/usr/lib/python2.7/dist-packages/dipy/align/tests/test_metrics.py is in python-dipy 0.10.1-1.
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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 | import numpy as np
from scipy import ndimage
from .. import floating
from ..metrics import SSDMetric, CCMetric, EMMetric
from numpy.testing import (assert_array_equal,
assert_array_almost_equal,
assert_raises)
def test_exceptions():
for invalid_dim in [-1,0,1,4,5]:
assert_raises(ValueError, CCMetric, invalid_dim)
assert_raises(ValueError, EMMetric, invalid_dim)
assert_raises(ValueError, SSDMetric, invalid_dim)
assert_raises(ValueError, SSDMetric, 3, step_type='unknown_metric_name')
assert_raises(ValueError, EMMetric, 3, step_type='unknown_metric_name')
def test_EMMetric_image_dynamics():
np.random.seed(7181309)
metric = EMMetric(2)
target_shape = (10, 10)
#create a random image
image = np.ndarray(target_shape, dtype=floating)
image[...] = np.random.randint(0, 10, np.size(image)).reshape(tuple(target_shape))
#compute the expected binary mask
expected = (image > 0).astype(np.int32)
metric.use_static_image_dynamics(image, None)
assert_array_equal(expected, metric.static_image_mask)
metric.use_moving_image_dynamics(image, None)
assert_array_equal(expected, metric.moving_image_mask)
def test_em_demons_step_2d():
r"""
Compares the output of the demons step in 2d against an analytical
step. The fixed image is given by $F(x) = \frac{1}{2}||x - c_f||^2$, the
moving image is given by $G(x) = \frac{1}{2}||x - c_g||^2$,
$x, c_f, c_g \in R^{2}$
References
----------
[Vercauteren09] Vercauteren, T., Pennec, X., Perchant, A., & Ayache, N.
(2009). Diffeomorphic demons: efficient non-parametric
image registration. NeuroImage, 45(1 Suppl), S61-72.
doi:10.1016/j.neuroimage.2008.10.040
"""
#Select arbitrary images' shape (same shape for both images)
sh = (20, 10)
#Select arbitrary centers
c_f = np.asarray(sh)/2
c_g = c_f + 0.5
#Compute the identity vector field I(x) = x in R^2
x_0 = np.asarray(range(sh[0]))
x_1 = np.asarray(range(sh[1]))
X = np.ndarray(sh + (2,), dtype = np.float64)
O = np.ones(sh)
X[...,0]= x_0[:, None] * O
X[...,1]= x_1[None, :] * O
#Compute the gradient fields of F and G
grad_F = X - c_f
grad_G = X - c_g
#The squared norm of grad_G to be used later
sq_norm_grad_F = np.sum(grad_F**2,-1)
sq_norm_grad_G = np.sum(grad_G**2,-1)
#Compute F and G
F = 0.5 * sq_norm_grad_F
G = 0.5 * sq_norm_grad_G
#Create an instance of EMMetric
metric = EMMetric(2)
metric.static_spacing = np.array([1.2, 1.2])
#The $\sigma_x$ (eq. 4 in [Vercauteren09]) parameter is computed in ANTS
#based on the image's spacing
sigma_x_sq = np.sum(metric.static_spacing**2)/metric.dim
#Set arbitrary values for $\sigma_i$ (eq. 4 in [Vercauteren09])
#The original Demons algorithm used simply |F(x) - G(x)| as an
#estimator, so let's use it as well
sigma_i_sq = (F - G)**2
#Set the properties relevant to the demons methods
metric.smooth = 3.0
metric.gradient_static = np.array(grad_F, dtype = floating)
metric.gradient_moving = np.array(grad_G, dtype = floating)
metric.static_image = np.array(F, dtype = floating)
metric.moving_image = np.array(G, dtype = floating)
metric.staticq_means_field = np.array(F, dtype = floating)
metric.staticq_sigma_sq_field = np.array(sigma_i_sq, dtype = floating)
metric.movingq_means_field = np.array(G, dtype = floating)
metric.movingq_sigma_sq_field = np.array(sigma_i_sq, dtype = floating)
#compute the step using the implementation under test
actual_forward = metric.compute_demons_step(True)
actual_backward = metric.compute_demons_step(False)
#Now directly compute the demons steps according to eq 4 in [Vercauteren09]
num_fwd = sigma_x_sq * (G - F)
den_fwd = sigma_x_sq * sq_norm_grad_F + sigma_i_sq
expected_fwd = -1 * np.array(grad_F) #This is $J^{P}$ in eq. 4 [Vercauteren09]
expected_fwd[..., 0] *= num_fwd / den_fwd
expected_fwd[..., 1] *= num_fwd / den_fwd
#apply Gaussian smoothing
expected_fwd[..., 0] = ndimage.filters.gaussian_filter(expected_fwd[..., 0], 3.0)
expected_fwd[..., 1] = ndimage.filters.gaussian_filter(expected_fwd[..., 1], 3.0)
num_bwd = sigma_x_sq * (F - G)
den_bwd = sigma_x_sq * sq_norm_grad_G + sigma_i_sq
expected_bwd = -1 * np.array(grad_G) #This is $J^{P}$ in eq. 4 [Vercauteren09]
expected_bwd[..., 0] *= num_bwd / den_bwd
expected_bwd[..., 1] *= num_bwd / den_bwd
#apply Gaussian smoothing
expected_bwd[..., 0] = ndimage.filters.gaussian_filter(expected_bwd[..., 0], 3.0)
expected_bwd[..., 1] = ndimage.filters.gaussian_filter(expected_bwd[..., 1], 3.0)
assert_array_almost_equal(actual_forward, expected_fwd)
assert_array_almost_equal(actual_backward, expected_bwd)
def test_em_demons_step_3d():
r"""
Compares the output of the demons step in 3d against an analytical
step. The fixed image is given by $F(x) = \frac{1}{2}||x - c_f||^2$, the
moving image is given by $G(x) = \frac{1}{2}||x - c_g||^2$,
$x, c_f, c_g \in R^{3}$
References
----------
[Vercauteren09] Vercauteren, T., Pennec, X., Perchant, A., & Ayache, N.
(2009). Diffeomorphic demons: efficient non-parametric
image registration. NeuroImage, 45(1 Suppl), S61-72.
doi:10.1016/j.neuroimage.2008.10.040
"""
#Select arbitrary images' shape (same shape for both images)
sh = (20, 15, 10)
#Select arbitrary centers
c_f = np.asarray(sh)/2
c_g = c_f + 0.5
#Compute the identity vector field I(x) = x in R^2
x_0 = np.asarray(range(sh[0]))
x_1 = np.asarray(range(sh[1]))
x_2 = np.asarray(range(sh[2]))
X = np.ndarray(sh + (3,), dtype = np.float64)
O = np.ones(sh)
X[...,0]= x_0[:, None, None] * O
X[...,1]= x_1[None, :, None] * O
X[...,2]= x_2[None, None, :] * O
#Compute the gradient fields of F and G
grad_F = X - c_f
grad_G = X - c_g
#The squared norm of grad_G to be used later
sq_norm_grad_F = np.sum(grad_F**2,-1)
sq_norm_grad_G = np.sum(grad_G**2,-1)
#Compute F and G
F = 0.5 * sq_norm_grad_F
G = 0.5 * sq_norm_grad_G
#Create an instance of EMMetric
metric = EMMetric(3)
metric.static_spacing = np.array([1.2, 1.2, 1.2])
#The $\sigma_x$ (eq. 4 in [Vercauteren09]) parameter is computed in ANTS
#based on the image's spacing
sigma_x_sq = np.sum(metric.static_spacing**2)/metric.dim
#Set arbitrary values for $\sigma_i$ (eq. 4 in [Vercauteren09])
#The original Demons algorithm used simply |F(x) - G(x)| as an
#estimator, so let's use it as well
sigma_i_sq = (F - G)**2
#Set the properties relevant to the demons methods
metric.smooth = 3.0
metric.gradient_static = np.array(grad_F, dtype = floating)
metric.gradient_moving = np.array(grad_G, dtype = floating)
metric.static_image = np.array(F, dtype = floating)
metric.moving_image = np.array(G, dtype = floating)
metric.staticq_means_field = np.array(F, dtype = floating)
metric.staticq_sigma_sq_field = np.array(sigma_i_sq, dtype = floating)
metric.movingq_means_field = np.array(G, dtype = floating)
metric.movingq_sigma_sq_field = np.array(sigma_i_sq, dtype = floating)
#compute the step using the implementation under test
actual_forward = metric.compute_demons_step(True)
actual_backward = metric.compute_demons_step(False)
#Now directly compute the demons steps according to eq 4 in [Vercauteren09]
num_fwd = sigma_x_sq * (G - F)
den_fwd = sigma_x_sq * sq_norm_grad_F + sigma_i_sq
expected_fwd = -1 * np.array(grad_F)
expected_fwd[..., 0] *= num_fwd / den_fwd
expected_fwd[..., 1] *= num_fwd / den_fwd
expected_fwd[..., 2] *= num_fwd / den_fwd
#apply Gaussian smoothing
expected_fwd[..., 0] = ndimage.filters.gaussian_filter(expected_fwd[..., 0], 3.0)
expected_fwd[..., 1] = ndimage.filters.gaussian_filter(expected_fwd[..., 1], 3.0)
expected_fwd[..., 2] = ndimage.filters.gaussian_filter(expected_fwd[..., 2], 3.0)
num_bwd = sigma_x_sq * (F - G)
den_bwd = sigma_x_sq * sq_norm_grad_G + sigma_i_sq
expected_bwd = -1 * np.array(grad_G)
expected_bwd[..., 0] *= num_bwd / den_bwd
expected_bwd[..., 1] *= num_bwd / den_bwd
expected_bwd[..., 2] *= num_bwd / den_bwd
#apply Gaussian smoothing
expected_bwd[..., 0] = ndimage.filters.gaussian_filter(expected_bwd[..., 0], 3.0)
expected_bwd[..., 1] = ndimage.filters.gaussian_filter(expected_bwd[..., 1], 3.0)
expected_bwd[..., 2] = ndimage.filters.gaussian_filter(expected_bwd[..., 2], 3.0)
assert_array_almost_equal(actual_forward, expected_fwd)
assert_array_almost_equal(actual_backward, expected_bwd)
if __name__=='__main__':
test_em_demons_step_2d()
test_em_demons_step_3d()
test_exceptions()
test_EMMetric_image_dynamics()
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