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# -*- coding: utf-8 -*-
"""
====================================================================================
OT for domain adaptation with image color adaptation [6] with mapping estimation [8]
====================================================================================
[6] Ferradans, S., Papadakis, N., Peyre, G., & Aujol, J. F. (2014). Regularized
discrete optimal transport. SIAM Journal on Imaging Sciences, 7(3), 1853-1882.
[8] M. Perrot, N. Courty, R. Flamary, A. Habrard, "Mapping estimation for
discrete optimal transport", Neural Information Processing Systems (NIPS), 2016.
"""
import numpy as np
import scipy.ndimage as spi
import matplotlib.pylab as pl
import ot
#%% Loading images
I1=spi.imread('../data/ocean_day.jpg').astype(np.float64)/256
I2=spi.imread('../data/ocean_sunset.jpg').astype(np.float64)/256
#%% Plot images
pl.figure(1)
pl.subplot(1,2,1)
pl.imshow(I1)
pl.title('Image 1')
pl.subplot(1,2,2)
pl.imshow(I2)
pl.title('Image 2')
pl.show()
#%% Image conversion and dataset generation
def im2mat(I):
"""Converts and image to matrix (one pixel per line)"""
return I.reshape((I.shape[0]*I.shape[1],I.shape[2]))
def mat2im(X,shape):
"""Converts back a matrix to an image"""
return X.reshape(shape)
X1=im2mat(I1)
X2=im2mat(I2)
# training samples
nb=1000
idx1=np.random.randint(X1.shape[0],size=(nb,))
idx2=np.random.randint(X2.shape[0],size=(nb,))
xs=X1[idx1,:]
xt=X2[idx2,:]
#%% Plot image distributions
pl.figure(2,(10,5))
pl.subplot(1,2,1)
pl.scatter(xs[:,0],xs[:,2],c=xs)
pl.axis([0,1,0,1])
pl.xlabel('Red')
pl.ylabel('Blue')
pl.title('Image 1')
pl.subplot(1,2,2)
#pl.imshow(I2)
pl.scatter(xt[:,0],xt[:,2],c=xt)
pl.axis([0,1,0,1])
pl.xlabel('Red')
pl.ylabel('Blue')
pl.title('Image 2')
pl.show()
#%% domain adaptation between images
def minmax(I):
return np.minimum(np.maximum(I,0),1)
# LP problem
da_emd=ot.da.OTDA() # init class
da_emd.fit(xs,xt) # fit distributions
X1t=da_emd.predict(X1) # out of sample
I1t=minmax(mat2im(X1t,I1.shape))
# sinkhorn regularization
lambd=1e-1
da_entrop=ot.da.OTDA_sinkhorn()
da_entrop.fit(xs,xt,reg=lambd)
X1te=da_entrop.predict(X1)
I1te=minmax(mat2im(X1te,I1.shape))
# linear mapping estimation
eta=1e-8 # quadratic regularization for regression
mu=1e0 # weight of the OT linear term
bias=True # estimate a bias
ot_mapping=ot.da.OTDA_mapping_linear()
ot_mapping.fit(xs,xt,mu=mu,eta=eta,bias=bias,numItermax = 20,verbose=True)
X1tl=ot_mapping.predict(X1) # use the estimated mapping
I1tl=minmax(mat2im(X1tl,I1.shape))
# nonlinear mapping estimation
eta=1e-2 # quadratic regularization for regression
mu=1e0 # weight of the OT linear term
bias=False # estimate a bias
sigma=1 # sigma bandwidth fot gaussian kernel
ot_mapping_kernel=ot.da.OTDA_mapping_kernel()
ot_mapping_kernel.fit(xs,xt,mu=mu,eta=eta,sigma=sigma,bias=bias,numItermax = 10,verbose=True)
X1tn=ot_mapping_kernel.predict(X1) # use the estimated mapping
I1tn=minmax(mat2im(X1tn,I1.shape))
#%% plot images
pl.figure(2,(10,8))
pl.subplot(2,3,1)
pl.imshow(I1)
pl.title('Im. 1')
pl.subplot(2,3,2)
pl.imshow(I2)
pl.title('Im. 2')
pl.subplot(2,3,3)
pl.imshow(I1t)
pl.title('Im. 1 Interp LP')
pl.subplot(2,3,4)
pl.imshow(I1te)
pl.title('Im. 1 Interp Entrop')
pl.subplot(2,3,5)
pl.imshow(I1tl)
pl.title('Im. 1 Linear mapping')
pl.subplot(2,3,6)
pl.imshow(I1tn)
pl.title('Im. 1 nonlinear mapping')
pl.show()
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