t = np.linspace(0,1,N)
R = 10
noise = 1/1.25
# Generate dataset
x = R*sin(theta)*np.exp(-t) + noise*np.random.random(len(t))
y = R*cos(theta)*np.exp(-t) + noise*np.random.random(len(t))
shuffle = np.random.permutation(np.arange(len(x)))
data = np.vstack((x[shuffle],y[shuffle])).T
x = R*sin(-theta)*np.exp(-t) + noise*np.random.random(len(t))
y = R*cos(-theta)*np.exp(-t) + noise*np.random.random(len(t))
data = np.vstack((data,np.vstack((x,y)).T))
dm = DiffusionMap(data, kernel=gauss_kernel, kernel_params={'eps': eps},
cache_filename=None)
w,v = dm.map(ndim=2)
plt.title('Time step %s' % T)
plt.subplot(311)
plt.plot(data[:,0],data[:,1],'x')
plt.axis('equal')
plt.subplot(312)
plt.imshow(dm.H, cmap='viridis')
plt.subplot(313)
for i,(x,y) in enumerate(zip(v[:,0].flat,v[:,1].flat)):
plt.plot([x],[y],'.b')
template = io.imread('template.png', as_grey=True)
shape = np.array(template.shape)
x_off,y_off = (shape-1)/2
data = np.empty((len(angles),np.prod(template.shape)),float)
dx,dy = data.shape
for i,a in enumerate(angles):
print("Rotating %i" % i)
data[i] = rotate_around_centre(template,angle=a,cval=255).flat
# EXPERIMENT: Simulate colour image
old_data = data.copy()
data = data.repeat(3, axis=1)
# Compute diffusion map on dataset
dm = DiffusionMap(data, kernel=gauss_kernel, kernel_params={'eps':1e9})
w,v = dm.map()
# Plot the raw data as seen by the diffusion map
plt.figure()
plt.imshow(data,aspect=float(dy)/dx,cmap=plt.cm.gray)
plt.xticks([])
# Plot the unsorted images on a circle on the x-y plane
plot_images(np.cos(angles_ord),np.sin(angles_ord),old_data,template.shape)
#plt.savefig('images_unordered.png')
# Plot the images on the diffusion coordinates, which should be sorted
plot_images(v[:,0],v[:,1],old_data,template.shape)
#plt.savefig('images_ordered.png')
template = io.imread('template.png', as_grey=True)
shape = np.array(template.shape)
x_off, y_off = (shape - 1) / 2
data = np.empty((len(angles), np.prod(template.shape)), float)
dx, dy = data.shape
for i, a in enumerate(angles):
print("Rotating %i" % i)
data[i] = rotate_around_centre(template, angle=a, cval=255).flat
# EXPERIMENT: Simulate colour image
old_data = data.copy()
data = data.repeat(3, axis=1)
# Compute diffusion map on dataset
dm = DiffusionMap(data, kernel=gauss_kernel, kernel_params={'eps': 1e9})
w, v = dm.map()
# Plot the raw data as seen by the diffusion map
plt.figure()
plt.imshow(data, aspect=float(dy) / dx, cmap=plt.cm.gray)
plt.xticks([])
# Plot the unsorted images on a circle on the x-y plane
plot_images(np.cos(angles_ord), np.sin(angles_ord), old_data,
template.shape)
#plt.savefig('images_unordered.png')
# Plot the images on the diffusion coordinates, which should be sorted
plot_images(v[:, 0], v[:, 1], old_data, template.shape)
#plt.savefig('images_ordered.png')
R = 10
noise = 1 / 1.25
# Generate dataset
x = R * sin(theta) * np.exp(-t) + noise * np.random.random(len(t))
y = R * cos(theta) * np.exp(-t) + noise * np.random.random(len(t))
shuffle = np.random.permutation(np.arange(len(x)))
data = np.vstack((x[shuffle], y[shuffle])).T
x = R * sin(-theta) * np.exp(-t) + noise * np.random.random(len(t))
y = R * cos(-theta) * np.exp(-t) + noise * np.random.random(len(t))
data = np.vstack((data, np.vstack((x, y)).T))
dm = DiffusionMap(data,
kernel=gauss_kernel,
kernel_params={'eps': eps},
cache_filename=None)
w, v = dm.map(ndim=2)
plt.title('Time step %s' % T)
plt.subplot(311)
plt.plot(data[:, 0], data[:, 1], 'x')
plt.axis('equal')
plt.subplot(312)
plt.imshow(dm.H, cmap='viridis')
plt.subplot(313)
for i, (x, y) in enumerate(zip(v[:, 0].flat, v[:, 1].flat)):
