def w_cycle_3d(n, k, delta_field, sigma_field, gradient_field, target,
lambda_param, displacement, depth = 0):
r'''
Multi-resolution Gauss-Seidel solver: solves the linear system by performing
two v-cycles at each resolution, which corresponds to the w-cycle scheme
proposed by Bruhn and Weickert[1].
[1] Andres Bruhn and Joachim Weickert, "Towards ultimate motion estimation:
combining highest accuracy with real-time performance",
10th IEEE International Conference on Computer Vision, 2005. ICCV 2005.
'''
#presmoothing
for i in range(k):
error = tf.iterate_residual_displacement_field_SSD3D(delta_field,
sigma_field,
gradient_field,
target,
lambda_param,
displacement)
if printEnergy and depth == 0:
energy = tf.compute_energy_SSD3D(delta_field,
sigma_field,
gradient_field,
lambda_param,
displacement)
print 'Energy after top-level iter', i+1, ' [first]:', energy
if n == 0:
return error
residual = tf.compute_residual_displacement_field_SSD3D(delta_field,
sigma_field,
gradient_field,
target,
lambda_param,
displacement,
None)
sub_residual = np.array(tf.downsample_displacement_field3D(residual))
del residual
#solve at coarcer grid
subsigma_field = None
if sigma_field != None:
subsigma_field = tf.downsample_scalar_field3D(sigma_field)
subdelta_field = tf.downsample_scalar_field3D(delta_field)
subgradient_field = np.array(
tf.downsample_displacement_field3D(gradient_field))
shape = np.array(displacement.shape).astype(np.int32)
sub_displacement = np.zeros(
shape = ((shape[0]+1)//2, (shape[1]+1)//2, (shape[2]+1)//2, 3 ),
dtype = np.float64)
sublambda_param = lambda_param*0.25
w_cycle_3d(n-1, k, subdelta_field, subsigma_field, subgradient_field,
sub_residual, sublambda_param, sub_displacement, depth+1)
displacement += np.array(
tf.upsample_displacement_field3D(sub_displacement, shape))
if printEnergy and depth == 0:
energy = tf.compute_energy_SSD3D(delta_field, sigma_field,
gradient_field, lambda_param,
displacement)
print 'Energy after low-res iteration[first]:', energy
#post-smoothing (second smoothing)
for i in range(k):
error = tf.iterate_residual_displacement_field_SSD3D(delta_field,
sigma_field,
gradient_field,
target,
lambda_param,
displacement)
if printEnergy and depth == 0:
energy = tf.compute_energy_SSD3D(delta_field,
sigma_field,
gradient_field,
lambda_param,
displacement)
print 'Energy after top-level iter', i+1, ' [second]:', energy
residual = tf.compute_residual_displacement_field_SSD3D(delta_field,
sigma_field,
gradient_field,
target,
lambda_param,
displacement,
None)
sub_residual = np.array(tf.downsample_displacement_field3D(residual))
del residual
sub_displacement[...] = 0
w_cycle_3d(n-1, k, subdelta_field, subsigma_field, subgradient_field,
sub_residual, sublambda_param, sub_displacement, depth+1)
displacement += np.array(
tf.upsample_displacement_field3D(sub_displacement, shape))
if printEnergy and depth == 0:
energy = tf.compute_energy_SSD3D(delta_field, sigma_field,
gradient_field, lambda_param,
displacement)
print 'Energy after low-res iteration[second]:', energy
for i in range(k):
error = tf.iterate_residual_displacement_field_SSD3D(delta_field,
sigma_field,
gradient_field,
target,
lambda_param,
displacement)
if printEnergy and depth == 0:
energy = tf.compute_energy_SSD3D(delta_field,
sigma_field,
gradient_field,
lambda_param,
displacement)
print 'Energy after top-level iter', i+1, ' [third]:', energy
try:
energy
except NameError:
energy = tf.compute_energy_SSD3D(delta_field, sigma_field,
gradient_field, lambda_param,
displacement)
return energy
def v_cycle_3d(n, k, delta_field, sigma_field, gradient_field, target,
lambda_param, displacement, depth = 0):
r'''
Multi-resolution Gauss-Seidel solver: solves the linear system by first
filtering (GS-iterate) the current level, then solves for the residual
at a coarcer resolution andfinally refines the solution at the current
resolution. This scheme corresponds to the V-cycle proposed by Bruhn and
Weickert[1].
[1] Andres Bruhn and Joachim Weickert, "Towards ultimate motion estimation:
combining highest accuracy with real-time performance",
10th IEEE International Conference on Computer Vision, 2005.
ICCV 2005.
'''
#presmoothing
for i in range(k):
tf.iterate_residual_displacement_field_SSD3D(delta_field,
sigma_field,
gradient_field,
target,
lambda_param,
displacement)
if printEnergy and depth == 0:
energy = tf.compute_energy_SSD3D(delta_field,
sigma_field,
gradient_field,
lambda_param,
displacement)
print 'Energy after top-level iter', i+1, ' [unique]:', energy
if n == 0:
try:
energy
except NameError:
energy = tf.compute_energy_SSD3D(delta_field, sigma_field,
gradient_field, lambda_param,
displacement)
return energy
#solve at coarcer grid
residual = tf.compute_residual_displacement_field_SSD3D(delta_field,
sigma_field,
gradient_field,
target,
lambda_param,
displacement,
None)
sub_residual = np.array(tf.downsample_displacement_field3D(residual))
del residual
subsigma_field = None
if sigma_field != None:
subsigma_field = tf.downsample_scalar_field3D(sigma_field)
subdelta_field = tf.downsample_scalar_field3D(delta_field)
subgradient_field = np.array(
tf.downsample_displacement_field3D(gradient_field))
shape = np.array(displacement.shape).astype(np.int32)
sub_displacement = np.zeros(
shape = ((shape[0]+1)//2, (shape[1]+1)//2, (shape[2]+1)//2, 3 ),
dtype = np.float64)
sublambda_param = lambda_param*0.25
v_cycle_3d(n-1, k, subdelta_field, subsigma_field, subgradient_field,
sub_residual, sublambda_param, sub_displacement, depth+1)
del subdelta_field
del subsigma_field
del subgradient_field
del sub_residual
tf.accumulate_upsample_displacement_field3D(sub_displacement, displacement)
del sub_displacement
if printEnergy and depth == 0:
energy = tf.compute_energy_SSD3D(delta_field, sigma_field,
gradient_field, lambda_param,
displacement)
print 'Energy after low-res iteration:', energy
#post-smoothing
for i in range(k):
tf.iterate_residual_displacement_field_SSD3D(delta_field,
sigma_field,
gradient_field,
target,
lambda_param,
displacement)
if printEnergy and depth == 0:
energy = tf.compute_energy_SSD3D(delta_field,
sigma_field,
gradient_field,
lambda_param,
displacement)
print 'Energy after top-level iter', i+1, ' [unique]:', energy
try:
energy
except NameError:
energy = tf.compute_energy_SSD3D(delta_field, sigma_field,
gradient_field, lambda_param,
displacement)
return energy
def single_cycle_3d(n, k, delta_field, sigma_field, gradient_field,
lambda_param, displacement, depth = 0):
r'''
One-pass multi-resolution Gauss-Seidel solver: solves the SSD-like linear
system starting at the coarcer resolution and then refining at the finer
resolution.
'''
if n == 0:
for i in range(k):
error = tf.iterate_residual_displacement_field_SSD3D(delta_field,
sigma_field,
gradient_field,
None,
lambda_param,
displacement)
if printEnergy and depth == 0:
energy = tf.compute_energy_SSD3D(delta_field,
sigma_field,
gradient_field,
lambda_param,
displacement)
print 'Energy after top-level iter', i+1, ' [unique]:', energy
return error
#solve at coarcer grid
subsigma_field = None
if sigma_field != None:
subsigma_field = tf.downsample_scalar_field3D(sigma_field)
subdelta_field = tf.downsample_scalar_field3D(delta_field)
subgradient_field = np.array(
tf.downsample_displacement_field3D(gradient_field))
shape = np.array(displacement.shape).astype(np.int32)
sub_displacement = np.zeros(
shape = ((shape[0]+1)//2, (shape[1]+1)//2, (shape[2]+1)//2, 3 ),
dtype = np.float64)
sublambda_param = lambda_param*0.25
single_cycle_3d(n-1, k, subdelta_field, subsigma_field, subgradient_field,
sublambda_param, sub_displacement, depth+1)
displacement += np.array(
tf.upsample_displacement_field3D(sub_displacement, shape))
if printEnergy and depth == 0:
energy = tf.compute_energy_SSD3D(delta_field, sigma_field,
gradient_field, lambda_param,
displacement)
print 'Energy after low-res iteration:', energy
#post-smoothing
for i in range(k):
error = tf.iterate_residual_displacement_field_SSD3D(delta_field,
sigma_field,
gradient_field,
None,
lambda_param,
displacement)
if printEnergy and depth == 0:
energy = tf.compute_energy_SSD3D(delta_field,
sigma_field,
gradient_field,
lambda_param,
displacement)
print 'Energy after top-level iter', i+1, ' [unique]:', energy
try:
energy
except NameError:
energy = tf.compute_energy_SSD3D(delta_field, sigma_field,
gradient_field, lambda_param,
displacement)
return energy
def w_cycle_3d(n,
k,
delta_field,
sigma_field,
gradient_field,
target,
lambda_param,
displacement,
depth=0):
r'''
Multi-resolution Gauss-Seidel solver: solves the linear system by performing
two v-cycles at each resolution, which corresponds to the w-cycle scheme
proposed by Bruhn and Weickert[1].
[1] Andres Bruhn and Joachim Weickert, "Towards ultimate motion estimation:
combining highest accuracy with real-time performance",
10th IEEE International Conference on Computer Vision, 2005. ICCV 2005.
'''
#presmoothing
for i in range(k):
error = tf.iterate_residual_displacement_field_SSD3D(
delta_field, sigma_field, gradient_field, target, lambda_param,
displacement)
if printEnergy and depth == 0:
energy = tf.compute_energy_SSD3D(delta_field, sigma_field,
gradient_field, lambda_param,
displacement)
print 'Energy after top-level iter', i + 1, ' [first]:', energy
if n == 0:
return error
residual = tf.compute_residual_displacement_field_SSD3D(
delta_field, sigma_field, gradient_field, target, lambda_param,
displacement, None)
sub_residual = np.array(tf.downsample_displacement_field3D(residual))
del residual
#solve at coarcer grid
subsigma_field = None
if sigma_field != None:
subsigma_field = tf.downsample_scalar_field3D(sigma_field)
subdelta_field = tf.downsample_scalar_field3D(delta_field)
subgradient_field = np.array(
tf.downsample_displacement_field3D(gradient_field))
shape = np.array(displacement.shape).astype(np.int32)
sub_displacement = np.zeros(shape=((shape[0] + 1) // 2,
(shape[1] + 1) // 2,
(shape[2] + 1) // 2, 3),
dtype=np.float64)
sublambda_param = lambda_param * 0.25
w_cycle_3d(n - 1, k, subdelta_field, subsigma_field, subgradient_field,
sub_residual, sublambda_param, sub_displacement, depth + 1)
displacement += np.array(
tf.upsample_displacement_field3D(sub_displacement, shape))
if printEnergy and depth == 0:
energy = tf.compute_energy_SSD3D(delta_field, sigma_field,
gradient_field, lambda_param,
displacement)
print 'Energy after low-res iteration[first]:', energy
#post-smoothing (second smoothing)
for i in range(k):
error = tf.iterate_residual_displacement_field_SSD3D(
delta_field, sigma_field, gradient_field, target, lambda_param,
displacement)
if printEnergy and depth == 0:
energy = tf.compute_energy_SSD3D(delta_field, sigma_field,
gradient_field, lambda_param,
displacement)
print 'Energy after top-level iter', i + 1, ' [second]:', energy
residual = tf.compute_residual_displacement_field_SSD3D(
delta_field, sigma_field, gradient_field, target, lambda_param,
displacement, None)
sub_residual = np.array(tf.downsample_displacement_field3D(residual))
del residual
sub_displacement[...] = 0
w_cycle_3d(n - 1, k, subdelta_field, subsigma_field, subgradient_field,
sub_residual, sublambda_param, sub_displacement, depth + 1)
displacement += np.array(
tf.upsample_displacement_field3D(sub_displacement, shape))
if printEnergy and depth == 0:
energy = tf.compute_energy_SSD3D(delta_field, sigma_field,
gradient_field, lambda_param,
displacement)
print 'Energy after low-res iteration[second]:', energy
for i in range(k):
error = tf.iterate_residual_displacement_field_SSD3D(
delta_field, sigma_field, gradient_field, target, lambda_param,
displacement)
if printEnergy and depth == 0:
energy = tf.compute_energy_SSD3D(delta_field, sigma_field,
gradient_field, lambda_param,
displacement)
print 'Energy after top-level iter', i + 1, ' [third]:', energy
try:
energy
except NameError:
energy = tf.compute_energy_SSD3D(delta_field, sigma_field,
gradient_field, lambda_param,
displacement)
return energy
def v_cycle_3d(n,
k,
delta_field,
sigma_field,
gradient_field,
target,
lambda_param,
displacement,
depth=0):
r'''
Multi-resolution Gauss-Seidel solver: solves the linear system by first
filtering (GS-iterate) the current level, then solves for the residual
at a coarcer resolution andfinally refines the solution at the current
resolution. This scheme corresponds to the V-cycle proposed by Bruhn and
Weickert[1].
[1] Andres Bruhn and Joachim Weickert, "Towards ultimate motion estimation:
combining highest accuracy with real-time performance",
10th IEEE International Conference on Computer Vision, 2005.
ICCV 2005.
'''
#presmoothing
for i in range(k):
tf.iterate_residual_displacement_field_SSD3D(delta_field, sigma_field,
gradient_field, target,
lambda_param,
displacement)
if printEnergy and depth == 0:
energy = tf.compute_energy_SSD3D(delta_field, sigma_field,
gradient_field, lambda_param,
displacement)
print 'Energy after top-level iter', i + 1, ' [unique]:', energy
if n == 0:
try:
energy
except NameError:
energy = tf.compute_energy_SSD3D(delta_field, sigma_field,
gradient_field, lambda_param,
displacement)
return energy
#solve at coarcer grid
residual = tf.compute_residual_displacement_field_SSD3D(
delta_field, sigma_field, gradient_field, target, lambda_param,
displacement, None)
sub_residual = np.array(tf.downsample_displacement_field3D(residual))
del residual
subsigma_field = None
if sigma_field != None:
subsigma_field = tf.downsample_scalar_field3D(sigma_field)
subdelta_field = tf.downsample_scalar_field3D(delta_field)
subgradient_field = np.array(
tf.downsample_displacement_field3D(gradient_field))
shape = np.array(displacement.shape).astype(np.int32)
sub_displacement = np.zeros(shape=((shape[0] + 1) // 2,
(shape[1] + 1) // 2,
(shape[2] + 1) // 2, 3),
dtype=np.float64)
sublambda_param = lambda_param * 0.25
v_cycle_3d(n - 1, k, subdelta_field, subsigma_field, subgradient_field,
sub_residual, sublambda_param, sub_displacement, depth + 1)
del subdelta_field
del subsigma_field
del subgradient_field
del sub_residual
tf.accumulate_upsample_displacement_field3D(sub_displacement, displacement)
del sub_displacement
if printEnergy and depth == 0:
energy = tf.compute_energy_SSD3D(delta_field, sigma_field,
gradient_field, lambda_param,
displacement)
print 'Energy after low-res iteration:', energy
#post-smoothing
for i in range(k):
tf.iterate_residual_displacement_field_SSD3D(delta_field, sigma_field,
gradient_field, target,
lambda_param,
displacement)
if printEnergy and depth == 0:
energy = tf.compute_energy_SSD3D(delta_field, sigma_field,
gradient_field, lambda_param,
displacement)
print 'Energy after top-level iter', i + 1, ' [unique]:', energy
try:
energy
except NameError:
energy = tf.compute_energy_SSD3D(delta_field, sigma_field,
gradient_field, lambda_param,
displacement)
return energy
def single_cycle_3d(n,
k,
delta_field,
sigma_field,
gradient_field,
lambda_param,
displacement,
depth=0):
r'''
One-pass multi-resolution Gauss-Seidel solver: solves the SSD-like linear
system starting at the coarcer resolution and then refining at the finer
resolution.
'''
if n == 0:
for i in range(k):
error = tf.iterate_residual_displacement_field_SSD3D(
delta_field, sigma_field, gradient_field, None, lambda_param,
displacement)
if printEnergy and depth == 0:
energy = tf.compute_energy_SSD3D(delta_field, sigma_field,
gradient_field, lambda_param,
displacement)
print 'Energy after top-level iter', i + 1, ' [unique]:', energy
return error
#solve at coarcer grid
subsigma_field = None
if sigma_field != None:
subsigma_field = tf.downsample_scalar_field3D(sigma_field)
subdelta_field = tf.downsample_scalar_field3D(delta_field)
subgradient_field = np.array(
tf.downsample_displacement_field3D(gradient_field))
shape = np.array(displacement.shape).astype(np.int32)
sub_displacement = np.zeros(shape=((shape[0] + 1) // 2,
(shape[1] + 1) // 2,
(shape[2] + 1) // 2, 3),
dtype=np.float64)
sublambda_param = lambda_param * 0.25
single_cycle_3d(n - 1, k, subdelta_field, subsigma_field,
subgradient_field, sublambda_param, sub_displacement,
depth + 1)
displacement += np.array(
tf.upsample_displacement_field3D(sub_displacement, shape))
if printEnergy and depth == 0:
energy = tf.compute_energy_SSD3D(delta_field, sigma_field,
gradient_field, lambda_param,
displacement)
print 'Energy after low-res iteration:', energy
#post-smoothing
for i in range(k):
error = tf.iterate_residual_displacement_field_SSD3D(
delta_field, sigma_field, gradient_field, None, lambda_param,
displacement)
if printEnergy and depth == 0:
energy = tf.compute_energy_SSD3D(delta_field, sigma_field,
gradient_field, lambda_param,
displacement)
print 'Energy after top-level iter', i + 1, ' [unique]:', energy
try:
energy
except NameError:
energy = tf.compute_energy_SSD3D(delta_field, sigma_field,
gradient_field, lambda_param,
displacement)
return energy