def visual_test_spherical_poly_conditional():
import experiments.registration.gproc as gp
import numpy.linalg as npl
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import numpy as np
#B = np.loadtxt('data/B.txt')[1:,:3]
B = np.loadtxt('Ramon_dwi.bvecs')[:,:3]
noise = np.array([21, 19, 26, 16, 20, 20, 26, 14, 24, 8,
37, 9, 39, 29, 17, 7, 13, 23, 12, 55, 40,
19, 6, 5, 20, 23, 31, 25, 14, 19, 22, 14], dtype=np.float64)
#signal = np.array([186, 107, 167, 250, 170, 135, 93, 250, 138, 95, 169,
# 207, 177, 160, 247, 188, 116, 235, 199, 192, 153, 237,
# 176, 115, 228, 200, 90, 157, 194, 216, 94, 128], dtype=np.float64)
signal = np.array(rcc_signal, dtype=np.float64)
mean_signal = signal.mean()
f_in = signal - mean_signal
x_in = B.copy()
sigmasq_signal = f_in.var()
sigmasq_noise = noise.var()
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
x = np.outer(np.cos(u), np.sin(v))
y = np.outer(np.sin(u), np.sin(v))
z = np.outer(np.ones(np.size(u)), np.cos(v))
x_out = np.array([x.reshape(-1),y.reshape(-1),z.reshape(-1)]).T
mean_out, S_out = gp.spherical_poly_conditional(x_in, f_in, x_out, sigmasq_signal, sigmasq_noise)
mean_out = np.array(mean_out)
predicted = mean_out.reshape(x.shape)
predicted += mean_signal
x *= predicted
y *= predicted
z *= predicted
fig = figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(x, y, z, rstride=4, cstride=4, color='b', alpha=0.2, shade=True)
points = diag(signal).dot(x_in)
ax.scatter(points[:,0].copy(), points[:,1].copy(), points[:,2].copy(), c='r', s=40)
ax.scatter(-1*points[:,0].copy(), -1*points[:,1].copy(), -1*points[:,2].copy(), c='r', s=40)
def draw_rect_dwi(event):
global global_figure
global sel_signal
if event.inaxes != global_figure.axes[0]:
return
global global_map
side = 2
px, py = int(event.xdata), int(event.ydata)
dwi = global_map['dwi']
bvecs = global_map['bvecs']
dwi_name = global_map['dwi_name']
shape = dwi.shape
residuals = global_map['residuals']
slice_type = global_map['slice_type']
slice_index = global_map['slice_index']
vmin = global_map['vmin']
vmax = global_map['vmax']
if slice_index is None:
slice_index = dwi.shape[slice_type]//2
subsample0=None
subsample1=None
x, y, z = None, None, None
plt.clf()
ax = global_figure.add_subplot(1,2,1)
if slice_type==0:
ax.imshow(residuals[slice_index,:,:].T, origin='lower', vmin=vmin, vmax=vmax)
x, y, z = slice_index, px, py
elif slice_type==1:
ax.imshow(residuals[:,slice_index,:].T, origin='lower', vmin=vmin, vmax=vmax)
x, y, z = px, slice_index, py
else:
ax.imshow(residuals[:,:,slice_index].T, origin='lower', vmin=vmin, vmax=vmax)
x, y, z = px, py, slice_index
print("V[%d,%d,%d]=%f\n"%(x,y,z,residuals[x,y,z]))
minx, maxx = max(0, x-side//2), min(shape[0]-1, x+side//2)
miny, maxy = max(0, y-side//2), min(shape[1]-1, y+side//2)
minz, maxz = max(0, z-side//2), min(shape[2]-1, z+side//2)
sel_signal=dwi[x,y,z,:].copy()
print(sel_signal)
# Duplicate the points in the opposite direction
points = np.empty((bvecs.shape[0] * 2, 3), dtype=np.float64)
points[:bvecs.shape[0],:] = diag(sel_signal).dot(bvecs)
points[bvecs.shape[0]:,:] = diag(sel_signal).dot(bvecs)*-1
# Fit Gaussian process
mean_signal = sel_signal.mean()
f_in = sel_signal - mean_signal
x_in = bvecs.copy()
sigmasq_signal = f_in.var()
sigmasq_noise = 100.0 # We need to estimate this from the data
# Create sampling points
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
x = np.outer(np.cos(u), np.sin(v))
y = np.outer(np.sin(u), np.sin(v))
z = np.outer(np.ones(np.size(u)), np.cos(v))
x_out = np.array([x.reshape(-1),y.reshape(-1),z.reshape(-1)]).T
# Get the conditional mean and covariance matrix
mean_out, S_out = gp.spherical_poly_conditional(x_in, f_in, x_out, sigmasq_signal, sigmasq_noise)
mean_out = np.array(mean_out)
# Get the predicted signal at the new sampling points
predicted = mean_out.reshape(x.shape)
predicted += mean_signal
x *= predicted
y *= predicted
z *= predicted
ax = global_figure.add_subplot(122, projection='3d')
ax.plot_surface(x, y, z, rstride=4, cstride=4, color='b', alpha=0.2, shade=True)
points = diag(sel_signal).dot(x_in)
ax.scatter(points[:,0].copy(), points[:,1].copy(), points[:,2].copy(), c='r', s=40)
ax.scatter(-1*points[:,0].copy(), -1*points[:,1].copy(), -1*points[:,2].copy(), c='r', s=40)
ax = global_figure.get_axes()[0]
R = Rectangle((px-side//2,py-side//2), side, side, facecolor='none', linewidth=3, edgecolor='#DD0000')
if len(ax.artists)>0:
ax.artists[-1].remove()
ax.add_artist(R)
draw()
