def test_mapmri_pdf_integral_unity(radial_order=6): gtab = get_gtab_taiwan_dsi() l1, l2, l3 = [0.0015, 0.0003, 0.0003] S, _ = generate_signal_crossing(gtab, l1, l2, l3) sphere = default_sphere # test MAPMRI fitting mapm = MapmriModel(gtab, radial_order=radial_order, laplacian_weighting=0.02) mapfit = mapm.fit(S) c_map = mapfit.mapmri_coeff # test if the analytical integral of the pdf is equal to one indices = mapmri_index_matrix(radial_order) integral = 0 for i in range(indices.shape[0]): n1, n2, n3 = indices[i] integral += c_map[i] * int_func(n1) * int_func(n2) * int_func(n3) assert_almost_equal(integral, 1.0, 3) # test if numerical integral of odf is equal to one odf = mapfit.odf(sphere, s=0) odf_sum = odf.sum() / sphere.vertices.shape[0] * (4 * np.pi) assert_almost_equal(odf_sum, 1.0, 2) # do the same for isotropic implementation radius_max = 0.04 # 40 microns gridsize = 17 r_points = mapmri.create_rspace(gridsize, radius_max) with warnings.catch_warnings(): warnings.filterwarnings("ignore", message=descoteaux07_legacy_msg, category=PendingDeprecationWarning) mapm = MapmriModel(gtab, radial_order=radial_order, laplacian_weighting=0.02, anisotropic_scaling=False) mapfit = mapm.fit(S) with warnings.catch_warnings(): warnings.filterwarnings("ignore", message=descoteaux07_legacy_msg, category=PendingDeprecationWarning) pdf = mapfit.pdf(r_points) pdf[r_points[:, 2] == 0.] /= 2 # for antipodal symmetry on z-plane point_volume = (radius_max / (gridsize // 2))**3 integral = pdf.sum() * point_volume * 2 assert_almost_equal(integral, 1.0, 3) with warnings.catch_warnings(): warnings.filterwarnings("ignore", message=descoteaux07_legacy_msg, category=PendingDeprecationWarning) odf = mapfit.odf(sphere, s=0) odf_sum = odf.sum() / sphere.vertices.shape[0] * (4 * np.pi) assert_almost_equal(odf_sum, 1.0, 2)
def test_shore_metrics(): gtab = get_gtab_taiwan_dsi() mevals = np.array(([0.0015, 0.0003, 0.0003], [0.0015, 0.0003, 0.0003])) angl = [(0, 0), (60, 0)] S, sticks = MultiTensor(gtab, mevals, S0=100.0, angles=angl, fractions=[50, 50], snr=None) # since we are testing without noise we can use higher order and lower lambdas, with respect to the default. radial_order = 6 lambd = 1e-8 # test mapmri_indices indices = mapmri_index_matrix(radial_order) n_c = indices.shape[0] F = radial_order / 2 n_gt = np.round(1 / 6.0 * (F + 1) * (F + 2) * (4 * F + 3)) assert_equal(n_c, n_gt) # test MAPMRI fitting mapm= MapmriModel(gtab, radial_order=radial_order, lambd=lambd) mapfit = mapm.fit(S) c_map=mapfit.mapmri_coeff R = mapfit.mapmri_R mu = mapfit.mapmri_mu S_reconst = mapfit.predict(gtab, 1.0) # test the signal reconstruction S = S / S[0] nmse_signal = np.sqrt(np.sum((S - S_reconst) ** 2)) / (S.sum()) assert_almost_equal(nmse_signal, 0.0, 3) # test if the analytical integral of the pdf is equal to one integral = 0 for i in range(indices.shape[0]): n1,n2,n3 = indices[i] integral += c_map[i] * int_func(n1) * int_func(n2) * int_func(n3) assert_almost_equal(integral, 1.0, 3) # compare the shore pdf with the ground truth multi_tensor pdf sphere = get_sphere('symmetric724') v = sphere.vertices radius = 10e-3 r_points = v * radius pdf_mt = multi_tensor_pdf(r_points, mevals=mevals, angles=angl, fractions= [50, 50]) pdf_map = mapmri_EAP(r_points, radial_order, c_map, mu, R) nmse_pdf = np.sqrt(np.sum((pdf_mt - pdf_map) ** 2)) / (pdf_mt.sum()) assert_almost_equal(nmse_pdf, 0.0, 2)
def test_mapmri_pdf_integral_unity(radial_order=6): gtab = get_gtab_taiwan_dsi() l1, l2, l3 = [0.0015, 0.0003, 0.0003] S, _ = generate_signal_crossing(gtab, l1, l2, l3) sphere = get_sphere('symmetric724') # test MAPMRI fitting mapm = MapmriModel(gtab, radial_order=radial_order, laplacian_weighting=0.02) mapfit = mapm.fit(S) c_map = mapfit.mapmri_coeff # test if the analytical integral of the pdf is equal to one indices = mapmri_index_matrix(radial_order) integral = 0 for i in range(indices.shape[0]): n1, n2, n3 = indices[i] integral += c_map[i] * int_func(n1) * int_func(n2) * int_func(n3) assert_almost_equal(integral, 1.0, 3) # test if numerical integral of odf is equal to one odf = mapfit.odf(sphere, s=0) odf_sum = odf.sum() / sphere.vertices.shape[0] * (4 * np.pi) assert_almost_equal(odf_sum, 1.0, 2) # do the same for isotropic implementation radius_max = 0.04 # 40 microns gridsize = 17 r_points = mapmri.create_rspace(gridsize, radius_max) mapm = MapmriModel(gtab, radial_order=radial_order, laplacian_weighting=0.02, anisotropic_scaling=False) mapfit = mapm.fit(S) pdf = mapfit.pdf(r_points) pdf[r_points[:, 2] == 0.] /= 2 # for antipodal symmetry on z-plane point_volume = (radius_max / (gridsize // 2)) ** 3 integral = pdf.sum() * point_volume * 2 assert_almost_equal(integral, 1.0, 3) odf = mapfit.odf(sphere, s=0) odf_sum = odf.sum() / sphere.vertices.shape[0] * (4 * np.pi) assert_almost_equal(odf_sum, 1.0, 2)
def test_signal_fitting_equality_anisotropic_isotropic(radial_order=6): gtab = get_gtab_taiwan_dsi() l1, l2, l3 = [0.0015, 0.0003, 0.0003] S, _ = generate_signal_crossing(gtab, l1, l2, l3, angle2=60) gridsize = 17 radius_max = 0.02 r_points = mapmri.create_rspace(gridsize, radius_max) tenmodel = dti.TensorModel(gtab) evals = tenmodel.fit(S).evals tau = 1 / (4 * np.pi**2) # estimate isotropic scale factor u0 = mapmri.isotropic_scale_factor(evals * 2 * tau) mu = np.array([u0, u0, u0]) qvals = np.sqrt(gtab.bvals / tau) / (2 * np.pi) q = gtab.bvecs * qvals[:, None] M_aniso = mapmri.mapmri_phi_matrix(radial_order, mu, q) K_aniso = mapmri.mapmri_psi_matrix(radial_order, mu, r_points) M_iso = mapmri.mapmri_isotropic_phi_matrix(radial_order, u0, q) K_iso = mapmri.mapmri_isotropic_psi_matrix(radial_order, u0, r_points) coef_aniso = np.dot(np.linalg.pinv(M_aniso), S) coef_iso = np.dot(np.linalg.pinv(M_iso), S) # test if anisotropic and isotropic implementation produce equal results # if the same isotropic scale factors are used s_fitted_aniso = np.dot(M_aniso, coef_aniso) s_fitted_iso = np.dot(M_iso, coef_iso) assert_array_almost_equal(s_fitted_aniso, s_fitted_iso) # the same test for the PDF pdf_fitted_aniso = np.dot(K_aniso, coef_aniso) pdf_fitted_iso = np.dot(K_iso, coef_iso) assert_array_almost_equal(pdf_fitted_aniso / pdf_fitted_iso, np.ones_like(pdf_fitted_aniso), 3) # test if the implemented version also produces the same result mapm = MapmriModel(gtab, radial_order=radial_order, laplacian_regularization=False, anisotropic_scaling=False) s_fitted_implemented_isotropic = mapm.fit(S).fitted_signal() # normalize non-implemented fitted signal with b0 value s_fitted_aniso_norm = s_fitted_aniso / s_fitted_aniso.max() assert_array_almost_equal(s_fitted_aniso_norm, s_fitted_implemented_isotropic) # test if norm of signal laplacians are the same laplacian_matrix_iso = mapmri.mapmri_isotropic_laplacian_reg_matrix( radial_order, mu[0]) ind_mat = mapmri.mapmri_index_matrix(radial_order) S_mat, T_mat, U_mat = mapmri.mapmri_STU_reg_matrices(radial_order) laplacian_matrix_aniso = mapmri.mapmri_laplacian_reg_matrix( ind_mat, mu, S_mat, T_mat, U_mat) norm_aniso = np.dot(coef_aniso, np.dot(coef_aniso, laplacian_matrix_aniso)) norm_iso = np.dot(coef_iso, np.dot(coef_iso, laplacian_matrix_iso)) assert_almost_equal(norm_iso, norm_aniso)
def test_mapmri_number_of_coefficients(radial_order=6): indices = mapmri_index_matrix(radial_order) n_c = indices.shape[0] F = radial_order / 2 n_gt = np.round(1 / 6.0 * (F + 1) * (F + 2) * (4 * F + 3)) assert_equal(n_c, n_gt)
def test_signal_fitting_equality_anisotropic_isotropic(radial_order=6): gtab = get_gtab_taiwan_dsi() l1, l2, l3 = [0.0015, 0.0003, 0.0003] S, _ = generate_signal_crossing(gtab, l1, l2, l3, angle2=60) gridsize = 17 radius_max = 0.02 r_points = mapmri.create_rspace(gridsize, radius_max) tenmodel = dti.TensorModel(gtab) evals = tenmodel.fit(S).evals tau = 1 / (4 * np.pi ** 2) # estimate isotropic scale factor u0 = mapmri.isotropic_scale_factor(evals * 2 * tau) mu = np.array([u0, u0, u0]) qvals = np.sqrt(gtab.bvals / tau) / (2 * np.pi) q = gtab.bvecs * qvals[:, None] M_aniso = mapmri.mapmri_phi_matrix(radial_order, mu, q) K_aniso = mapmri.mapmri_psi_matrix(radial_order, mu, r_points) M_iso = mapmri.mapmri_isotropic_phi_matrix(radial_order, u0, q) K_iso = mapmri.mapmri_isotropic_psi_matrix(radial_order, u0, r_points) coef_aniso = np.dot(np.linalg.pinv(M_aniso), S) coef_iso = np.dot(np.linalg.pinv(M_iso), S) # test if anisotropic and isotropic implementation produce equal results # if the same isotropic scale factors are used s_fitted_aniso = np.dot(M_aniso, coef_aniso) s_fitted_iso = np.dot(M_iso, coef_iso) assert_array_almost_equal(s_fitted_aniso, s_fitted_iso) # the same test for the PDF pdf_fitted_aniso = np.dot(K_aniso, coef_aniso) pdf_fitted_iso = np.dot(K_iso, coef_iso) assert_array_almost_equal(pdf_fitted_aniso / pdf_fitted_iso, np.ones_like(pdf_fitted_aniso), 3) # test if the implemented version also produces the same result mapm = MapmriModel(gtab, radial_order=radial_order, laplacian_regularization=False, anisotropic_scaling=False) s_fitted_implemented_isotropic = mapm.fit(S).fitted_signal() # normalize non-implemented fitted signal with b0 value s_fitted_aniso_norm = s_fitted_aniso / s_fitted_aniso.max() assert_array_almost_equal(s_fitted_aniso_norm, s_fitted_implemented_isotropic) # test if norm of signal laplacians are the same laplacian_matrix_iso = mapmri.mapmri_isotropic_laplacian_reg_matrix( radial_order, mu[0]) ind_mat = mapmri.mapmri_index_matrix(radial_order) S_mat, T_mat, U_mat = mapmri.mapmri_STU_reg_matrices(radial_order) laplacian_matrix_aniso = mapmri.mapmri_laplacian_reg_matrix( ind_mat, mu, S_mat, T_mat, U_mat) norm_aniso = np.dot(coef_aniso, np.dot(coef_aniso, laplacian_matrix_aniso)) norm_iso = np.dot(coef_iso, np.dot(coef_iso, laplacian_matrix_iso)) assert_almost_equal(norm_iso, norm_aniso)
def test_mapmri_metrics(): gtab = get_gtab_taiwan_dsi() mevals = np.array(([0.0015, 0.0003, 0.0003], [0.0015, 0.0003, 0.0003])) angl = [(0, 0), (60, 0)] S, sticks = MultiTensor(gtab, mevals, S0=100.0, angles=angl, fractions=[50, 50], snr=None) # since we are testing without noise we can use higher order and lower # lambdas, with respect to the default. radial_order = 6 lambd = 1e-8 # test mapmri_indices indices = mapmri_index_matrix(radial_order) n_c = indices.shape[0] F = radial_order / 2 n_gt = np.round(1 / 6.0 * (F + 1) * (F + 2) * (4 * F + 3)) assert_equal(n_c, n_gt) # test MAPMRI fitting mapm = MapmriModel(gtab, radial_order=radial_order, lambd=lambd) mapfit = mapm.fit(S) c_map = mapfit.mapmri_coeff R = mapfit.mapmri_R mu = mapfit.mapmri_mu S_reconst = mapfit.predict(gtab, 1.0) # test the signal reconstruction S = S / S[0] nmse_signal = np.sqrt(np.sum((S - S_reconst)**2)) / (S.sum()) assert_almost_equal(nmse_signal, 0.0, 3) # test if the analytical integral of the pdf is equal to one integral = 0 for i in range(indices.shape[0]): n1, n2, n3 = indices[i] integral += c_map[i] * int_func(n1) * int_func(n2) * int_func(n3) assert_almost_equal(integral, 1.0, 3) # compare the shore pdf with the ground truth multi_tensor pdf sphere = get_sphere('symmetric724') v = sphere.vertices radius = 10e-3 r_points = v * radius pdf_mt = multi_tensor_pdf(r_points, mevals=mevals, angles=angl, fractions=[50, 50]) pdf_map = mapmri_EAP(r_points, radial_order, c_map, mu, R) nmse_pdf = np.sqrt(np.sum((pdf_mt - pdf_map)**2)) / (pdf_mt.sum()) assert_almost_equal(nmse_pdf, 0.0, 2) # test MAPMRI metrics tau = 1 / (4 * np.pi**2) angl = [(0, 0), (0, 0)] S, sticks = MultiTensor(gtab, mevals, S0=100.0, angles=angl, fractions=[50, 50], snr=None) mapm = MapmriModel(gtab, radial_order=radial_order, lambd=lambd) mapfit = mapm.fit(S) # RTOP gt_rtop = 1.0 / np.sqrt( (4 * np.pi * tau)**3 * mevals[0, 0] * mevals[0, 1] * mevals[0, 2]) rtop = mapfit.rtop() assert_almost_equal(rtop, gt_rtop, 4) # RTAP gt_rtap = 1.0 / np.sqrt((4 * np.pi * tau)**2 * mevals[0, 1] * mevals[0, 2]) rtap = mapfit.rtap() assert_almost_equal(rtap, gt_rtap, 4) # RTPP gt_rtpp = 1.0 / np.sqrt((4 * np.pi * tau) * mevals[0, 0]) rtpp = mapfit.rtpp() assert_almost_equal(rtpp, gt_rtpp, 4)