/usr/lib/python2.7/dist-packages/dipy/align/streamlinear.py is in python-dipy 0.10.1-1.
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import numpy as np
from dipy.utils.six import with_metaclass
from dipy.core.optimize import Optimizer
from dipy.align.bundlemin import (_bundle_minimum_distance,
distance_matrix_mdf)
from dipy.tracking.streamline import (transform_streamlines,
unlist_streamlines,
center_streamlines)
from dipy.core.geometry import (compose_transformations,
compose_matrix,
decompose_matrix)
from dipy.utils.six import string_types
MAX_DIST = 1e10
LOG_MAX_DIST = np.log(MAX_DIST)
class StreamlineDistanceMetric(with_metaclass(abc.ABCMeta, object)):
def __init__(self, num_threads=None):
""" An abstract class for the metric used for streamline registration
If the two sets of streamlines match exactly then method ``distance``
of this object should be minimum.
Parameters
----------
num_threads : int
Number of threads. If None (default) then all available threads
will be used. Only metrics using OpenMP will use this variable.
"""
self.static = None
self.moving = None
self.num_threads = num_threads
@abc.abstractmethod
def setup(self, static, moving):
pass
@abc.abstractmethod
def distance(self, xopt):
""" calculate distance for current set of parameters
"""
pass
class BundleMinDistanceMetric(StreamlineDistanceMetric):
""" Bundle-based Minimum Distance aka BMD
This is the cost function used by the StreamlineLinearRegistration
Methods
-------
setup(static, moving)
distance(xopt)
References
----------
.. [Garyfallidis14] Garyfallidis et al., "Direct native-space fiber
bundle alignment for group comparisons", ISMRM,
2014.
"""
def setup(self, static, moving):
""" Setup static and moving sets of streamlines
Parameters
----------
static : streamlines
Fixed or reference set of streamlines.
moving : streamlines
Moving streamlines.
num_threads : int
Number of threads. If None (default) then all available threads
will be used.
Notes
-----
Call this after the object is initiated and before distance.
"""
self._set_static(static)
self._set_moving(moving)
def _set_static(self, static):
static_centered_pts, st_idx = unlist_streamlines(static)
self.static_centered_pts = np.ascontiguousarray(static_centered_pts,
dtype=np.float64)
self.block_size = st_idx[0]
def _set_moving(self, moving):
self.moving_centered_pts, _ = unlist_streamlines(moving)
def distance(self, xopt):
""" Distance calculated from this Metric
Parameters
----------
xopt : sequence
List of affine parameters as an 1D vector,
"""
return bundle_min_distance_fast(xopt,
self.static_centered_pts,
self.moving_centered_pts,
self.block_size,
self.num_threads)
class BundleMinDistanceMatrixMetric(StreamlineDistanceMetric):
""" Bundle-based Minimum Distance aka BMD
This is the cost function used by the StreamlineLinearRegistration
Methods
-------
setup(static, moving)
distance(xopt)
Notes
-----
The difference with BundleMinDistanceMetric is that this creates
the entire distance matrix and therefore requires more memory.
"""
def setup(self, static, moving):
""" Setup static and moving sets of streamlines
Parameters
----------
static : streamlines
Fixed or reference set of streamlines.
moving : streamlines
Moving streamlines.
Notes
-----
Call this after the object is initiated and before distance.
Num_threads is not used in this class. Use ``BundleMinDistanceMetric``
for a faster, threaded and less memory hungry metric
"""
self.static = static
self.moving = moving
def distance(self, xopt):
""" Distance calculated from this Metric
Parameters
----------
xopt : sequence
List of affine parameters as an 1D vector
"""
return bundle_min_distance(xopt, self.static, self.moving)
class BundleSumDistanceMatrixMetric(BundleMinDistanceMatrixMetric):
""" Bundle-based Sum Distance aka BMD
This is a cost function that can be used by the
StreamlineLinearRegistration class.
Methods
-------
setup(static, moving)
distance(xopt)
Notes
-----
The difference with BundleMinDistanceMatrixMetric is that it uses
uses the sum of the distance matrix and not the sum of mins.
"""
def distance(self, xopt):
""" Distance calculated from this Metric
Parameters
----------
xopt : sequence
List of affine parameters as an 1D vector
"""
return bundle_sum_distance(xopt, self.static, self.moving)
class StreamlineLinearRegistration(object):
def __init__(self, metric=None, x0="rigid", method='L-BFGS-B',
bounds=None, verbose=False, options=None,
evolution=False, num_threads=None):
r""" Linear registration of 2 sets of streamlines [Garyfallidis14]_.
Parameters
----------
metric : StreamlineDistanceMetric,
If None and fast is False then the BMD distance is used. If fast
is True then a faster implementation of BMD is used. Otherwise,
use the given distance metric.
x0 : array or int or str
Initial parametrization for the optimization.
If 1D array with:
a) 6 elements then only rigid registration is parformed with
the 3 first elements for translation and 3 for rotation.
b) 7 elements also isotropic scaling is performed (similarity).
c) 12 elements then translation, rotation (in degrees),
scaling and shearing is performed (affine).
Here is an example of x0 with 12 elements:
``x0=np.array([0, 10, 0, 40, 0, 0, 2., 1.5, 1, 0.1, -0.5, 0])``
This has translation (0, 10, 0), rotation (40, 0, 0) in
degrees, scaling (2., 1.5, 1) and shearing (0.1, -0.5, 0).
If int:
a) 6
``x0 = np.array([0, 0, 0, 0, 0, 0])``
b) 7
``x0 = np.array([0, 0, 0, 0, 0, 0, 1.])``
c) 12
``x0 = np.array([0, 0, 0, 0, 0, 0, 1., 1., 1, 0, 0, 0])``
If str:
a) "rigid"
``x0 = np.array([0, 0, 0, 0, 0, 0])``
b) "similarity"
``x0 = np.array([0, 0, 0, 0, 0, 0, 1.])``
c) "affine"
``x0 = np.array([0, 0, 0, 0, 0, 0, 1., 1., 1, 0, 0, 0])``
method : str,
'L_BFGS_B' or 'Powell' optimizers can be used. Default is
'L_BFGS_B'.
bounds : list of tuples or None,
If method == 'L_BFGS_B' then we can use bounded optimization.
For example for the six parameters of rigid rotation we can set
the bounds = [(-30, 30), (-30, 30), (-30, 30),
(-45, 45), (-45, 45), (-45, 45)]
That means that we have set the bounds for the three translations
and three rotation axes (in degrees).
verbose : bool,
If True then information about the optimization is shown.
options : None or dict,
Extra options to be used with the selected method.
evolution : boolean
If True save the transformation for each iteration of the
optimizer. Default is False. Supported only with Scipy >= 0.11.
num_threads : int
Number of threads. If None (default) then all available threads
will be used. Only metrics using OpenMP will use this variable.
References
----------
.. [Garyfallidis14] Garyfallidis et al., "Direct native-space fiber
bundle alignment for group comparisons", ISMRM,
2014.
"""
self.x0 = self._set_x0(x0)
self.metric = metric
if self.metric is None:
self.metric = BundleMinDistanceMetric(num_threads=num_threads)
self.verbose = verbose
self.method = method
if self.method not in ['Powell', 'L-BFGS-B']:
raise ValueError('Only Powell and L-BFGS-B can be used')
self.bounds = bounds
self.options = options
self.evolution = evolution
def optimize(self, static, moving, mat=None):
""" Find the minimum of the provided metric.
Parameters
----------
static : streamlines
Reference or fixed set of streamlines.
moving : streamlines
Moving set of streamlines.
mat : array
Transformation (4, 4) matrix to start the registration. ``mat``
is applied to moving. Default value None which means that initial
transformation will be generated by shifting the centers of moving
and static sets of streamlines to the origin.
Returns
-------
map : StreamlineRegistrationMap
"""
msg = 'need to have the same number of points. Use '
msg += 'set_number_of_points from dipy.tracking.streamline'
if not np.all(np.array(list(map(len, static))) == static[0].shape[0]):
raise ValueError('Static streamlines ' + msg)
if not np.all(np.array(list(map(len, moving))) == moving[0].shape[0]):
raise ValueError('Moving streamlines ' + msg)
if not np.all(np.array(list(map(len, moving))) == static[0].shape[0]):
raise ValueError('Static and moving streamlines ' + msg)
if mat is None:
static_centered, static_shift = center_streamlines(static)
moving_centered, moving_shift = center_streamlines(moving)
static_mat = compose_matrix44([static_shift[0], static_shift[1],
static_shift[2], 0, 0, 0])
moving_mat = compose_matrix44([-moving_shift[0], -moving_shift[1],
-moving_shift[2], 0, 0, 0])
else:
static_centered = static
moving_centered = transform_streamlines(moving, mat)
static_mat = np.eye(4)
moving_mat = mat
self.metric.setup(static_centered, moving_centered)
distance = self.metric.distance
if self.method == 'Powell':
if self.options is None:
self.options = {'xtol': 1e-6, 'ftol': 1e-6, 'maxiter': 1e6}
opt = Optimizer(distance, self.x0.tolist(),
method=self.method, options=self.options,
evolution=self.evolution)
if self.method == 'L-BFGS-B':
if self.options is None:
self.options = {'maxcor': 10, 'ftol': 1e-7,
'gtol': 1e-5, 'eps': 1e-8,
'maxiter': 100}
opt = Optimizer(distance, self.x0.tolist(),
method=self.method,
bounds=self.bounds, options=self.options,
evolution=self.evolution)
if self.verbose:
opt.print_summary()
opt_mat = compose_matrix44(opt.xopt)
mat = compose_transformations(moving_mat, opt_mat, static_mat)
mat_history = []
if opt.evolution is not None:
for vecs in opt.evolution:
mat_history.append(
compose_transformations(moving_mat,
compose_matrix44(vecs),
static_mat))
srm = StreamlineRegistrationMap(mat, opt.xopt, opt.fopt,
mat_history, opt.nfev, opt.nit)
del opt
return srm
def _set_x0(self, x0):
""" check if input is of correct type"""
if hasattr(x0, 'ndim'):
if len(x0) not in [6, 7, 12]:
msg = 'Only 1D arrays of 6, 7 and 12 elements are allowed'
raise ValueError(msg)
if x0.ndim != 1:
raise ValueError("Array should have only one dimension")
return x0
if isinstance(x0, string_types):
if x0.lower() == 'rigid':
return np.zeros(6)
if x0.lower() == 'similarity':
return np.array([0, 0, 0, 0, 0, 0, 1.])
if x0.lower() == 'affine':
return np.array([0, 0, 0, 0, 0, 0, 1., 1., 1., 0, 0, 0])
if isinstance(x0, int):
if x0 not in [6, 7, 12]:
msg = 'Only 6, 7 and 12 are accepted as integers'
raise ValueError(msg)
else:
if x0 == 6:
return np.zeros(6)
if x0 == 7:
return np.array([0, 0, 0, 0, 0, 0, 1.])
if x0 == 12:
return np.array([0, 0, 0, 0, 0, 0, 1., 1., 1., 0, 0, 0])
raise ValueError('Wrong input')
class StreamlineRegistrationMap(object):
def __init__(self, matopt, xopt, fopt, matopt_history, funcs, iterations):
r""" A map holding the optimum affine matrix and some other parameters
of the optimization
Parameters
----------
matrix : array,
4x4 affine matrix which transforms the moving to the static
streamlines
xopt : array,
1d array with the parameters of the transformation after centering
fopt : float,
final value of the metric
matrix_history : array
All transformation matrices created during the optimization
funcs : int,
Number of function evaluations of the optimizer
iterations : int
Number of iterations of the optimizer
"""
self.matrix = matopt
self.xopt = xopt
self.fopt = fopt
self.matrix_history = matopt_history
self.funcs = funcs
self.iterations = iterations
def transform(self, moving):
""" Transform moving streamlines to the static.
Parameters
----------
moving : streamlines
Returns
-------
moved : streamlines
Notes
-----
All this does is apply ``self.matrix`` to the input streamlines.
"""
return transform_streamlines(moving, self.matrix)
def bundle_sum_distance(t, static, moving, num_threads=None):
""" MDF distance optimization function (SUM)
We minimize the distance between moving streamlines as they align
with the static streamlines.
Parameters
-----------
t : ndarray
t is a vector of of affine transformation parameters with
size at least 6.
If size is 6, t is interpreted as translation + rotation.
If size is 7, t is interpreted as translation + rotation +
isotropic scaling.
If size is 12, t is interpreted as translation + rotation +
scaling + shearing.
static : list
Static streamlines
moving : list
Moving streamlines. These will be transform to align with
the static streamlines
Returns
-------
cost: float
"""
aff = compose_matrix44(t)
moving = transform_streamlines(moving, aff)
d01 = distance_matrix_mdf(static, moving)
return np.sum(d01)
def bundle_min_distance(t, static, moving):
""" MDF-based pairwise distance optimization function (MIN)
We minimize the distance between moving streamlines as they align
with the static streamlines.
Parameters
-----------
t : ndarray
t is a vector of of affine transformation parameters with
size at least 6.
If size is 6, t is interpreted as translation + rotation.
If size is 7, t is interpreted as translation + rotation +
isotropic scaling.
If size is 12, t is interpreted as translation + rotation +
scaling + shearing.
static : list
Static streamlines
moving : list
Moving streamlines.
num_threads : int
Number of threads. If None (default) then all available threads
will be used.
Returns
-------
cost: float
"""
aff = compose_matrix44(t)
moving = transform_streamlines(moving, aff)
d01 = distance_matrix_mdf(static, moving)
rows, cols = d01.shape
return 0.25 * (np.sum(np.min(d01, axis=0)) / float(cols) +
np.sum(np.min(d01, axis=1)) / float(rows)) ** 2
def bundle_min_distance_fast(t, static, moving, block_size, num_threads):
""" MDF-based pairwise distance optimization function (MIN)
We minimize the distance between moving streamlines as they align
with the static streamlines.
Parameters
-----------
t : array
1D array. t is a vector of of affine transformation parameters with
size at least 6.
If size is 6, t is interpreted as translation + rotation.
If size is 7, t is interpreted as translation + rotation +
isotropic scaling.
If size is 12, t is interpreted as translation + rotation +
scaling + shearing.
static : array
N*M x 3 array. All the points of the static streamlines. With order of
streamlines intact. Where N is the number of streamlines and M
is the number of points per streamline.
moving : array
K*M x 3 array. All the points of the moving streamlines. With order of
streamlines intact. Where K is the number of streamlines and M
is the number of points per streamline.
block_size : int
Number of points per streamline. All streamlines in static and moving
should have the same number of points M.
num_threads : int
Number of threads. If None (default) then all available threads
will be used.
Returns
-------
cost: float
Notes
-----
This is a faster implementation of ``bundle_min_distance``, which requires
that all the points of each streamline are allocated into an ndarray
(of shape N*M by 3, with N the number of points per streamline and M the
number of streamlines). This can be done by calling
`dipy.tracking.streamlines.unlist_streamlines`.
"""
aff = compose_matrix44(t)
moving = np.dot(aff[:3, :3], moving.T).T + aff[:3, 3]
moving = np.ascontiguousarray(moving, dtype=np.float64)
rows = static.shape[0] / block_size
cols = moving.shape[0] / block_size
return _bundle_minimum_distance(static, moving,
rows,
cols,
block_size,
num_threads)
def _threshold(x, th):
return np.maximum(np.minimum(x, th), -th)
def compose_matrix44(t, dtype=np.double):
""" Compose a 4x4 transformation matrix
Parameters
-----------
t : ndarray
This is a 1D vector of of affine transformation parameters with
size at least 6.
If size is 6, t is interpreted as translation + rotation.
If size is 7, t is interpreted as translation + rotation +
isotropic scaling.
If size is 12, t is interpreted as translation + rotation +
scaling + shearing.
Returns
-------
T : ndarray
Homogeneous transformation matrix of size 4x4.
"""
if isinstance(t, list):
t = np.array(t)
size = t.size
if size not in [6, 7, 12]:
raise ValueError('Accepted number of parameters is 6, 7 and 12')
scale, shear, angles, translate = (None, ) * 4
if size in [6, 7, 12]:
translate = _threshold(t[0:3], MAX_DIST)
angles = np.deg2rad(t[3:6])
if size == 7:
scale = np.array((t[6],) * 3)
if size == 12:
scale = t[6: 9]
shear = t[9: 12]
return compose_matrix(scale=scale, shear=shear,
angles=angles,
translate=translate)
def decompose_matrix44(mat, size=12):
""" Given a 4x4 homogeneous matrix return the parameter vector
Parameters
-----------
mat : array
Homogeneous 4x4 transformation matrix
size : int
Size of output vector. 6 for rigid, 7 for similarity and 12
for affine. Default is 12.
Returns
-------
t : ndarray
One dimensional ndarray of 6, 7 or 12 affine parameters.
"""
scale, shear, angles, translate, _ = decompose_matrix(mat)
t = np.zeros(12)
t[:3] = translate
t[3: 6] = np.rad2deg(angles)
if size == 6:
return t[:6]
if size == 7:
t[6] = np.mean(scale)
return t[:7]
if size == 12:
t[6: 9] = scale
t[9: 12] = shear
return t
raise ValueError('Size can be 6, 7 or 12')
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