def load_original():
root = join('..','..','..','data','brain')
# Get the dataset info
dataset = pd.read_excel(join(root,'brain_info.xlsx'))
# Initialise the data and label arrays
n_imgs = len(dataset['status'])
# X = np.zeros((n_imgs,109,91))
X = np.zeros((n_imgs,54,45))
y = np.zeros(n_imgs, dtype='uint8')
for i in range(n_imgs):
print('Image {} of {}'.format(i+1, n_imgs))
# Load the image and scale by factor of 0.5
fpath = join(root, 'images', dataset['ptid'][i] + '.png')
tmp = misc.imread(fpath, flatten=True)
tmp = misc.imresize(tmp, 0.25)
tmp = np.rot90(tmp, 2)
X[i] = signal_to_pdf(tmp.astype(np.float64))
if dataset['status'][i] == 'p':
y[i] = 1
np.savez(join('optrans','datasets','adni_data'), X=X, y=y)
return
def generate_radoncdt():
with np.load(join('optrans','datasets','adni_data.npz')) as data:
X = data['X']
y = data['y']
img0 = signal_to_pdf(X.mean(axis=0))
radoncdt = RadonCDT()
rcdt = []
transport_map = []
displacements = []
for i,img1 in enumerate(X):
print('R-CDT {} of {}'.format(i+1, X.shape[0]))
rcdt.append(radoncdt.forward(img0, img1))
transport_map.append(radoncdt.transport_map_)
displacements.append(radoncdt.displacements_)
rcdt = np.array(rcdt)
transport_map = np.array(transport_map)
displacements = np.array(displacements)
np.save(join('optrans','datasets','adni_img0'), img0)
np.savez(join('optrans','datasets','adni_rcdt'), rcdt=rcdt, y=y)
np.savez(join('optrans','datasets','adni_rcdt_maps'), y=y,
transport_map=transport_map)
np.savez(join('optrans','datasets','adni_rcdt_disp'), y=y,
displacements=displacements)
return
def generate_radoncdt():
X, y = gaussians.load_data()
n_imgs, h, w = X.shape
img0 = signal_to_pdf(np.ones((h,w)))
radoncdt = RadonCDT()
rcdt = []
transport_map = []
displacements = []
for i,img1 in enumerate(X):
print('R-CDT {} of {}'.format(i+1, n_imgs))
rcdt.append(radoncdt.forward(img0, img1))
transport_map.append(radoncdt.transport_map_)
displacements.append(radoncdt.displacements_)
rcdt = np.array(rcdt)
transport_map = np.array(transport_map)
displacements = np.array(displacements)
np.save(join('optrans','datasets','gaussians_img0'), img0)
np.savez(join('optrans','datasets','gaussians_rcdt'), rcdt=rcdt, y=y)
np.savez(join('optrans','datasets','gaussians_rcdt_maps'), y=y,
transport_map=transport_map)
np.savez(join('optrans','datasets','gaussians_rcdt_disp'), y=y,
displacements=displacements)
return
def generate_image():
X, y = gaussians.make_gaussians(n_samples=100, n_dots=[1,2,3])
for i in range(X.shape[0]):
X[i] = signal_to_pdf(X[i])
np.savez(join('optrans','datasets','gaussians_data'), X=X, y=y)
return
def load_original():
root = 'X:/Data/MRI/oasis_cross-sectional'
dataset = pd.read_excel(join(root, 'oasis_cross-sectional.xlsx'))
# Only get session 1 data
dataset = dataset[dataset['Session'] == 1]
pid = dataset['ID'].tolist()
y = np.array([0 if row == 'hc' else 1 for row in dataset['Dx'].tolist()])
sex = [0 if row == 'F' else 1 for row in dataset['M/F'].tolist()]
age = dataset['Age'].tolist()
edu = dataset['Educ'].tolist()
ses = dataset['SES'].tolist()
mmse = dataset['MMSE'].tolist()
cdr = dataset['CDR'].tolist()
etiv = dataset['eTIV'].tolist()
nwbv = dataset['nWBV'].tolist()
asf = dataset['ASF'].tolist()
metadata = np.array([sex, age, edu, ses, mmse, cdr, etiv, nwbv, asf]).T
n_samples = len(dataset)
X = np.zeros((n_samples, 208, 176))
for i, p in enumerate(pid):
print(i, p)
fname = '*111_t88_masked_gfc.img'
fpath = glob.glob(
join(root, p, 'PROCESSED', 'MPRAGE', 'T88_111', fname))[0]
vol = sitk.GetArrayFromImage(sitk.ReadImage(fpath))
print(vol[85].shape)
tmp = np.rot90(vol[85], 2)
X[i] = signal_to_pdf(tmp.astype(np.float64), total=1000.)
np.savez(join('..', 'optrans', 'datasets', 'oasis_data'),
X=X,
y=y,
metadata=metadata)
return
- RadonCDT
- VOT2D
- MultiVOT2D
- CLOT
- SPOT2D
Liam Cattell -- June 2018
"""
# Load sample data
img0 = oasis.load_img0()
X, _, _ = oasis.load_data()
img1 = X[0]
# Convert images to PDFs
img0 = signal_to_pdf(img0, sigma=1., total=100.)
img1 = signal_to_pdf(img1, sigma=1., total=100.)
# Initialise optimal transport methods
methods = [RadonCDT(),
VOT2D(alpha=0.001),
MultiVOT2D(alpha=0.001),
CLOT(lr=1e-7, tol=1e-4),
SPOT2D()]
# Plot settings
fs = 16
vmin = min(img0.min(), img1.min())
vmax = max(img0.max(), img1.max())
# Initialise figure and plot original images
Liam Cattell -- May 2018 """ # Normalization parameters sigma = 1. epsilon = 8. total = 100. # Load images X, _ = adni.load_data() img0 = adni.load_img0() img1 = X[1] # CLOT is *very* sensitive to the image normalization img0 = signal_to_pdf(img0, sigma=sigma, epsilon=epsilon, total=total) img1 = signal_to_pdf(img1, sigma=sigma, epsilon=epsilon, total=total) # Continuous LOT clot = CLOT(max_iter=500, lr=1e-5, momentum=0.9, verbose=1) lot = clot.forward(img0, img1) # Reconstruct images using initial map img0_recon0 = clot.apply_forward_map(clot.transport_map_initial_, img1) img1_recon0 = clot.apply_inverse_map(clot.transport_map_initial_, img0) # Reconstruct images using final map img0_recon = clot.apply_forward_map(clot.transport_map_, img1) img1_recon = clot.apply_inverse_map(clot.transport_map_, img0) # Colour scaling
from optrans.continuous import RadonCDT
"""
Compute the forward and inverse Radon-CDT of a sample image.
Liam Cattell -- January 2018
"""
# Load a sample image
img = img_as_float(data.camera()[::2, ::2])
# Select two patches to be our sample images
img0 = img[50:162, 70:134]
img1 = img[32:144, 64:128]
# Convert images to PDFs
img0 = signal_to_pdf(img0, sigma=1.)
img1 = signal_to_pdf(img1, sigma=1.)
# Compute Radon-CDT of img1 w.r.t img0
theta = np.arange(0, 179, 2)
radoncdt = RadonCDT(theta=theta)
img1_hat = radoncdt.forward(img0, img1)
# Apply transport map in order to reconstruct images
img0_recon = radoncdt.apply_forward_map(radoncdt.transport_map_, img1)
img1_recon = radoncdt.apply_inverse_map(radoncdt.transport_map_, img0)
# img1_recon = radoncdt.inverse()
fig, ax = plt.subplots(3, 2)
ax[0, 0].imshow(img0)
ax[0, 0].set_title('Reference img0')
from optrans.utils import signal_to_pdf
from optrans.continuous import CDT
"""
Compute the forward and inverse CDT of a Gaussian w.r.t a uniform distribution.
Liam Cattell -- January 2018
"""
# Create the uniform reference and Gaussian signal
x = np.linspace(-5, 5, 256)
sig0 = np.ones(x.size)
sig1 = 1 / np.sqrt(2 * np.pi) * np.exp(-0.5 * x**2)
# Convert signals to PDFs
sig0 = signal_to_pdf(sig0)
sig1 = signal_to_pdf(sig1)
# Compute CDT of sig1 w.r.t sig0
cdt = CDT()
sig1_hat = cdt.forward(sig0, sig1)
# Apply transport map in order to reconstruct signals
sig0_recon = cdt.apply_forward_map(cdt.transport_map_, sig1)
sig1_recon = cdt.apply_inverse_map(cdt.transport_map_, sig0)
# sig1_recon = cdt.inverse()
# Plot results
fig, ax = plt.subplots(3, 2, sharex=True)
ax[0, 0].plot(sig0)
ax[0, 0].set_title('Reference sig0')
"""
Compute the geodesic between two 1D Gaussians.
Liam Cattell -- January 2018
"""
# Create two translated delta functions as test signals
n = 128
sig0 = np.zeros(n)
sig1 = np.zeros(n)
sig0[32] = 1.
sig1[96] = 1.
# Smooth the delta functions into Gaussians and convert to PDFs
sig0 = signal_to_pdf(sig0, sigma=6.)
sig1 = signal_to_pdf(sig1, sigma=6.)
# Compute the CDT of sig1 w.r.t. sig0
cdt = CDT()
sig1_hat = cdt.forward(sig0, sig1)
# Get the domain of our signal
x = cdt.transport_map_ + cdt.displacements_
# Plot linear interpolation in signal space and CDT space
fig, ax = plt.subplots(2, 5, sharex=True, sharey=True, figsize=(10,6))
for i,alpha in enumerate(np.linspace(0, 1, 5)):
# Interpolation in signal space
sig_interp = (1. - alpha) * sig0 + alpha * sig1
ax[0,i].plot(sig_interp)