def fun_rcdt_single(self, I):
# I: (width, height)
radoncdt = RadonCDT(self.thetas)
Ircdt = radoncdt.forward(x0_range,
self.template / np.sum(self.template),
x_range, I / np.sum(I), self.rm_edge)
return Ircdt
def fun_rcdt_single(self, I):
# I: (rows, columns)
radoncdt = RadonCDT(self.thetas)
template = np.ones(I.shape, dtype=I.dtype)
Ircdt = radoncdt.forward(x0_range, template / np.sum(template),
x_range, I / np.sum(I), self.rm_edge)
return Ircdt
def forward_seq(self, X, template):
self.template = template
radoncdt = RadonCDT(self.thetas)
x_hat = []
for i in range(X.shape[0]):
x_hat.append(
radoncdt.forward(x0_range,
self.template / np.sum(self.template),
x_range, X[i, :] / np.sum(X[i, :]),
self.rm_edge))
return np.asarray(x_hat)
assert not args.use_gpu
import torch
import skorch
from torch import nn
from skorch import NeuralNetClassifier
num_classes, img_size, po_train_max, rm_edge = dataset_config(args.dataset)
theta = np.linspace(0, 176, 45)
# Functions to calculate RCDT when MLP classifier is used
from pytranskit.optrans.continuous.radoncdt import RadonCDT
eps = 1e-6
x0_range = [0, 1]
x_range = [0, 1]
radoncdt = RadonCDT(theta)
def fun_rcdt_single(I):
# I: (width, height)
template = np.ones(I.shape, dtype=I.dtype)
Ircdt = radoncdt.forward(x0_range, template / np.sum(template), x_range,
I / np.sum(I), rm_edge)
return Ircdt
def fun_rcdt_batch(data):
# data: (n_samples, width, height)
dataRCDT = [
fun_rcdt_single(data[j, :, :] + eps) for j in range(data.shape[0])
]
def fun_ircdt_single(self, Ihat):
radoncdt = RadonCDT(self.thetas)
Iircdt = radoncdt.apply_inverse_map(Ihat, self.template, x_range)
return Iircdt
def visualize(self, directions=5, points=5, thetas=theta, SD_spread=1):
dir_num = directions
gI_num = points
b_hat1 = self.basis_hat1
b_hat2 = self.basis_hat2
s_tilde_tr1 = self.cca_proj_tr1
s_tilde_tr2 = self.cca_proj_tr2
s_tilde_te1 = self.cca_proj_te1
s_tilde_te2 = self.cca_proj_te2
cca_dirs1 = b_hat1[:dir_num, :]
cca_dirs2 = b_hat2[:dir_num, :]
cca_proj1 = s_tilde_tr1[:, :dir_num]
cca_proj2 = s_tilde_tr2[:, :dir_num]
radoncdt = RadonCDT(thetas)
## figure 1 of 3
viz_cca1 = np.zeros((dir_num, self.R, self.C * gI_num))
viz_cca2 = np.zeros((dir_num, self.R, self.C * gI_num))
for a in range(dir_num):
lamb1 = np.linspace(-SD_spread * np.std(cca_proj1[:, a]),
SD_spread * np.std(cca_proj1[:, a]),
num=gI_num)
lamb2 = np.linspace(-SD_spread * np.std(cca_proj2[:, a]),
SD_spread * np.std(cca_proj2[:, a]),
num=gI_num)
mode_var1 = np.zeros([gI_num, self.Rtr, self.Ctr])
mode_var2 = np.zeros([gI_num, self.Rtr, self.Ctr])
mode_var_recon1 = np.zeros([gI_num, self.R, self.C])
mode_var_recon2 = np.zeros([gI_num, self.R, self.C])
for b in range(gI_num):
mode_var1[b, :, :] = self.mean_tr + lamb1[b] * cca_dirs1[a, :]
mode_var2[b, :, :] = self.mean_tr + lamb2[b] * cca_dirs2[a, :]
mode_var_recon1[b, :, :] = radoncdt.apply_inverse_map(
mode_var1[b, :, :], self.template, x_range)
mode_var_recon2[b, :, :] = radoncdt.apply_inverse_map(
mode_var2[b, :, :], self.template, x_range)
t1 = mode_var_recon1[b]
t2 = mode_var_recon2[b]
t1 = t1 - np.min(t1)
t1 = t1 / np.max(t1)
t2 = t2 - np.min(t2)
t2 = t2 / np.max(t2)
mode_var_recon1[b] = t1
mode_var_recon2[b] = t2
viz_cca1[a, :] = mode_var_recon1.transpose(2, 0,
1).reshape(self.C, -1)
viz_cca2[a, :] = mode_var_recon2.transpose(2, 0,
1).reshape(self.C, -1)
for a in range(dir_num):
if a == 0:
F1 = viz_cca1[a, :]
F2 = viz_cca2[a, :]
else:
F1 = np.concatenate((F1, viz_cca1[a, :]), axis=0)
F2 = np.concatenate((F2, viz_cca2[a, :]), axis=0)
r1, c1 = np.shape(F1)
r2, c2 = np.shape(F2)
fig, (ax0, ax1) = plt.subplots(ncols=2,
figsize=(16, 8),
sharex=True,
sharey=True)
ax0.imshow(np.transpose(F1), cmap='gray')
ax0.set_xlabel('Modes of variation', fontsize=12)
ax0.set_ylabel('($\sigma$)', fontsize=12)
ax0.set_title('Variation along the prominant CCA modes (Class 0)')
plt.xticks(
np.linspace(r1 / (2 * dir_num), r1 - r1 / (2 * dir_num), dir_num),
np.array(range(1, dir_num + 1)))
plt.yticks(
np.linspace(1, c1, 5),
np.array([-SD_spread, -SD_spread / 2, 0, SD_spread / 2,
SD_spread]))
ax1.imshow(np.transpose(F2), cmap='gray')
ax1.set_xlabel('Modes of variation', fontsize=12)
ax1.set_ylabel('($\sigma$)', fontsize=12)
ax1.set_title('Variation along the prominant CCA modes (Class 1)')
plt.xticks(
np.linspace(r1 / (2 * dir_num), r1 - r1 / (2 * dir_num), dir_num),
np.array(range(1, dir_num + 1)))
plt.yticks(
np.linspace(1, c1, 5),
np.array([-SD_spread, -SD_spread / 2, 0, SD_spread / 2,
SD_spread]))
plt.show()
## figure 2 of 3
viz_dirs1 = viz_cca1[:2, :]
viz_dirs2 = viz_cca2[:2, :]
proj_tr1 = s_tilde_tr1[:, :2]
proj_tr2 = s_tilde_tr2[:, :2]
proj_te1 = s_tilde_te1[:, :2]
proj_te2 = s_tilde_te2[:, :2]
plt.figure(figsize=(18, 7))
leg_str = ['Variable X', 'Variable Y']
bas1 = np.array([0, 1])
bas1a = bas1 * np.min(proj_tr1[:, 0])
bas1b = bas1 * np.max(proj_tr1[:, 0])
basy = [bas1a[0], bas1b[0]]
basx = [bas1a[1], bas1b[1]]
ax0 = plt.subplot2grid((4, 10), (0, 1), colspan=3, rowspan=3)
ax0.grid(linestyle='--')
X = proj_tr1
Y = proj_tr2
ax0.scatter(X[:, 0], X[:, 1], color='C' + str(1))
ax0.scatter(Y[:, 0], Y[:, 1], color='C' + str(2))
ax0.legend(leg_str)
ax0.plot(basx, basy, color='C4')
ax0.set_title(
'Projection of training data on the first 2 CCA directions')
ax1 = plt.subplot2grid((4, 10), (3, 1), colspan=3, rowspan=1)
xax = viz_dirs1[0, :]
ax1.imshow(xax, cmap='gray')
ax1.set_xticks([])
ax1.set_yticks([])
ax2 = plt.subplot2grid((4, 10), (0, 0), colspan=1, rowspan=3)
yax = np.transpose(viz_dirs1[1, :])
ax2.imshow(yax, cmap='gray')
ax2.set_xticks([])
ax2.set_yticks([])
bas1a = bas1 * np.min(proj_te1[:, 0])
bas1b = bas1 * np.max(proj_te1[:, 0])
basy = [bas1a[0], bas1b[0]]
basx = [bas1a[1], bas1b[1]]
ax0 = plt.subplot2grid((4, 10), (0, 6), colspan=3, rowspan=3)
ax0.grid(linestyle='--')
X = proj_te1
Y = proj_te2
ax0.scatter(X[:, 0], X[:, 1], color='C' + str(1))
ax0.scatter(Y[:, 0], Y[:, 1], color='C' + str(2))
ax0.legend(leg_str)
ax0.plot(basx, basy, color='C4')
ax0.set_title('Projection of test data on the first 2 CCA directions')
ax1 = plt.subplot2grid((4, 10), (3, 6), colspan=3, rowspan=1)
xax = viz_dirs1[0, :]
ax1.imshow(xax, cmap='gray')
ax1.set_xticks([])
ax1.set_yticks([])
ax2 = plt.subplot2grid((4, 10), (0, 5), colspan=1, rowspan=3)
yax = np.transpose(viz_dirs1[1, :])
ax2.imshow(yax, cmap='gray')
ax2.set_xticks([])
ax2.set_yticks([])
## figure 3 of 3
which_direction = 1
viz_dirs1 = viz_cca1[which_direction - 1:which_direction, :]
viz_dirs2 = viz_cca2[which_direction - 1:which_direction, :]
proj_tr1 = s_tilde_tr1[:, which_direction - 1]
proj_te1 = s_tilde_te1[:, which_direction - 1]
proj_tr2 = s_tilde_tr2[:, which_direction - 1]
proj_te2 = s_tilde_te2[:, which_direction - 1]
plt.figure(figsize=(16, 7))
leg_str = ['Variable X']
ax0 = plt.subplot2grid((4, 8), (0, 0), colspan=3, rowspan=2)
ax0.grid(linestyle='--')
XX = proj_tr1
ax0.hist(XX, color=['C1'])
ax0.legend(leg_str)
ax0.set_title('Projection of training data on the first CCA direction')
ax1 = plt.subplot2grid((4, 8), (2, 0), colspan=3, rowspan=1)
ax1.imshow(viz_dirs1[0, :], cmap='gray')
ax1.set_xticks([])
ax1.set_yticks([])
ax0 = plt.subplot2grid((4, 8), (0, 5), colspan=3, rowspan=2)
ax0.grid(linestyle='--')
XX = proj_te1
ax0.hist(XX, color=['C1'])
ax0.legend(leg_str)
ax0.set_title('Projection of test data on the first CCA direction')
ax1 = plt.subplot2grid((4, 8), (2, 5), colspan=3, rowspan=1)
ax1.imshow(viz_dirs1[0, :], cmap='gray')
ax1.set_xticks([])
ax1.set_yticks([])
plt.figure(figsize=(16, 7))
leg_str = ['Variable Y']
ax0 = plt.subplot2grid((4, 8), (0, 0), colspan=3, rowspan=2)
ax0.grid(linestyle='--')
XX = proj_tr2
ax0.hist(XX, color=['C2'])
ax0.legend(leg_str)
ax0.set_title('Projection of training data on the first CCA direction')
ax1 = plt.subplot2grid((4, 8), (2, 0), colspan=3, rowspan=1)
ax1.imshow(viz_dirs2[0, :], cmap='gray')
ax1.set_xticks([])
ax1.set_yticks([])
ax0 = plt.subplot2grid((4, 8), (0, 5), colspan=3, rowspan=2)
ax0.grid(linestyle='--')
XX = proj_te2
ax0.hist(XX, color=['C2'])
ax0.legend(leg_str)
ax0.set_title('Projection of test data on the first CCA direction')
ax1 = plt.subplot2grid((4, 8), (2, 5), colspan=3, rowspan=1)
ax1.imshow(viz_dirs2[0, :], cmap='gray')
ax1.set_xticks([])
ax1.set_yticks([])
def visualize(self, directions=5, points=5, thetas=theta, SD_spread=1):
dir_num = directions
gI_num = points
b_hat = self.basis_hat
s_tilde_tr = self.plda_proj_tr
s_tilde_te = self.plda_proj_te
plda_dirs = b_hat[:dir_num, :]
plda_proj = s_tilde_tr[:, :dir_num]
radoncdt = RadonCDT(thetas)
## figure 1 of 3
viz_plda = np.zeros((dir_num, self.R, self.C * gI_num))
for a in range(dir_num):
lamb = np.linspace(-SD_spread * np.std(plda_proj[:, a]),
SD_spread * np.std(plda_proj[:, a]),
num=gI_num)
mode_var = np.zeros([gI_num, self.Rtr, self.Ctr])
mode_var_recon = np.zeros([gI_num, self.R, self.C])
for b in range(gI_num):
mode_var[b, :, :] = self.mean_tr + lamb[b] * plda_dirs[a, :]
mode_var_recon[b, :, :] = radoncdt.apply_inverse_map(
mode_var[b, :, :], self.template, x_range)
t = mode_var_recon[b]
t = t - np.min(t)
t = t / np.max(t)
mode_var_recon[b] = t
viz_plda[a, :] = mode_var_recon.transpose(2, 0,
1).reshape(self.C, -1)
for a in range(dir_num):
if a == 0:
F1 = viz_plda[a, :]
else:
F1 = np.concatenate((F1, viz_plda[a, :]), axis=0)
r, c = np.shape(F1)
plt.figure(figsize=(7, 7))
plt.imshow(np.transpose(F1), cmap='gray')
plt.xticks(
np.linspace(r / (2 * dir_num), r - r / (2 * dir_num), dir_num),
np.array(range(1, dir_num + 1)))
plt.xlabel('Modes of variation', fontsize=12)
plt.yticks(
np.linspace(1, c, 5),
np.array([-SD_spread, -SD_spread / 2, 0, SD_spread / 2,
SD_spread]))
plt.ylabel('($\sigma$)', fontsize=12)
plt.title('Variation along the prominant PLDA modes')
## figure 2 of 3
y_train = self.y_train
y_test = self.y_test
viz_dirs = viz_plda[:2, :]
proj_tr = self.plda_proj_tr[:, :2]
proj_te = self.plda_proj_te[:, :2]
plt.figure(figsize=(18, 7))
leg_str = ['class 1', 'class 2']
bas1 = np.array([0, 1])
bas1a = bas1 * np.min(proj_tr[:, 0])
bas1b = bas1 * np.max(proj_tr[:, 0])
basy = [bas1a[0], bas1b[0]]
basx = [bas1a[1], bas1b[1]]
ax0 = plt.subplot2grid((4, 10), (0, 1), colspan=3, rowspan=3)
ax0.grid(linestyle='--')
y_unique = np.unique(y_train)
for a in range(len(y_unique)):
t = np.where(a == y_train)
X = proj_tr[t]
ax0.scatter(X[:, 0], X[:, 1], color='C' + str(a + 1))
ax0.legend(leg_str)
ax0.plot(basx, basy, color='C4')
ax0.set_title(
'Projection of training data on the first 2 PLDA directions')
ax1 = plt.subplot2grid((4, 10), (3, 1), colspan=3, rowspan=1)
xax = viz_dirs[0, :]
ax1.imshow(xax, cmap='gray')
ax1.set_xticks([])
ax1.set_yticks([])
ax2 = plt.subplot2grid((4, 10), (0, 0), colspan=1, rowspan=3)
yax = np.transpose(viz_dirs[1, :])
ax2.imshow(yax, cmap='gray')
ax2.set_xticks([])
ax2.set_yticks([])
bas1a = bas1 * np.min(proj_te[:, 0])
bas1b = bas1 * np.max(proj_te[:, 0])
basy = [bas1a[0], bas1b[0]]
basx = [bas1a[1], bas1b[1]]
ax0 = plt.subplot2grid((4, 10), (0, 6), colspan=3, rowspan=3)
ax0.grid(linestyle='--')
y_unique = np.unique(y_test)
for a in range(len(y_unique)):
t = np.where(a == y_test)
X = proj_te[t]
ax0.scatter(X[:, 0], X[:, 1], color='C' + str(a + 1))
ax0.legend(leg_str)
ax0.plot(basx, basy, color='C4')
ax0.set_title('Projection of test data on the first 2 PLDA directions')
ax1 = plt.subplot2grid((4, 10), (3, 6), colspan=3, rowspan=1)
xax = viz_dirs[0, :]
ax1.imshow(xax, cmap='gray')
ax1.set_xticks([])
ax1.set_yticks([])
ax2 = plt.subplot2grid((4, 10), (0, 5), colspan=1, rowspan=3)
yax = np.transpose(viz_dirs[1, :])
ax2.imshow(yax, cmap='gray')
ax2.set_xticks([])
ax2.set_yticks([])
## figure 3 of 3
which_direction = 1
viz_dirs = viz_plda[which_direction - 1:which_direction, :]
proj_tr = s_tilde_tr[:, which_direction - 1]
proj_te = s_tilde_te[:, which_direction - 1]
plt.figure(figsize=(16, 7))
leg_str = ['class 1', 'class 2']
ax0 = plt.subplot2grid((4, 8), (0, 0), colspan=3, rowspan=2)
ax0.grid(linestyle='--')
y_unique = np.unique(y_train)
for a in range(len(y_unique)):
t = np.where(a == y_train)
y = y_train[t]
X = proj_tr[t]
X = np.reshape(X, (len(y)))
if a == 0:
XX = [X]
else:
XX.append(X)
ax0.hist(XX, color=['C1', 'C2'])
ax0.legend(leg_str)
ax0.set_title(
'Projection of training data on the first PLDA direction')
ax1 = plt.subplot2grid((4, 8), (2, 0), colspan=3, rowspan=1)
ax1.imshow(viz_dirs[0, :], cmap='gray')
ax1.set_xticks([])
ax1.set_yticks([])
ax0 = plt.subplot2grid((4, 8), (0, 5), colspan=3, rowspan=2)
ax0.grid(linestyle='--')
y_unique = np.unique(y_test)
for a in range(len(y_unique)):
t = np.where(a == y_test)
y = y_test[t]
X = proj_te[t]
X = np.reshape(X, (len(y)))
if a == 0:
XX = [X]
else:
XX.append(X)
ax0.hist(XX, color=['C1', 'C2'])
ax0.legend(leg_str)
ax0.set_title('Projection of test data on the first PLDA direction')
ax1 = plt.subplot2grid((4, 8), (2, 5), colspan=3, rowspan=1)
ax1.imshow(viz_dirs[0, :], cmap='gray')
ax1.set_xticks([])
ax1.set_yticks([])
from pypapi import events, papi_high as high
import numpy as np
from pytranskit.optrans.continuous.radoncdt import RadonCDT
import sys
from skimage.transform import rotate
input_size = int(sys.argv[1])
eps = 1e-6
x0_range = [0, 1]
x_range = [0, 1]
Rdown = 4 # downsample radon projections (w.r.t. angles)
theta = np.linspace(0, 176, 180 // Rdown)
radoncdt = RadonCDT(theta)
I = np.random.rand(input_size, input_size)
template = np.ones(I.shape, dtype=I.dtype)
high.start_counters([
events.PAPI_FP_OPS,
])
rcdt = radoncdt.forward(x0_range, template / np.sum(template), x_range,
I / np.sum(I), False)
print(high.stop_counters()[0] / 1e9)
def discrete_radon_transform(image, steps):
R = np.zeros((steps, image.shape[0]), dtype=np.float32)
for s in range(steps):
rotation = rotate(image, -s * 180 / steps).astype(np.float32)
R[s] = np.sum(rotation, axis=1)