From 181fcd3275e378668b4bb35e3584c5b245fbe896 Mon Sep 17 00:00:00 2001 From: Slasnista Date: Fri, 25 Aug 2017 15:12:20 +0200 Subject: refactoring examples according to new DA classes --- examples/da/plot_otda_classes.py | 142 +++++++++++++++++++++ examples/da/plot_otda_color_images.py | 151 ++++++++++++++++++++++ examples/da/plot_otda_d2.py | 163 ++++++++++++++++++++++++ examples/da/plot_otda_mapping.py | 119 +++++++++++++++++ examples/da/plot_otda_mapping_colors_images.py | 169 +++++++++++++++++++++++++ 5 files changed, 744 insertions(+) create mode 100644 examples/da/plot_otda_classes.py create mode 100644 examples/da/plot_otda_color_images.py create mode 100644 examples/da/plot_otda_d2.py create mode 100644 examples/da/plot_otda_mapping.py create mode 100644 examples/da/plot_otda_mapping_colors_images.py (limited to 'examples/da') diff --git a/examples/da/plot_otda_classes.py b/examples/da/plot_otda_classes.py new file mode 100644 index 0000000..1bfe2bb --- /dev/null +++ b/examples/da/plot_otda_classes.py @@ -0,0 +1,142 @@ +# -*- coding: utf-8 -*- +""" +======================== +OT for domain adaptation +======================== + +This example introduces a domain adaptation in a 2D setting and the 4 OTDA +approaches currently supported in POT. + +""" + +# Authors: Remi Flamary +# Stanilslas Chambon +# +# License: MIT License + +import matplotlib.pylab as pl +import ot + + +# number of source and target points to generate +ns = 150 +nt = 150 + +Xs, ys = ot.datasets.get_data_classif('3gauss', ns) +Xt, yt = ot.datasets.get_data_classif('3gauss2', nt) + +# Instantiate the different transport algorithms and fit them + +# EMD Transport +ot_emd = ot.da.EMDTransport() +ot_emd.fit(Xs=Xs, Xt=Xt) + +# Sinkhorn Transport +ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1) +ot_sinkhorn.fit(Xs=Xs, Xt=Xt) + +# Sinkhorn Transport with Group lasso regularization +ot_lpl1 = ot.da.SinkhornLpl1Transport(reg_e=1e-1, reg_cl=1e0) +ot_lpl1.fit(Xs=Xs, ys=ys, Xt=Xt) + +# Sinkhorn Transport with Group lasso regularization l1l2 +ot_l1l2 = ot.da.SinkhornL1l2Transport(reg_e=1e-1, reg_cl=2e0, max_iter=20, + verbose=True) +ot_l1l2.fit(Xs=Xs, ys=ys, Xt=Xt) + +# transport source samples onto target samples +transp_Xs_emd = ot_emd.transform(Xs=Xs) +transp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=Xs) +transp_Xs_lpl1 = ot_lpl1.transform(Xs=Xs) +transp_Xs_l1l2 = ot_l1l2.transform(Xs=Xs) + +############################################################################## +# Fig 1 : plots source and target samples +############################################################################## + +pl.figure(1, figsize=(10, 5)) +pl.subplot(1, 2, 1) +pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') +pl.xticks([]) +pl.yticks([]) +pl.legend(loc=0) +pl.title('Source samples') + +pl.subplot(1, 2, 2) +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') +pl.xticks([]) +pl.yticks([]) +pl.legend(loc=0) +pl.title('Target samples') +pl.tight_layout() + +############################################################################## +# Fig 2 : plot optimal couplings and transported samples +############################################################################## + +param_img = {'interpolation': 'nearest', 'cmap': 'spectral'} + +pl.figure(2, figsize=(15, 8)) +pl.subplot(2, 4, 1) +pl.imshow(ot_emd.coupling_, **param_img) +pl.xticks([]) +pl.yticks([]) +pl.title('Optimal coupling\nEMDTransport') + +pl.subplot(2, 4, 2) +pl.imshow(ot_sinkhorn.coupling_, **param_img) +pl.xticks([]) +pl.yticks([]) +pl.title('Optimal coupling\nSinkhornTransport') + +pl.subplot(2, 4, 3) +pl.imshow(ot_lpl1.coupling_, **param_img) +pl.xticks([]) +pl.yticks([]) +pl.title('Optimal coupling\nSinkhornLpl1Transport') + +pl.subplot(2, 4, 4) +pl.imshow(ot_l1l2.coupling_, **param_img) +pl.xticks([]) +pl.yticks([]) +pl.title('Optimal coupling\nSinkhornL1l2Transport') + +pl.subplot(2, 4, 5) +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=0.3) +pl.scatter(transp_Xs_emd[:, 0], transp_Xs_emd[:, 1], c=ys, + marker='+', label='Transp samples', s=30) +pl.xticks([]) +pl.yticks([]) +pl.title('Transported samples\nEmdTransport') +pl.legend(loc="lower left") + +pl.subplot(2, 4, 6) +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=0.3) +pl.scatter(transp_Xs_sinkhorn[:, 0], transp_Xs_sinkhorn[:, 1], c=ys, + marker='+', label='Transp samples', s=30) +pl.xticks([]) +pl.yticks([]) +pl.title('Transported samples\nSinkhornTransport') + +pl.subplot(2, 4, 7) +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=0.3) +pl.scatter(transp_Xs_lpl1[:, 0], transp_Xs_lpl1[:, 1], c=ys, + marker='+', label='Transp samples', s=30) +pl.xticks([]) +pl.yticks([]) +pl.title('Transported samples\nSinkhornLpl1Transport') + +pl.subplot(2, 4, 8) +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=0.3) +pl.scatter(transp_Xs_l1l2[:, 0], transp_Xs_l1l2[:, 1], c=ys, + marker='+', label='Transp samples', s=30) +pl.xticks([]) +pl.yticks([]) +pl.title('Transported samples\nSinkhornL1l2Transport') +pl.tight_layout() + +pl.show() diff --git a/examples/da/plot_otda_color_images.py b/examples/da/plot_otda_color_images.py new file mode 100644 index 0000000..a46ac29 --- /dev/null +++ b/examples/da/plot_otda_color_images.py @@ -0,0 +1,151 @@ +# -*- coding: utf-8 -*- +""" +======================================================== +OT for domain adaptation with image color adaptation [6] +======================================================== + +This example presents a way of transferring colors between two image +with Optimal Transport as introduced in [6] + +[6] Ferradans, S., Papadakis, N., Peyre, G., & Aujol, J. F. (2014). +Regularized discrete optimal transport. +SIAM Journal on Imaging Sciences, 7(3), 1853-1882. +""" + +# Authors: Remi Flamary +# Stanilslas Chambon +# +# License: MIT License + +import numpy as np +from scipy import ndimage +import matplotlib.pylab as pl + +import ot + + +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) + + +def minmax(I): + return np.clip(I, 0, 1) + + +# Loading images +I1 = ndimage.imread('../../data/ocean_day.jpg').astype(np.float64) / 256 +I2 = ndimage.imread('../../data/ocean_sunset.jpg').astype(np.float64) / 256 + +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, :] + +# EMDTransport +ot_emd = ot.da.EMDTransport() +ot_emd.fit(Xs=Xs, Xt=Xt) + +# SinkhornTransport +ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1) +ot_sinkhorn.fit(Xs=Xs, Xt=Xt) + +# prediction between images (using out of sample prediction as in [6]) +transp_Xs_emd = ot_emd.transform(Xs=X1) +transp_Xt_emd = ot_emd.inverse_transform(Xt=X2) + +transp_Xs_sinkhorn = ot_emd.transform(Xs=X1) +transp_Xt_sinkhorn = ot_emd.inverse_transform(Xt=X2) + +I1t = minmax(mat2im(transp_Xs_emd, I1.shape)) +I2t = minmax(mat2im(transp_Xt_emd, I2.shape)) + +I1te = minmax(mat2im(transp_Xs_sinkhorn, I1.shape)) +I2te = minmax(mat2im(transp_Xt_sinkhorn, I2.shape)) + +############################################################################## +# plot original image +############################################################################## + +pl.figure(1, figsize=(6.4, 3)) + +pl.subplot(1, 2, 1) +pl.imshow(I1) +pl.axis('off') +pl.title('Image 1') + +pl.subplot(1, 2, 2) +pl.imshow(I2) +pl.axis('off') +pl.title('Image 2') + +############################################################################## +# scatter plot of colors +############################################################################## + +pl.figure(2, figsize=(6.4, 3)) + +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.scatter(Xt[:, 0], Xt[:, 2], c=Xt) +pl.axis([0, 1, 0, 1]) +pl.xlabel('Red') +pl.ylabel('Blue') +pl.title('Image 2') +pl.tight_layout() + +############################################################################## +# plot new images +############################################################################## + +pl.figure(3, figsize=(8, 4)) + +pl.subplot(2, 3, 1) +pl.imshow(I1) +pl.axis('off') +pl.title('Image 1') + +pl.subplot(2, 3, 2) +pl.imshow(I1t) +pl.axis('off') +pl.title('Image 1 Adapt') + +pl.subplot(2, 3, 3) +pl.imshow(I1te) +pl.axis('off') +pl.title('Image 1 Adapt (reg)') + +pl.subplot(2, 3, 4) +pl.imshow(I2) +pl.axis('off') +pl.title('Image 2') + +pl.subplot(2, 3, 5) +pl.imshow(I2t) +pl.axis('off') +pl.title('Image 2 Adapt') + +pl.subplot(2, 3, 6) +pl.imshow(I2te) +pl.axis('off') +pl.title('Image 2 Adapt (reg)') +pl.tight_layout() + +pl.show() diff --git a/examples/da/plot_otda_d2.py b/examples/da/plot_otda_d2.py new file mode 100644 index 0000000..78c0372 --- /dev/null +++ b/examples/da/plot_otda_d2.py @@ -0,0 +1,163 @@ +# -*- coding: utf-8 -*- +""" +============================== +OT for empirical distributions +============================== + +This example introduces a domain adaptation in a 2D setting. It explicits +the problem of domain adaptation and introduces some optimal transport +approaches to solve it. + +Quantities such as optimal couplings, greater coupling coefficients and +transported samples are represented in order to give a visual understanding +of what the transport methods are doing. +""" + +# Authors: Remi Flamary +# Stanilslas Chambon +# +# License: MIT License + +import matplotlib.pylab as pl +import ot + +# number of source and target points to generate +ns = 150 +nt = 150 + +Xs, ys = ot.datasets.get_data_classif('3gauss', ns) +Xt, yt = ot.datasets.get_data_classif('3gauss2', nt) + +# Cost matrix +M = ot.dist(Xs, Xt) + +# Instantiate the different transport algorithms and fit them + +# EMD Transport +ot_emd = ot.da.EMDTransport() +ot_emd.fit(Xs=Xs, Xt=Xt) + +# Sinkhorn Transport +ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1) +ot_sinkhorn.fit(Xs=Xs, Xt=Xt) + +# Sinkhorn Transport with Group lasso regularization +ot_lpl1 = ot.da.SinkhornLpl1Transport(reg_e=1e-1, reg_cl=1e0) +ot_lpl1.fit(Xs=Xs, ys=ys, Xt=Xt) + +# transport source samples onto target samples +transp_Xs_emd = ot_emd.transform(Xs=Xs) +transp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=Xs) +transp_Xs_lpl1 = ot_lpl1.transform(Xs=Xs) + +############################################################################## +# Fig 1 : plots source and target samples + matrix of pairwise distance +############################################################################## + +pl.figure(1, figsize=(10, 10)) +pl.subplot(2, 2, 1) +pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') +pl.xticks([]) +pl.yticks([]) +pl.legend(loc=0) +pl.title('Source samples') + +pl.subplot(2, 2, 2) +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') +pl.xticks([]) +pl.yticks([]) +pl.legend(loc=0) +pl.title('Target samples') + +pl.subplot(2, 2, 3) +pl.imshow(M, interpolation='nearest') +pl.xticks([]) +pl.yticks([]) +pl.title('Matrix of pairwise distances') +pl.tight_layout() + +############################################################################## +# Fig 2 : plots optimal couplings for the different methods +############################################################################## + +pl.figure(2, figsize=(10, 6)) + +pl.subplot(2, 3, 1) +pl.imshow(ot_emd.coupling_, interpolation='nearest') +pl.xticks([]) +pl.yticks([]) +pl.title('Optimal coupling\nEMDTransport') + +pl.subplot(2, 3, 2) +pl.imshow(ot_sinkhorn.coupling_, interpolation='nearest') +pl.xticks([]) +pl.yticks([]) +pl.title('Optimal coupling\nSinkhornTransport') + +pl.subplot(2, 3, 3) +pl.imshow(ot_lpl1.coupling_, interpolation='nearest') +pl.xticks([]) +pl.yticks([]) +pl.title('Optimal coupling\nSinkhornLpl1Transport') + +pl.subplot(2, 3, 4) +ot.plot.plot2D_samples_mat(Xs, Xt, ot_emd.coupling_, c=[.5, .5, 1]) +pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') +pl.xticks([]) +pl.yticks([]) +pl.title('Main coupling coefficients\nEMDTransport') + +pl.subplot(2, 3, 5) +ot.plot.plot2D_samples_mat(Xs, Xt, ot_sinkhorn.coupling_, c=[.5, .5, 1]) +pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') +pl.xticks([]) +pl.yticks([]) +pl.title('Main coupling coefficients\nSinkhornTransport') + +pl.subplot(2, 3, 6) +ot.plot.plot2D_samples_mat(Xs, Xt, ot_lpl1.coupling_, c=[.5, .5, 1]) +pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') +pl.xticks([]) +pl.yticks([]) +pl.title('Main coupling coefficients\nSinkhornLpl1Transport') +pl.tight_layout() + +############################################################################## +# Fig 3 : plot transported samples +############################################################################## + +# display transported samples +pl.figure(4, figsize=(10, 4)) +pl.subplot(1, 3, 1) +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=0.5) +pl.scatter(transp_Xs_emd[:, 0], transp_Xs_emd[:, 1], c=ys, + marker='+', label='Transp samples', s=30) +pl.title('Transported samples\nEmdTransport') +pl.legend(loc=0) +pl.xticks([]) +pl.yticks([]) + +pl.subplot(1, 3, 2) +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=0.5) +pl.scatter(transp_Xs_sinkhorn[:, 0], transp_Xs_sinkhorn[:, 1], c=ys, + marker='+', label='Transp samples', s=30) +pl.title('Transported samples\nSinkhornTransport') +pl.xticks([]) +pl.yticks([]) + +pl.subplot(1, 3, 3) +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=0.5) +pl.scatter(transp_Xs_lpl1[:, 0], transp_Xs_lpl1[:, 1], c=ys, + marker='+', label='Transp samples', s=30) +pl.title('Transported samples\nSinkhornLpl1Transport') +pl.xticks([]) +pl.yticks([]) + +pl.tight_layout() +pl.show() diff --git a/examples/da/plot_otda_mapping.py b/examples/da/plot_otda_mapping.py new file mode 100644 index 0000000..ed234f5 --- /dev/null +++ b/examples/da/plot_otda_mapping.py @@ -0,0 +1,119 @@ +# -*- coding: utf-8 -*- +""" +=============================================== +OT mapping estimation for domain adaptation [8] +=============================================== + +This example presents how to use MappingTransport to estimate at the same +time both the coupling transport and approximate the transport map with either +a linear or a kernelized mapping as introduced in [8] + +[8] M. Perrot, N. Courty, R. Flamary, A. Habrard, + "Mapping estimation for discrete optimal transport", + Neural Information Processing Systems (NIPS), 2016. +""" + +# Authors: Remi Flamary +# Stanilslas Chambon +# +# License: MIT License + +import numpy as np +import matplotlib.pylab as pl +import ot + + +np.random.seed(0) + +############################################################################## +# generate +############################################################################## + +n = 100 # nb samples in source and target datasets +theta = 2 * np.pi / 20 +nz = 0.1 +Xs, ys = ot.datasets.get_data_classif('gaussrot', n, nz=nz) +Xs_new, _ = ot.datasets.get_data_classif('gaussrot', n, nz=nz) +Xt, yt = ot.datasets.get_data_classif('gaussrot', n, theta=theta, nz=nz) + +# one of the target mode changes its variance (no linear mapping) +Xt[yt == 2] *= 3 +Xt = Xt + 4 + + +# MappingTransport with linear kernel +ot_mapping_linear = ot.da.MappingTransport( + kernel="linear", mu=1e0, eta=1e-8, bias=True, + max_iter=20, verbose=True) + +ot_mapping_linear.fit( + Xs=Xs, Xt=Xt) + +# for original source samples, transform applies barycentric mapping +transp_Xs_linear = ot_mapping_linear.transform(Xs=Xs) + +# for out of source samples, transform applies the linear mapping +transp_Xs_linear_new = ot_mapping_linear.transform(Xs=Xs_new) + + +# MappingTransport with gaussian kernel +ot_mapping_gaussian = ot.da.MappingTransport( + kernel="gaussian", eta=1e-5, mu=1e-1, bias=True, sigma=1, + max_iter=10, verbose=True) +ot_mapping_gaussian.fit(Xs=Xs, Xt=Xt) + +# for original source samples, transform applies barycentric mapping +transp_Xs_gaussian = ot_mapping_gaussian.transform(Xs=Xs) + +# for out of source samples, transform applies the gaussian mapping +transp_Xs_gaussian_new = ot_mapping_gaussian.transform(Xs=Xs_new) + + +############################################################################## +# plot data +############################################################################## + +pl.figure(1, (10, 5)) +pl.clf() +pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') +pl.legend(loc=0) +pl.title('Source and target distributions') + +############################################################################## +# plot transported samples +############################################################################## + +pl.figure(2) +pl.clf() +pl.subplot(2, 2, 1) +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=.2) +pl.scatter(transp_Xs_linear[:, 0], transp_Xs_linear[:, 1], c=ys, marker='+', + label='Mapped source samples') +pl.title("Bary. mapping (linear)") +pl.legend(loc=0) + +pl.subplot(2, 2, 2) +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=.2) +pl.scatter(transp_Xs_linear_new[:, 0], transp_Xs_linear_new[:, 1], + c=ys, marker='+', label='Learned mapping') +pl.title("Estim. mapping (linear)") + +pl.subplot(2, 2, 3) +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=.2) +pl.scatter(transp_Xs_gaussian[:, 0], transp_Xs_gaussian[:, 1], c=ys, + marker='+', label='barycentric mapping') +pl.title("Bary. mapping (kernel)") + +pl.subplot(2, 2, 4) +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=.2) +pl.scatter(transp_Xs_gaussian_new[:, 0], transp_Xs_gaussian_new[:, 1], c=ys, + marker='+', label='Learned mapping') +pl.title("Estim. mapping (kernel)") +pl.tight_layout() + +pl.show() diff --git a/examples/da/plot_otda_mapping_colors_images.py b/examples/da/plot_otda_mapping_colors_images.py new file mode 100644 index 0000000..56b5a6f --- /dev/null +++ b/examples/da/plot_otda_mapping_colors_images.py @@ -0,0 +1,169 @@ +# -*- 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. + +""" + +# Authors: Remi Flamary +# Stanilslas Chambon +# +# License: MIT License + +import numpy as np +from scipy import ndimage +import matplotlib.pylab as pl +import ot + + +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) + + +def minmax(I): + return np.clip(I, 0, 1) + + +############################################################################## +# Generate data +############################################################################## + +# Loading images +# I1 = ndimage.imread('../../data/ocean_day.jpg').astype(np.float64) / 256 +# I2 = ndimage.imread('../../data/ocean_sunset.jpg').astype(np.float64) / 256 + +I1 = ndimage.imread('data/ocean_day.jpg').astype(np.float64) / 256 +I2 = ndimage.imread('data/ocean_sunset.jpg').astype(np.float64) / 256 + + +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, :] + + +############################################################################## +# Domain adaptation for pixel distribution transfer +############################################################################## + +# EMDTransport +ot_emd = ot.da.EMDTransport() +ot_emd.fit(Xs=Xs, Xt=Xt) +transp_Xs_emd = ot_emd.transform(Xs=X1) +Image_emd = minmax(mat2im(transp_Xs_emd, I1.shape)) + +# SinkhornTransport +ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1) +ot_sinkhorn.fit(Xs=Xs, Xt=Xt) +transp_Xs_sinkhorn = ot_emd.transform(Xs=X1) +Image_sinkhorn = minmax(mat2im(transp_Xs_sinkhorn, I1.shape)) + +ot_mapping_linear = ot.da.MappingTransport( + mu=1e0, eta=1e-8, bias=True, max_iter=20, verbose=True) +ot_mapping_linear.fit(Xs=Xs, Xt=Xt) + +X1tl = ot_mapping_linear.transform(X1) +Image_mapping_linear = minmax(mat2im(X1tl, I1.shape)) + +ot_mapping_gaussian = ot.da.MappingTransport( + mu=1e0, eta=1e-2, sigma=1, bias=False, max_iter=10, verbose=True) +ot_mapping_gaussian.fit(Xs=Xs, Xt=Xt) + +X1tn = ot_mapping_gaussian.transform(X1) # use the estimated mapping +Image_mapping_gaussian = minmax(mat2im(X1tn, I1.shape)) + +############################################################################## +# plot original images +############################################################################## + +pl.figure(1, figsize=(6.4, 3)) +pl.subplot(1, 2, 1) +pl.imshow(I1) +pl.axis('off') +pl.title('Image 1') + +pl.subplot(1, 2, 2) +pl.imshow(I2) +pl.axis('off') +pl.title('Image 2') +pl.tight_layout() + +############################################################################## +# plot pixel values distribution +############################################################################## + +pl.figure(2, figsize=(6.4, 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.scatter(Xt[:, 0], Xt[:, 2], c=Xt) +pl.axis([0, 1, 0, 1]) +pl.xlabel('Red') +pl.ylabel('Blue') +pl.title('Image 2') +pl.tight_layout() + +############################################################################## +# plot transformed images +############################################################################## + +pl.figure(2, figsize=(10, 5)) + +pl.subplot(2, 3, 1) +pl.imshow(I1) +pl.axis('off') +pl.title('Im. 1') + +pl.subplot(2, 3, 4) +pl.imshow(I2) +pl.axis('off') +pl.title('Im. 2') + +pl.subplot(2, 3, 2) +pl.imshow(Image_emd) +pl.axis('off') +pl.title('EmdTransport') + +pl.subplot(2, 3, 5) +pl.imshow(Image_sinkhorn) +pl.axis('off') +pl.title('SinkhornTransport') + +pl.subplot(2, 3, 3) +pl.imshow(Image_mapping_linear) +pl.axis('off') +pl.title('MappingTransport (linear)') + +pl.subplot(2, 3, 6) +pl.imshow(Image_mapping_gaussian) +pl.axis('off') +pl.title('MappingTransport (gaussian)') +pl.tight_layout() + +pl.show() -- cgit v1.2.3