/usr/share/pyshared/dipy/reconst/gqi.py is in python-dipy 0.7.1-2.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 | """ Classes and functions for generalized q-sampling """
import numpy as np
from .odf import OdfModel, OdfFit, gfa
from .cache import Cache
import warnings
from .multi_voxel import multi_voxel_fit
from .recspeed import local_maxima, remove_similar_vertices
class GeneralizedQSamplingModel(OdfModel, Cache):
def __init__(self,
gtab,
method='gqi2',
sampling_length=1.2,
normalize_peaks=False):
r""" Generalized Q-Sampling Imaging [1]_
This model has the same assumptions as the DSI method i.e. Cartesian
grid sampling in q-space and fast gradient switching.
Implements equations 2.14 from [2]_ for standard GQI and equation 2.16
from [2]_ for GQI2. You can think of GQI2 as an analytical solution of
the DSI ODF.
Parameters
----------
gtab : object,
GradientTable
method : str,
'standard' or 'gqi2'
sampling_length : float,
diffusion sampling length (lambda in eq. 2.14 and 2.16)
References
----------
.. [1] Yeh F-C et. al, "Generalized Q-Sampling Imaging", IEEE TMI, 2010
.. [2] Garyfallidis E, "Towards an accurate brain tractography", PhD
thesis, University of Cambridge, 2012.
Examples
--------
Here we create an example where we provide the data, a gradient table
and a reconstruction sphere and calculate the ODF for the first
voxel in the data.
>>> from dipy.data import dsi_voxels
>>> data, gtab = dsi_voxels()
>>> from dipy.core.subdivide_octahedron import create_unit_sphere
>>> sphere = create_unit_sphere(5)
>>> from dipy.reconst.gqi import GeneralizedQSamplingModel
>>> gq = GeneralizedQSamplingModel(gtab, 'gqi2', 1.4)
>>> voxel_signal = data[0, 0, 0]
>>> odf = gq.fit(voxel_signal).odf(sphere)
See Also
--------
dipy.reconst.dsi.DiffusionSpectrumModel
"""
OdfModel.__init__(self, gtab)
self.method = method
self.Lambda = sampling_length
self.normalize_peaks = normalize_peaks
# 0.01506 = 6*D where D is the free water diffusion coefficient
# l_values sqrt(6 D tau) D free water diffusion coefficient and
# tau included in the b-value
scaling = np.sqrt(self.gtab.bvals * 0.01506)
tmp = np.tile(scaling, (3, 1))
gradsT = self.gtab.bvecs.T
b_vector = gradsT * tmp # element-wise product
self.b_vector = b_vector.T
@multi_voxel_fit
def fit(self, data):
return GeneralizedQSamplingFit(self, data)
class GeneralizedQSamplingFit(OdfFit):
def __init__(self, model, data):
""" Calculates PDF and ODF for a single voxel
Parameters
----------
model : object,
DiffusionSpectrumModel
data : 1d ndarray,
signal values
"""
OdfFit.__init__(self, model, data)
self._gfa = None
self.npeaks = 5
self._peak_values = None
self._peak_indices = None
self._qa = None
def odf(self, sphere):
""" Calculates the discrete ODF for a given discrete sphere.
"""
self.gqi_vector = self.model.cache_get('gqi_vector', key=sphere)
if self.gqi_vector is None:
if self.model.method == 'gqi2':
H=squared_radial_component
#print self.gqi_vector.shape
self.gqi_vector = np.real(H(np.dot(self.model.b_vector, sphere.vertices.T) * self.model.Lambda / np.pi))
if self.model.method == 'standard':
self.gqi_vector = np.real(np.sinc(np.dot(self.model.b_vector, sphere.vertices.T) * self.model.Lambda / np.pi))
self.model.cache_set('gqi_vector', sphere, self.gqi_vector)
return np.dot(self.data, self.gqi_vector)
def normalize_qa(qa, max_qa=None):
""" Normalize quantitative anisotropy.
Used mostly with GQI rather than GQI2.
Parameters
----------
qa : array, shape (X, Y, Z, N)
where N is the maximum number of peaks stored
max_qa : float,
maximum qa value. Usually found in the CSF (corticospinal fluid).
Returns
-------
nqa : array, shape (x, Y, Z, N)
normalized quantitative anisotropy
Notes
-----
Normalized quantitative anisotropy has the very useful property
to be very small near gray matter and background areas. Therefore,
it can be used to mask out white matter areas.
"""
if max_qa is None:
return qa / qa.max()
return qa / max_qa
def squared_radial_component(x, tol=0.01):
""" Part of the GQI2 integral
Eq.8 in the referenced paper by Yeh et al. 2010
"""
with warnings.catch_warnings():
warnings.simplefilter("ignore")
result = (2 * x * np.cos(x) + (x * x - 2) * np.sin(x)) / (x ** 3)
x_near_zero = (x < tol) & (x > -tol)
return np.where(x_near_zero, 1./3, result)
def npa(self, odf, width=5):
""" non-parametric anisotropy
Nimmo-Smith et. al ISMRM 2011
"""
#odf = self.odf(s)
t0, t1, t2 = triple_odf_maxima(self.odf_vertices, odf, width)
psi0 = t0[1] ** 2
psi1 = t1[1] ** 2
psi2 = t2[1] ** 2
npa = np.sqrt((psi0 - psi1) ** 2 + (psi1 - psi2) ** 2 + (psi2 - psi0) ** 2) / np.sqrt(2 * (psi0 ** 2 + psi1 ** 2 + psi2 ** 2))
#print 'tom >>>> ',t0,t1,t2,npa
return t0,t1,t2,npa
def equatorial_zone_vertices(vertices, pole, width=5):
"""
finds the 'vertices' in the equatorial zone conjugate
to 'pole' with width half 'width' degrees
"""
return [i for i,v in enumerate(vertices) if np.abs(np.dot(v,pole)) < np.abs(np.sin(np.pi*width/180))]
def polar_zone_vertices(vertices, pole, width=5):
"""
finds the 'vertices' in the equatorial band around
the 'pole' of radius 'width' degrees
"""
return [i for i,v in enumerate(vertices) if np.abs(np.dot(v,pole)) > np.abs(np.cos(np.pi*width/180))]
def upper_hemi_map(v):
"""
maps a 3-vector into the z-upper hemisphere
"""
return np.sign(v[2])*v
def equatorial_maximum(vertices, odf, pole, width):
eqvert = equatorial_zone_vertices(vertices, pole, width)
#need to test for whether eqvert is empty or not
if len(eqvert) == 0:
print('empty equatorial band at %s pole with width %f' % (np.array_str(pole), width))
return None, None
eqvals = [odf[i] for i in eqvert]
eqargmax = np.argmax(eqvals)
eqvertmax = eqvert[eqargmax]
eqvalmax = eqvals[eqargmax]
return eqvertmax, eqvalmax
def patch_vertices(vertices,pole, width):
"""
find 'vertices' within the cone of 'width' degrees around 'pole'
"""
return [i for i,v in enumerate(vertices) if np.abs(np.dot(v,pole)) > np.abs(np.cos(np.pi*width/180))]
def patch_maximum(vertices, odf, pole, width):
eqvert = patch_vertices(vertices, pole, width)
#need to test for whether eqvert is empty or not
if len(eqvert) == 0:
print('empty cone around pole %s with with width %f' % (np.array_str(pole), width))
return np.Null, np.Null
eqvals = [odf[i] for i in eqvert]
eqargmax = np.argmax(eqvals)
eqvertmax = eqvert[eqargmax]
eqvalmax = eqvals[eqargmax]
return eqvertmax, eqvalmax
def odf_sum(odf):
return np.sum(odf)
def patch_sum(vertices, odf, pole, width):
eqvert = patch_vertices(vertices, pole, width)
#need to test for whether eqvert is empty or not
if len(eqvert) == 0:
print('empty cone around pole %s with with width %f' % (np.array_str(pole), width))
return np.Null
return np.sum([odf[i] for i in eqvert])
def triple_odf_maxima(vertices, odf, width):
indmax1 = np.argmax([odf[i] for i,v in enumerate(vertices)])
odfmax1 = odf[indmax1]
pole = vertices[indmax1]
eqvert = equatorial_zone_vertices(vertices, pole, width)
indmax2, odfmax2 = equatorial_maximum(vertices,\
odf, pole, width)
indmax3 = eqvert[np.argmin([np.abs(np.dot(vertices[indmax2],vertices[p])) for p in eqvert])]
odfmax3 = odf[indmax3]
"""
cross12 = np.cross(vertices[indmax1],vertices[indmax2])
cross12 = cross12/np.sqrt(np.sum(cross12**2))
indmax3, odfmax3 = patch_maximum(vertices, odf, cross12, 2*width)
"""
return [(indmax1, odfmax1),(indmax2, odfmax2),(indmax3, odfmax3)]
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