def quiver_3d(svf, flow=None, sample=(1, 1, 1), scale=1):
omega_svf = qr.check_is_vf(svf)
omega_flow = qr.check_is_vf(flow)
np.testing.assert_array_equal(omega_flow, omega_svf)
id_field = gen_id.id_eulerian_like(svf)
fig = plt.figure()
ax = fig.gca(projection='3d')
x = id_field[::sample[0], ::sample[1], ::sample[2], 0, 0]
y = id_field[::sample[0], ::sample[1], ::sample[2], 0, 1]
z = id_field[::sample[0], ::sample[1], ::sample[2], 0, 2]
x = x.reshape(np.product(x.shape))
y = y.reshape(np.product(y.shape))
z = z.reshape(np.product(z.shape))
svf_x = svf[::sample[0], ::sample[1], ::sample[2], 0, 0]
svf_y = svf[::sample[0], ::sample[1], ::sample[2], 0, 1]
svf_z = svf[::sample[0], ::sample[1], ::sample[2], 0, 2]
svf_x = svf_x.reshape(np.product(svf_x.shape))
svf_y = svf_y.reshape(np.product(svf_y.shape))
svf_z = svf_z.reshape(np.product(svf_z.shape))
lengths = scale * np.sqrt(svf_x**2 + svf_y**2 + svf_z**2)
for x1, y1, z1, u1, v1, w1, l in zip(x, y, z, svf_x, svf_y, svf_z,
lengths):
ax.quiver(x1,
y1,
z1,
u1,
v1,
w1,
pivot='tail',
length=l,
color='r',
linewidths=0.1)
if flow is not None:
flow_x = flow[::sample[0], ::sample[1], ::sample[2], 0, 0]
flow_y = flow[::sample[0], ::sample[1], ::sample[2], 0, 1]
flow_z = flow[::sample[0], ::sample[1], ::sample[2], 0, 2]
flow_x = flow_x.reshape(np.product(flow_x.shape))
flow_y = flow_y.reshape(np.product(flow_y.shape))
flow_z = flow_z.reshape(np.product(flow_z.shape))
lengthsflow = scale * np.sqrt(svf_x**2 + svf_y**2 + svf_z**2)
for x1, y1, z1, u1, v1, w1, l in zip(x, y, z, flow_x, flow_y, flow_z,
lengthsflow):
ax.quiver(x1,
y1,
z1,
u1,
v1,
w1,
pivot='tail',
length=l,
color='b',
linewidths=0.1)
if __name__ == '__main__':
field_0 = gen.generate_random(omega=(20, 20), parameters=(7, 2))
t0, tEnd, dt = 0, 1, 0.1
ic = [[i, j] for i in range(8, 15) for j in range(8, 15)]
colors = ['b'] * len(ic)
r = ode(vf).set_integrator('vode', method='bdf', max_step=dt)
fig = plt.figure(num=1)
ax = fig.add_subplot(111)
# Plot vector field
id_field = gen_id.id_eulerian_like(field_0)
input_field_copy = copy.deepcopy(field_0)
ax.quiver(
id_field[..., 0, 0, 0],
id_field[..., 0, 0, 1],
input_field_copy[..., 0, 0, 0],
input_field_copy[..., 0, 0, 1],
color='r',
alpha=0.8,
linewidths=0.01,
width=0.05,
scale=1,
scale_units='xy',
units='xy',
def see_field(input_vf,
anatomical_plane='axial',
h_slice=0,
sample=(1, 1),
window_title_input='quiver',
title_input='2d vector field',
long_title=False,
fig_tag=1,
scale=1,
subtract_id=False,
input_color='b',
annotate=None,
annotate_position=(1, 1),
width=0.03):
qr.check_is_vf(input_vf)
id_field = gen_id.id_eulerian_like(input_vf)
fig = plt.figure(fig_tag)
ax0 = fig.add_subplot(111)
fig.canvas.set_window_title(window_title_input)
input_field_copy = copy.deepcopy(input_vf)
if subtract_id:
input_field_copy -= id_field
if anatomical_plane == 'axial':
ax0.quiver(id_field[::sample[0], ::sample[1], h_slice, 0, 0],
id_field[::sample[0], ::sample[1], h_slice, 0, 1],
input_field_copy[::sample[0], ::sample[1], h_slice, 0, 0],
input_field_copy[::sample[0], ::sample[1], h_slice, 0, 1],
color=input_color,
linewidths=0.01,
width=width,
scale=scale,
scale_units='xy',
units='xy',
angles='xy')
ax0.set_xlabel('x')
ax0.set_ylabel('y')
elif anatomical_plane == 'sagittal':
ax0.quiver(id_field[::sample[0], h_slice, ::sample[1], 0, 0],
id_field[::sample[0], h_slice, ::sample[1], 0, 1],
input_field_copy[::sample[0], h_slice, ::sample[1], 0, 0],
input_field_copy[::sample[0], h_slice, ::sample[1], 0, 1],
color=input_color,
linewidths=0.01,
width=width,
units='xy',
angles='xy',
scale=scale,
scale_units='xy')
elif anatomical_plane == 'coronal':
ax0.quiver(id_field[h_slice, ::sample[0], ::sample[1], 0, 0],
id_field[h_slice, ::sample[0], ::sample[1], 0, 1],
input_field_copy[h_slice, ::sample[0], ::sample[1], 0, 0],
input_field_copy[h_slice, ::sample[0], ::sample[1], 0, 1],
color=input_color,
linewidths=0.01,
width=width,
units='xy',
angles='xy',
scale=scale,
scale_units='xy')
else:
raise TypeError('Anatomical_plane must be axial, sagittal or coronal')
ax0.xaxis.grid(True,
linestyle='-',
which='major',
color='lightgrey',
alpha=0.5)
ax0.yaxis.grid(True,
linestyle='-',
which='major',
color='lightgrey',
alpha=0.5)
ax0.set_axisbelow(True)
if long_title:
ax0.set_title(title_input + ', ' + str(anatomical_plane) +
' plane, slice ' + str(h_slice))
else:
ax0.set_title(title_input)
if annotate is not None:
ax0.text(annotate_position[0], annotate_position[1], annotate)
plt.axes().set_aspect('equal', 'datalim')
return fig
def see_2_fields(input_obj_0,
input_obj_1,
anatomical_plane_0='axial',
anatomical_plane_1='axial',
h_slice_0=0,
h_slice_1=0,
sample_0=(1, 1),
sample_1=(1, 1),
window_title_input='quiver 2 screens',
title_input_0='Vector field',
title_input_1='Vector field',
long_title_0=False,
long_title_1=False,
fig_tag=1,
scale_0=1,
scale_1=1,
subtract_id_0=False,
subtract_id_1=False,
input_color='b'):
"""
:param input_obj_0:
:param input_obj_1:
:param anatomical_plane_0:
:param anatomical_plane_1:
:param h_slice_0:
:param h_slice_1:
:param sample_0:
:param sample_1:
:param window_title_input:
:param title_input_0:
:param title_input_1:
:param long_title_0:
:param long_title_1:
:param fig_tag:
:param scale_0:
:param scale_1:
:param subtract_id_0:
:param subtract_id_1:
:param input_color:
:return:
"""
qr.check_is_vf(input_obj_0)
qr.check_is_vf(input_obj_1)
id_field_0 = gen_id.id_eulerian_like(
input_obj_0) # other option is casting with Field()
id_field_1 = gen_id.id_eulerian_like(input_obj_1)
input_field_0 = copy.deepcopy(input_obj_0)
input_field_1 = copy.deepcopy(input_obj_1)
if subtract_id_0:
input_field_0 -= id_field_0
if subtract_id_1:
input_field_1 -= id_field_1
fig = plt.figure(fig_tag)
ax0 = fig.add_subplot(121)
ax1 = fig.add_subplot(122)
fig.canvas.set_window_title(window_title_input)
# figure 0
if anatomical_plane_0 == 'axial':
ax0.quiver(id_field_0[::sample_0[0], ::sample_0[1], h_slice_0, 0, 0],
id_field_0[::sample_0[0], ::sample_0[1], h_slice_0, 0, 1],
input_field_0[::sample_0[0], ::sample_0[1], h_slice_0, 0,
0],
input_field_0[::sample_0[0], ::sample_0[1], h_slice_0, 0,
1],
color=input_color,
linewidths=0.01,
width=0.03,
units='xy',
angles='xy',
scale=scale_0,
scale_units='xy')
elif anatomical_plane_0 == 'sagittal':
ax0.quiver(id_field_0[::sample_0[0], h_slice_0, ::sample_0[1], 0, 0],
id_field_0[::sample_0[0], h_slice_0, ::sample_0[1], 0, 1],
input_field_0[::sample_0[0], h_slice_0, ::sample_0[1], 0,
0],
input_field_0[::sample_0[0], h_slice_0, ::sample_0[1], 0,
1],
color=input_color,
linewidths=0.01,
width=0.03,
units='xy',
angles='xy',
scale=scale_0,
scale_units='xy')
elif anatomical_plane_0 == 'coronal':
ax0.quiver(id_field_0[h_slice_0, ::sample_0[0], ::sample_0[1], 0, 0],
id_field_0[h_slice_0, ::sample_0[0], ::sample_0[1], 0, 1],
input_field_0[h_slice_0, ::sample_0[0], ::sample_0[1], 0,
0],
input_field_0[h_slice_0, ::sample_0[0], ::sample_0[1], 0,
1],
color=input_color,
linewidths=0.01,
width=0.03,
units='xy',
angles='xy',
scale=scale_0,
scale_units='xy')
else:
raise TypeError(
'anatomical_plane_0 must be axial, sagittal or coronal')
if long_title_0:
ax0.set_title(title_input_0 + ', ' + str(anatomical_plane_0) +
' plane, slice ' + str(h_slice_0))
else:
ax0.set_title(title_input_0)
ax0.xaxis.grid(True,
linestyle='-',
which='major',
color='lightgrey',
alpha=0.5)
ax0.yaxis.grid(True,
linestyle='-',
which='major',
color='lightgrey',
alpha=0.5)
ax0.set_axisbelow(True)
# figure 1
if anatomical_plane_1 == 'axial':
ax1.quiver(id_field_1[::sample_1[0], ::sample_1[1], h_slice_1, 0, 0],
id_field_1[::sample_1[0], ::sample_1[1], h_slice_1, 0, 1],
input_field_1[::sample_1[0], ::sample_1[1], h_slice_1, 0,
0],
input_field_1[::sample_1[0], ::sample_1[1], h_slice_1, 0,
1],
color=input_color,
linewidths=0.01,
width=0.03,
units='xy',
angles='xy',
scale=scale_1,
scale_units='xy')
elif anatomical_plane_1 == 'sagittal':
ax1.quiver(id_field_0[::sample_1[0], h_slice_0, ::sample_1[1], 0, 0],
id_field_0[::sample_1[0], h_slice_0, ::sample_1[1], 0, 1],
input_field_0[::sample_1[0], h_slice_0, ::sample_1[1], 0,
0],
input_field_0[::sample_1[0], h_slice_0, ::sample_1[1], 0,
1],
color=input_color,
linewidths=0.01,
width=0.03,
units='xy',
angles='xy',
scale=scale_1,
scale_units='xy')
elif anatomical_plane_1 == 'coronal':
ax1.quiver(id_field_1[h_slice_1, ::sample_1[0], ::sample_1[1], 0, 0],
id_field_1[h_slice_1, ::sample_1[0], ::sample_1[1], 0, 1],
input_field_1[h_slice_1, ::sample_1[0], ::sample_1[1], 0,
0],
input_field_1[h_slice_1, ::sample_1[0], ::sample_1[1], 0,
1],
color=input_color,
linewidths=0.01,
width=0.03,
units='xy',
angles='xy',
scale=scale_1,
scale_units='xy')
else:
raise TypeError(
'anatomical_plane_1 must be axial, sagittal or coronal')
if long_title_1:
ax1.set_title(title_input_1 + ', ' + str(anatomical_plane_1) +
' plane, slice ' + str(h_slice_1))
else:
ax1.set_title(title_input_1)
ax1.xaxis.grid(True,
linestyle='-',
which='major',
color='lightgrey',
alpha=0.5)
ax1.yaxis.grid(True,
linestyle='-',
which='major',
color='lightgrey',
alpha=0.5)
ax1.set_axisbelow(True)
fig.set_tight_layout(True)
def lagrangian_to_eulerian(input_vf_lag):
return input_vf_lag + gen_id.id_eulerian_like(input_vf_lag)
def eulerian_to_lagrangian(input_vf_eul):
return input_vf_eul - gen_id.id_eulerian_like(input_vf_eul)
def test_vf_identity_eulerian_like_wrong_input():
with assert_raises(IOError):
gen_id.id_eulerian_like(np.zeros([3, 3, 3, 3, 7]))
def see_overlay_of_n_fields_and_flow(list_of_obj,
list_of_integral_curves,
list_of_alpha_for_obj=None,
alpha_for_integral_curves=None,
anatomical_plane='axial',
h_slice=0,
sample=(1, 1),
window_title_input='quiver',
title_input='2d vector field',
long_title=False,
fig_tag=1,
scale=1,
subtract_id=None,
input_color=('r', 'b'),
input_label=None,
see_tips=False):
fig = plt.figure(fig_tag)
ax0 = fig.add_subplot(111)
fig.canvas.set_window_title(window_title_input)
if subtract_id is None:
subtract_id = [
False,
] * len(list_of_obj)
if list_of_alpha_for_obj is None:
list_of_alpha_for_obj = [
0.8,
] * len(list_of_obj)
if alpha_for_integral_curves is None:
alpha_for_integral_curves = 0.8
for num_obj, input_obj in enumerate(list_of_obj):
if input_obj is not None:
assert qr.check_is_vf(input_obj) == 2
id_field = gen_id.id_eulerian_like(input_obj)
input_field_copy = copy.deepcopy(input_obj)
if subtract_id[num_obj]:
input_field_copy -= id_field
if anatomical_plane == 'axial':
q = ax0.quiver(id_field[::sample[0], ::sample[1], h_slice, 0, 0],
id_field[::sample[0], ::sample[1], h_slice, 0, 1],
input_field_copy[::sample[0], ::sample[1], h_slice,
0, 0],
input_field_copy[::sample[0], ::sample[1], h_slice,
0, 1],
color=input_color[num_obj],
linewidths=0.01,
width=0.03,
scale=scale,
scale_units='xy',
units='xy',
angles='xy',
alpha=list_of_alpha_for_obj[num_obj])
elif anatomical_plane == 'sagittal':
q = ax0.quiver(id_field[::sample[0], h_slice, ::sample[1], 0, 0],
id_field[::sample[0], h_slice, ::sample[1], 0, 1],
input_field_copy[::sample[0], h_slice, ::sample[1],
0, 0],
input_field_copy[::sample[0], h_slice, ::sample[1],
0, 1],
color=input_color[num_obj],
linewidths=1,
units='xy',
angles='xy',
scale=scale,
scale_units='xy',
alpha=list_of_alpha_for_obj[num_obj])
elif anatomical_plane == 'coronal':
q = ax0.quiver(id_field[h_slice, ::sample[0], ::sample[1], 0, 0],
id_field[h_slice, ::sample[0], ::sample[1], 0, 1],
input_field_copy[h_slice, ::sample[0], ::sample[1],
0, 0],
input_field_copy[h_slice, ::sample[0], ::sample[1],
0, 1],
color=input_color[num_obj],
linewidths=1,
units='xy',
angles='xy',
scale=scale,
scale_units='xy',
alpha=list_of_alpha_for_obj[num_obj])
else:
raise TypeError(
'Anatomical_plane must be axial, sagittal or coronal')
# add the integral curves:
for fl in list_of_integral_curves:
ax0.plot(fl[:, 0],
fl[:, 1],
color='m',
lw=1,
alpha=alpha_for_integral_curves)
if see_tips:
ax0.plot(fl[0, 0], fl[0, 1], 'go', alpha=0.3)
ax0.plot(fl[fl.shape[0] - 1, 0],
fl[fl.shape[0] - 1, 1],
'mo',
alpha=0.5)
if input_label is not None:
ax0.quiverkey(q,
1.2,
0.515,
2,
input_label[num_obj],
coordinates='data')
ax0.xaxis.grid(True,
linestyle='-',
which='major',
color='lightgrey',
alpha=0.5)
ax0.yaxis.grid(True,
linestyle='-',
which='major',
color='lightgrey',
alpha=0.5)
ax0.set_axisbelow(True)
if long_title:
ax0.set_title(title_input + ', ' + str(anatomical_plane) +
' plane, slice ' + str(h_slice))
else:
ax0.set_title(title_input)
fig.set_tight_layout(True)
def image_quiver_image(image_1,
input_vf,
image_2,
fig_tag=5,
input_fig_size=(15, 5),
window_title_input='triptych',
h_slice=1,
sampling_svf=(1, 1),
anatomical_plane='axial',
subtract_id=False,
scale=1,
input_color='r',
line_arrowwidths=0.01,
arrowwidths=0.5,
integral_curves=(),
curve_width=0.5,
show_overlay=False):
pyplot.cla()
fig = pyplot.figure(fig_tag,
figsize=input_fig_size,
dpi=100,
facecolor='w',
edgecolor='k')
fig.subplots_adjust(left=0.04, right=0.96, top=0.92, bottom=0.08)
font = {
'family': 'serif',
'color': 'darkblue',
'weight': 'normal',
'size': 12
}
fig.canvas.set_window_title(window_title_input)
# First axis on the left
ax_1 = pyplot.subplot(131)
ax_1.imshow(image_1, cmap='Greys', interpolation='nearest', origin='lower')
# ax_1.axes.xaxis.set_ticklabels([])
# ax_1.axes.yaxis.set_ticklabels([])
ax_1.set_xlabel('Input image', fontdict=font)
ax_1.set_aspect('equal')
# Central vector field
ax_2 = pyplot.subplot(132)
# add background warped
if show_overlay:
ax_2.imshow(image_2,
cmap='Greys',
interpolation='none',
origin='lower')
# add integral curves if any
for int_curve in integral_curves:
ax_2.plot(int_curve[:, 0], int_curve[:, 1], color='b', lw=curve_width)
ax_2.plot(int_curve[int_curve.shape[0] - 1, 0],
int_curve[int_curve.shape[0] - 1, 1],
'bo',
alpha=0.5)
qr.check_is_vf(input_vf)
id_field = gen_id.id_eulerian_like(input_vf)
input_field_copy = copy.deepcopy(input_vf)
if subtract_id:
input_field_copy -= id_field
if anatomical_plane == 'axial':
ax_2.quiver(id_field[::sampling_svf[0], ::sampling_svf[1], h_slice, 0,
0],
id_field[::sampling_svf[0], ::sampling_svf[1], h_slice, 0,
1],
input_field_copy[::sampling_svf[0], ::sampling_svf[1],
h_slice, 0, 0],
input_field_copy[::sampling_svf[0], ::sampling_svf[1],
h_slice, 0, 1],
color=input_color,
linewidths=line_arrowwidths,
width=arrowwidths,
scale=scale,
scale_units='xy',
units='xy',
angles='xy')
elif anatomical_plane == 'sagittal':
ax_2.quiver(id_field[::sampling_svf[0], h_slice, ::sampling_svf[1], 0,
0],
id_field[::sampling_svf[0], h_slice, ::sampling_svf[1], 0,
1],
input_field_copy[::sampling_svf[0],
h_slice, ::sampling_svf[1], 0, 0],
input_field_copy[::sampling_svf[0],
h_slice, ::sampling_svf[1], 0, 1],
color=input_color,
linewidths=line_arrowwidths,
width=arrowwidths,
units='xy',
angles='xy',
scale=scale,
scale_units='xy')
elif anatomical_plane == 'coronal':
ax_2.quiver(
id_field[h_slice, ::sampling_svf[0], ::sampling_svf[1], 0, 0],
id_field[h_slice, ::sampling_svf[0], ::sampling_svf[1], 0, 1],
input_field_copy[h_slice, ::sampling_svf[0], ::sampling_svf[1], 0,
0],
input_field_copy[h_slice, ::sampling_svf[0], ::sampling_svf[1], 0,
1],
color=input_color,
linewidths=line_arrowwidths,
width=arrowwidths,
units='xy',
angles='xy',
scale=scale,
scale_units='xy')
else:
raise TypeError('Anatomical_plane must be axial, sagittal or coronal')
ax_2.set_xlim(0, image_1.shape[0])
ax_2.set_ylim(0, image_1.shape[1])
# ax_2.set_xlabel('x')
# ax_2.set_ylabel('y')
# ax_2.axes.xaxis.set_ticklabels([])
# ax_2.axes.yaxis.set_ticklabels([])
ax_2.set_xlabel('Transformation', fontdict=font)
ax_2.set_aspect('equal')
# Third axis:
ax_3 = pyplot.subplot(133)
ax_3.imshow(image_2, cmap='Greys', interpolation='none', origin='lower')
# ax_3.axes.xaxis.set_ticklabels([])
# ax_3.axes.yaxis.set_ticklabels([])
ax_3.set_xlabel('Transformed image', fontdict=font)
ax_3.set_aspect('equal')
fig.set_tight_layout(True)
return fig