tf.sqrt(tf.square(u2x) + tf.square(u2y) + self.GRAD_IS_ZERO));
p22 = (p22 + taut * u2y) / (
1.0 + taut * tf.sqrt(tf.square(u2x) + tf.square(u2y) + self.GRAD_IS_ZERO));
return u1, u2, rho
def tvnet_flow(self, x1, x2,
tau=0.25, # time step
lbda=0.15, # weight parameter for the data term
theta=0.3, # weight parameter for (u - v)^2
warps=5, # number of warpings per scale
zfactor=0.5, # factor for building the image piramid
max_scales=5, # maximum number of scales for image piramid
max_iterations=5 # maximum number of iterations for optimization
):
for i in xrange(len(x1.shape)):
assert x1.shape[i].value == x2.shape[i].value
zfactor = np.float32(zfactor)
height = x1.shape[-3].value
width = x1.shape[-2].value
n_scales = 1 + np.log(np.sqrt(height ** 2 + width ** 2) / 4.0) / np.log(1 / zfactor);
n_scales = min(n_scales, max_scales)
# n_scales = 1
with tf.variable_scope('tvl1_flow'):
grey_x1 = self.grey_scale_image(x1)
grey_x2 = self.grey_scale_image(x2)
norm_imgs = self.normalize_images(grey_x1, grey_x2)
smooth_x1 = self.gaussian_smooth(norm_imgs[0])
smooth_x2 = self.gaussian_smooth(norm_imgs[1])
for ss in xrange(n_scales - 1, -1, -1):
with tf.variable_scope('scale%d' % ss):
down_sample_factor = zfactor ** ss
down_height, down_width = self.zoom_size(height, width, down_sample_factor)
if ss == n_scales - 1:
u1 = tf.get_variable('u1', shape=[1, down_height, down_width, 1], dtype=tf.float32,
initializer=tf.zeros_initializer)
u2 = tf.get_variable('u2', shape=[1, down_height, down_width, 1], dtype=tf.float32,
initializer=tf.zeros_initializer)
u1 = tf.tile(u1, [tf.shape(smooth_x1)[0], 1, 1, 1])
u2 = tf.tile(u2, [tf.shape(smooth_x1)[0], 1, 1, 1])
down_x1 = self.zoom_image(smooth_x1, down_height, down_width)
down_x2 = self.zoom_image(smooth_x2, down_height, down_width)
u1, u2, rho = self.dual_tvl1_optic_flow(down_x1, down_x2, u1, u2,
tau=tau, lbda=lbda, theta=theta, warps=warps,
max_iterations=max_iterations)
if ss == 0:
return u1, u2, rho
up_sample_factor = zfactor ** (ss - 1)
up_height, up_width = self.zoom_size(height, width, up_sample_factor)
u1 = self.zoom_image(u1, up_height, up_width) / zfactor
u2 = self.zoom_image(u2, up_height, up_width) / zfactor
def get_loss(self, x1, x2,
tau=0.25, # time step
lbda=0.15, # weight parameter for the data term
theta=0.3, # weight parameter for (u - v)^2
warps=5, # number of warpings per scale
zfactor=0.5, # factor for building the image piramid
max_scales=5, # maximum number of scales for image piramid
max_iterations=5 # maximum number of iterations for optimization
):
u1, u2, rho = self.tvnet_flow(x1, x2,
tau=tau, lbda=lbda, theta=theta, warps=warps,
zfactor=zfactor, max_scales=max_scales,
max_iterations=max_iterations)
# computing loss
u1x, u1y = self.forward_gradient(u1, 'u1')
u2x, u2y = self.forward_gradient(u2, 'u2')
u1_flat = tf.reshape(u1, (tf.shape(x2)[0], 1, x2.shape[1].value * x2.shape[2].value))
u2_flat = tf.reshape(u2, (tf.shape(x2)[0], 1, x2.shape[1].value * x2.shape[2].value))
x2_warp = self.warp_image(x2, u1_flat, u2_flat)
x2_warp = tf.reshape(x2_warp, tf.shape(x2))
loss = lbda * tf.reduce_mean(tf.abs(x2_warp - x1)) + tf.reduce_mean(
tf.abs(u1x) + tf.abs(u1y) + tf.abs(u2x) + tf.abs(u2y))
return loss, u1, u2