def greens(self, shape, **backend):
opt = dict(absolute=self.absolute,
membrane=self.membrane,
bending=self.bending,
lame=self.lame,
factor=self.factor)
kernel = spatial.greens(shape, **opt, **backend)
return kernel
def set_kernel(self, kernel=None):
if kernel is None:
kernel = spatial.greens(self.shape, **self.penalty,
factor=self.factor / py.prod(self.shape),
voxel_size=self.voxel_size,
**utils.backend(self.dat))
self.kernel = kernel
return self
def __init__(self, *args, **kwargs):
super().__init__(*args, **kwargs)
if self.dim1d is None:
shape = self.spatial_shape
vx = self.voxel_size
else:
shape = [self.spatial_shape[self.dim1d]]
vx = self.voxel_size[self.dim1d]
self.kernel = spatial.greens(shape,
**self.reg_prm,
factor=self.factor,
voxel_size=vx,
**utils.backend(self))
def register(fixed=None,
moving=None,
dim=None,
lam=1.,
loss='mse',
optim='nesterov',
hilbert=None,
max_iter=500,
sub_iter=16,
lr=None,
ls=0,
plot=False,
klosure=RegisterStep,
kernel=None,
**prm):
"""Nonlinear registration between two images using smooth displacements.
Parameters
----------
fixed : (..., K, *spatial) tensor
Fixed image
moving : (..., K, *spatial) tensor
Moving image
dim : int, default=`fixed.dim() - 1`
Number of spatial dimensions
lam : float, default=1
Modulate regularisation
loss : {'mse', 'cat'} or OptimizationLoss, default='mse'
'mse': Mean-squared error
'cat': Categorical cross-entropy
optim : {'relax', 'cg', 'gd', 'momentum', 'nesterov'}, default='relax'
'relax' : Gauss-Newton (linear system solved by relaxation)
'cg' : Gauss-Newton (linear system solved by conjugate gradient)
'gd' : Gradient descent
'momentum' : Gradient descent with momentum
'nesterov' : Nesterov-accelerated gradient descent
'lbfgs' : Limited-memory BFGS
hilbert : bool, default=True
Use hilbert preconditioning (not used if optim is second order)
max_iter : int, default=100
Maximum number of Gauss-Newton or Gradient descent iterations
sub_iter : int, default=16
Number of relax/cg iterations per GN step
lr : float, default=1
Learning rate.
ls : int, default=0
Number of line search iterations.
absolute : float, default=1e-4
Penalty on absolute displacements
membrane : float, default=1e-3
Penalty on first derivatives
bending : float, default=0.2
Penalty on second derivatives
lame : (float, float), default=(0.05, 0.2)
Penalty on zooms and shears
Returns
-------
disp : (..., *spatial, dim) tensor
Displacement field.
"""
defaults_velocity(prm)
# If no inputs provided: demo "circle to square"
if fixed is None or moving is None:
fixed, moving = phantoms.demo_register(cat=(loss == 'cat'))
# init tensors
fixed, moving = utils.to_max_backend(fixed, moving)
dim = dim or (fixed.dim() - 1)
shape = fixed.shape[-dim:]
lam = lam / py.prod(shape)
prm['factor'] = lam
velshape = [*fixed.shape[:-dim - 1], *shape, dim]
vel = torch.zeros(velshape, **utils.backend(fixed))
# init optimizer
optim = regutils.make_iteroptim_grid(optim, lr, ls, max_iter, sub_iter,
**prm)
if hilbert is None:
hilbert = not optim.requires_hess
if hilbert and kernel is None:
kernel = spatial.greens(shape, **prm, **utils.backend(fixed))
if kernel is not None:
optim.preconditioner = lambda x: spatial.greens_apply(x, kernel)
# init loss
loss = losses.make_loss(loss, dim)
print(
f'{"it":3s} | {"fit":^12s} + {"reg":^12s} = {"obj":^12s} | {"gain":^12s}'
)
print('-' * 63)
closure = klosure(moving,
fixed,
loss,
plot=plot,
max_iter=optim.max_iter,
**prm)
vel = optim.iter(vel, closure)
print('')
return vel
def __call__(self,
vel,
grad=False,
hess=False,
gradmov=False,
hessmov=False):
# This loop performs the forward pass, and computes
# derivatives along the way.
dim = vel.shape[-1]
pullopt = dict(bound=self.bound, extrapolate=self.extrapolate)
in_line_search = not grad and not hess
logplot = max(self.max_iter // 20, 1)
do_plot = (not in_line_search) and self.plot \
and (self.n_iter - 1) % logplot == 0
# forward
if self.kernel is None:
self.kernel = spatial.greens(vel.shape[-dim - 1:-1], **self.prm,
**utils.backend(vel))
grid = spatial.shoot(vel, self.kernel, steps=self.steps, **self.prm)
warped = spatial.grid_pull(self.moving,
grid,
bound='dct2',
extrapolate=True)
if do_plot:
iscat = isinstance(self.loss, losses.Cat)
plt.mov2fix(self.fixed,
self.moving,
warped,
vel,
cat=iscat,
dim=dim)
# gradient/Hessian of the log-likelihood in observed space
if not grad and not hess:
llx = self.loss.loss(warped, self.fixed)
elif not hess:
llx, grad = self.loss.loss_grad(warped, self.fixed)
if gradmov:
gradmov = spatial.grid_push(grad, grid, **pullopt)
else:
llx, grad, hess = self.loss.loss_grad_hess(warped, self.fixed)
if gradmov:
gradmov = spatial.grid_push(grad, grid, **pullopt)
if hessmov:
hessmov = spatial.grid_push(hess, grid, **pullopt)
del warped
# compose with spatial gradients
if grad is not False or hess is not False:
if self.mugrad is None:
self.mugrad = spatial.diff(self.moving,
dim=list(range(-dim, 0)),
bound='dct2')
if grad is not False:
grad = grad.neg_() # "final inverse" to "initial"
grad = spatial.grid_push(grad, grid)
grad = jg(self.mugrad, grad)
if hess is not False:
hess = spatial.grid_push(hess, grid)
hess = jhj(self.mugrad, hess)
# add regularization term
vgrad = spatial.regulariser_grid(vel, **self.prm, kernel=True)
llv = 0.5 * (vel * vgrad).sum()
if grad is not False:
grad += vgrad
del vgrad
# print objective
llx = llx.item()
llv = llv.item()
ll = llx + llv
if self.verbose and not in_line_search:
self.n_iter += 1
if self.ll_prev is None:
print(
f'{self.n_iter:03d} | {llx:12.6g} + {llv:12.6g} = {ll:12.6g}',
end='\r')
else:
gain = (self.ll_prev - ll) / max(abs(self.ll_max - ll), 1e-8)
print(
f'{self.n_iter:03d} | {llx:12.6g} + {llv:12.6g} = {ll:12.6g} | {gain:12.6g}',
end='\r')
self.ll_prev = ll
self.ll_max = max(self.ll_max, ll)
out = [ll]
if grad is not False:
out.append(grad)
if hess is not False:
out.append(hess)
if gradmov is not False:
out.append(gradmov)
if hessmov is not False:
out.append(hessmov)
return tuple(out) if len(out) > 1 else out[0]
def __call__(self, vel, grad=False):
# This loop performs the forward pass, and computes
# derivatives along the way.
# select correct gradient mode
if grad:
vel.requires_grad_()
if vel.grad is not None:
vel.grad.zero_()
if grad and not torch.is_grad_enabled():
with torch.enable_grad():
return self(vel, grad)
elif not grad and torch.is_grad_enabled():
with torch.no_grad():
return self(vel, grad)
dim = vel.shape[-1]
nvox = py.prod(vel.shape[-dim - 1:-1])
in_line_search = not grad
do_plot = (not in_line_search) and self.plot \
and (self.n_iter - 1) % 20 == 0
# forward
if self.kernel is None:
self.kernel = spatial.greens(vel.shape[-dim - 1:-1], **self.prm,
**utils.backend(vel))
grid = spatial.shoot(vel, self.kernel, steps=self.steps, **self.prm)
warped = spatial.grid_pull(self.moving,
grid,
bound='dct2',
extrapolate=True)
if do_plot:
iscat = isinstance(self.loss, losses.Cat)
plt.mov2fix(self.fixed,
self.moving,
warped,
vel,
cat=iscat,
dim=dim)
# log-likelihood in observed space
llx = self.loss.loss(warped, self.fixed)
del warped
# add regularization term
vgrad = spatial.regulariser_grid(vel, **self.prm).div_(nvox)
llv = 0.5 * (vel * vgrad).sum()
lll = llx + llv
del vgrad
# print objective
llx = llx.item()
llv = llv.item()
ll = lll.item()
if not in_line_search:
self.n_iter += 1
if self.ll_prev is None:
print(
f'{self.n_iter:03d} | {llx:12.6g} + {llv:12.6g} = {ll:12.6g}',
end='\r')
else:
gain = (self.ll_prev - ll) / max(abs(self.ll_max - ll), 1e-8)
print(
f'{self.n_iter:03d} | {llx:12.6g} + {llv:12.6g} = {ll:12.6g} | {gain:12.6g}',
end='\r')
out = [lll]
if grad:
lll.backward()
out.append(vel.grad)
vel.requires_grad_(False)
return tuple(out) if len(out) > 1 else out[0]
def forward(self, batch=1, **overload):
"""
Parameters
----------
batch : int, default=1
Batch size
overload : dict
Returns
-------
field : (batch, channel, *shape) tensor
Generated random field
"""
# get arguments
shape = overload.get('shape', self.shape)
mean = overload.get('mean', self.mean)
voxel_size = overload.get('voxel_size', self.voxel_size)
dtype = overload.get('dtype', self.dtype)
device = overload.get('device', self.device)
backend = dict(dtype=dtype, device=device)
# sample if parameters are callable
nb_dim = len(shape)
voxel_size = utils.make_vector(voxel_size, nb_dim, **backend)
voxel_size = voxel_size.tolist()
lame = py.make_list(self.lame, 2)
if (hasattr(self, '_greens')
and self._voxel_size == voxel_size
and self._shape == shape):
greens = self._greens.to(dtype=dtype, device=device)
else:
greens = spatial.greens(
shape,
absolute=self.absolute,
membrane=self.membrane,
bending=self.bending,
lame=self.lame,
voxel_size=voxel_size,
device=device,
dtype=dtype)
if any(lame):
greens, scale, _ = torch.svd(greens)
scale = scale.sqrt_()
greens *= scale.unsqueeze(-1)
else:
greens = greens.sqrt_()
if self.cache_greens:
self._greens = greens
self._voxel_size = voxel_size
self._shape = shape
sample = torch.randn([2, batch, *shape, nb_dim], **backend)
# multiply by square root of greens
if greens.dim() > nb_dim: # lame
sample = linalg.matvec(greens, sample)
else:
sample = sample * greens.unsqueeze(-1)
voxel_size = utils.make_vector(voxel_size, nb_dim, **backend)
sample = sample / voxel_size.sqrt()
sample = fft.complex(sample[0], sample[1])
# inverse Fourier transform
dims = list(range(-nb_dim-1, -1))
sample = fft.real(fft.ifftn(sample, dim=dims))
sample *= py.prod(shape)
# add mean
sample += mean
return sample
def forward(self, batch=1, **overload):
"""
Parameters
----------
batch : int, default=1
Batch size
Other Parameters
----------------
shape : sequence[int], optional
channel : int, optional
voxel_size : float or (dim,) vector_like, optional
device : torch.device, optional
dtype : torch.dtype, optional
Returns
-------
field : (batch, channel, *shape) tensor
Generated random field
"""
# get arguments
shape = overload.get('shape', self.shape)
channel = overload.get('channel', self.channel)
voxel_size = overload.get('voxel_size', self.voxel_size)
dtype = overload.get('dtype', self.dtype)
device = overload.get('device', self.device)
backend = dict(dtype=dtype, device=device)
# sample if parameters are callable
nb_dim = len(shape)
voxel_size = utils.make_vector(voxel_size, nb_dim, **backend)
voxel_size = voxel_size.tolist()
if (hasattr(self, '_greens')
and self._voxel_size == voxel_size
and self._channel == channel
and self._shape == shape):
greens = self._greens.to(dtype=dtype, device=device)
else:
mean = utils.make_vector(self.mean, channel, **backend)
absolute = utils.make_vector(self.absolute, channel, **backend)
membrane = utils.make_vector(self.membrane, channel, **backend)
bending = utils.make_vector(self.bending, channel, **backend)
greens = []
for c in range(channel):
greens.append(spatial.greens(
shape,
absolute=absolute[c],
membrane=membrane[c],
bending=bending[c],
lame=0,
voxel_size=voxel_size,
device=device,
dtype=dtype))
greens = torch.stack(greens)
greens = greens.sqrt_()
if self.cache_greens:
self._greens = greens
self._voxel_size = voxel_size
self._shape = shape
# sample white noise
sample = torch.randn([2, batch, channel, *shape], **backend)
sample *= greens.unsqueeze(-1)
sample = fft.complex(sample[0], sample[1])
# inverse Fourier transform
dims = list(range(-nb_dim, 0))
sample = fft.real(fft.ifftn(sample, dim=dims))
sample *= py.prod(shape)
# add mean
sample += utils.unsqueeze(mean, -1, len(shape))
return sample
def forward(self, velocity, fwd=None, inv=None, voxel_size=None):
"""
Parameters
----------
velocity :(batch, *spatial, dim) tensor
Initial velocity field.
fwd : bool, default=self.fwd
inv : bool, default=self.inv
voxel_size : sequence[float], default=self.voxel_size
Returns
-------
forward : (batch, *spatial, dim) tensor, if `forward is True`
Forward displacement (if `displacement is True`) or
transformation (if `displacement is False`) field.
inverse : (batch, *spatial, dim) tensor, if `inverse is True`
Inverse displacement (if `displacement is True`) or
transformation (if `displacement is False`) field.
"""
fwd = fwd if fwd is not None else self.fwd
inv = inv if inv is not None else self.inv
voxel_size = voxel_size if voxel_size is not None else self.voxel_size
shoot_opt = {
'steps': self.steps,
'displacement': self.displacement,
'voxel_size': voxel_size,
'absolute': self.absolute,
'membrane': self.membrane,
'bending': self.bending,
'lame': self.lame,
'factor': self.factor,
}
greens_prm = {
'absolute': self.absolute,
'membrane': self.membrane,
'bending': self.bending,
'lame': self.lame,
'factor': self.factor,
'voxel_size': voxel_size,
'shape': velocity.shape[1:-1],
}
if self.cache_greens:
if getattr(self, '_greens_prm', None) == greens_prm:
greens = self._greens.to(**utils.backend(velocity))
else:
greens = spatial.greens(**greens_prm,
**utils.backend(velocity))
self._greens = greens
self._greens_prm = greens_prm
else:
greens = spatial.greens(**greens_prm, **utils.backend(velocity))
shoot_fn = spatial.shoot_approx if self.approx else spatial.shoot
output = []
if inv:
y, iy = shoot_fn(velocity,
greens,
return_inverse=True,
**shoot_opt)
if fwd:
output.append(y)
output.append(iy)
elif fwd:
y = shoot_fn(velocity, greens, **shoot_opt)
output.append(y)
return output if len(output) > 1 else \
output[0] if len(output) == 1 else \
None