import re import textwrap import numpy as np import pytest from numpy.testing import (assert_almost_equal, assert_array_almost_equal, assert_equal) from skimage.transform._geometric import (_affine_matrix_from_vector, _center_and_normalize_points, _euler_rotation_matrix, GeometricTransform) from skimage.transform import (estimate_transform, matrix_transform, EuclideanTransform, SimilarityTransform, AffineTransform, FundamentalMatrixTransform, EssentialMatrixTransform, ProjectiveTransform, PolynomialTransform, PiecewiseAffineTransform) SRC = np.array([ [-12.3705, -10.5075], [-10.7865, 15.4305], [8.6985, 10.8675], [11.4975, -9.5715], [7.8435, 7.4835], [-5.3325, 6.5025], [6.7905, -6.3765], [-6.1695, -0.8235], ]) DST = np.array([ [0, 0], [0, 5800], [4900, 5800], [4900, 0], [4479, 4580], [1176, 3660], [3754, 790], [1024, 1931], ]) def test_estimate_transform(): for tform in ('euclidean', 'similarity', 'affine', 'projective', 'polynomial'): estimate_transform(tform, SRC[:2, :], DST[:2, :]) with pytest.raises(ValueError): estimate_transform('foobar', SRC[:2, :], DST[:2, :]) def test_matrix_transform(): tform = AffineTransform(scale=(0.1, 0.5), rotation=2) assert_equal(tform(SRC), matrix_transform(SRC, tform.params)) def test_euclidean_estimation(): # exact solution tform = estimate_transform('euclidean', SRC[:2, :], SRC[:2, :] + 10) assert_almost_equal(tform(SRC[:2, :]), SRC[:2, :] + 10) assert_almost_equal(tform.params[0, 0], tform.params[1, 1]) assert_almost_equal(tform.params[0, 1], - tform.params[1, 0]) # over-determined tform2 = estimate_transform('euclidean', SRC, DST) assert_almost_equal(tform2.inverse(tform2(SRC)), SRC) assert_almost_equal(tform2.params[0, 0], tform2.params[1, 1]) assert_almost_equal(tform2.params[0, 1], - tform2.params[1, 0]) # via estimate method tform3 = EuclideanTransform() assert tform3.estimate(SRC, DST) assert_almost_equal(tform3.params, tform2.params) def test_euclidean_init(): # init with implicit parameters rotation = 1 translation = (1, 1) tform = EuclideanTransform(rotation=rotation, translation=translation) assert_almost_equal(tform.rotation, rotation) assert_almost_equal(tform.translation, translation) # init with transformation matrix tform2 = EuclideanTransform(tform.params) assert_almost_equal(tform2.rotation, rotation) assert_almost_equal(tform2.translation, translation) # test special case for scale if rotation=0 rotation = 0 translation = (1, 1) tform = EuclideanTransform(rotation=rotation, translation=translation) assert_almost_equal(tform.rotation, rotation) assert_almost_equal(tform.translation, translation) # test special case for scale if rotation=90deg rotation = np.pi / 2 translation = (1, 1) tform = EuclideanTransform(rotation=rotation, translation=translation) assert_almost_equal(tform.rotation, rotation) assert_almost_equal(tform.translation, translation) def test_similarity_estimation(): # exact solution tform = estimate_transform('similarity', SRC[:2, :], DST[:2, :]) assert_almost_equal(tform(SRC[:2, :]), DST[:2, :]) assert_almost_equal(tform.params[0, 0], tform.params[1, 1]) assert_almost_equal(tform.params[0, 1], - tform.params[1, 0]) # over-determined tform2 = estimate_transform('similarity', SRC, DST) assert_almost_equal(tform2.inverse(tform2(SRC)), SRC) assert_almost_equal(tform2.params[0, 0], tform2.params[1, 1]) assert_almost_equal(tform2.params[0, 1], - tform2.params[1, 0]) # via estimate method tform3 = SimilarityTransform() assert tform3.estimate(SRC, DST) assert_almost_equal(tform3.params, tform2.params) def test_similarity_init(): # init with implicit parameters scale = 0.1 rotation = 1 translation = (1, 1) tform = SimilarityTransform(scale=scale, rotation=rotation, translation=translation) assert_almost_equal(tform.scale, scale) assert_almost_equal(tform.rotation, rotation) assert_almost_equal(tform.translation, translation) # init with transformation matrix tform2 = SimilarityTransform(tform.params) assert_almost_equal(tform2.scale, scale) assert_almost_equal(tform2.rotation, rotation) assert_almost_equal(tform2.translation, translation) # test special case for scale if rotation=0 scale = 0.1 rotation = 0 translation = (1, 1) tform = SimilarityTransform(scale=scale, rotation=rotation, translation=translation) assert_almost_equal(tform.scale, scale) assert_almost_equal(tform.rotation, rotation) assert_almost_equal(tform.translation, translation) # test special case for scale if rotation=90deg scale = 0.1 rotation = np.pi / 2 translation = (1, 1) tform = SimilarityTransform(scale=scale, rotation=rotation, translation=translation) assert_almost_equal(tform.scale, scale) assert_almost_equal(tform.rotation, rotation) assert_almost_equal(tform.translation, translation) # test special case for scale where the rotation isn't exactly 90deg, # but very close scale = 1.0 rotation = np.pi / 2 translation = (0, 0) params = np.array([[0, -1, 1.33226763e-15], [1, 2.22044605e-16, -1.33226763e-15], [0, 0, 1]]) tform = SimilarityTransform(params) assert_almost_equal(tform.scale, scale) assert_almost_equal(tform.rotation, rotation) assert_almost_equal(tform.translation, translation) def test_affine_estimation(): # exact solution tform = estimate_transform('affine', SRC[:3, :], DST[:3, :]) assert_almost_equal(tform(SRC[:3, :]), DST[:3, :]) # over-determined tform2 = estimate_transform('affine', SRC, DST) assert_almost_equal(tform2.inverse(tform2(SRC)), SRC) # via estimate method tform3 = AffineTransform() assert tform3.estimate(SRC, DST) assert_almost_equal(tform3.params, tform2.params) def test_affine_init(): # init with implicit parameters scale = (0.1, 0.13) rotation = 1 shear = 0.1 translation = (1, 1) tform = AffineTransform(scale=scale, rotation=rotation, shear=shear, translation=translation) assert_almost_equal(tform.scale, scale) assert_almost_equal(tform.rotation, rotation) assert_almost_equal(tform.shear, shear) assert_almost_equal(tform.translation, translation) # init with transformation matrix tform2 = AffineTransform(tform.params) assert_almost_equal(tform2.scale, scale) assert_almost_equal(tform2.rotation, rotation) assert_almost_equal(tform2.shear, shear) assert_almost_equal(tform2.translation, translation) # scalar vs. tuple scale arguments assert_almost_equal(AffineTransform(scale=0.5).scale, AffineTransform(scale=(0.5, 0.5)).scale) def test_piecewise_affine(): tform = PiecewiseAffineTransform() assert tform.estimate(SRC, DST) # make sure each single affine transform is exactly estimated assert_almost_equal(tform(SRC), DST) assert_almost_equal(tform.inverse(DST), SRC) def test_fundamental_matrix_estimation(): src = np.array([1.839035, 1.924743, 0.543582, 0.375221, 0.473240, 0.142522, 0.964910, 0.598376, 0.102388, 0.140092, 15.994343, 9.622164, 0.285901, 0.430055, 0.091150, 0.254594]).reshape(-1, 2) dst = np.array([1.002114, 1.129644, 1.521742, 1.846002, 1.084332, 0.275134, 0.293328, 0.588992, 0.839509, 0.087290, 1.779735, 1.116857, 0.878616, 0.602447, 0.642616, 1.028681]).reshape(-1, 2) tform = estimate_transform('fundamental', src, dst) # Reference values obtained using COLMAP SfM library. tform_ref = np.array([[-0.217859, 0.419282, -0.0343075], [-0.0717941, 0.0451643, 0.0216073], [0.248062, -0.429478, 0.0221019]]) assert_almost_equal(tform.params, tform_ref, 6) def test_fundamental_matrix_residuals(): essential_matrix_tform = EssentialMatrixTransform( rotation=np.eye(3), translation=np.array([1, 0, 0])) tform = FundamentalMatrixTransform() tform.params = essential_matrix_tform.params src = np.array([[0, 0], [0, 0], [0, 0]]) dst = np.array([[2, 0], [2, 1], [2, 2]]) assert_almost_equal(tform.residuals(src, dst)**2, [0, 0.5, 2]) def test_fundamental_matrix_forward(): essential_matrix_tform = EssentialMatrixTransform( rotation=np.eye(3), translation=np.array([1, 0, 0])) tform = FundamentalMatrixTransform() tform.params = essential_matrix_tform.params src = np.array([[0, 0], [0, 1], [1, 1]]) assert_almost_equal(tform(src), [[0, -1, 0], [0, -1, 1], [0, -1, 1]]) def test_fundamental_matrix_inverse(): essential_matrix_tform = EssentialMatrixTransform( rotation=np.eye(3), translation=np.array([1, 0, 0])) tform = FundamentalMatrixTransform() tform.params = essential_matrix_tform.params src = np.array([[0, 0], [0, 1], [1, 1]]) assert_almost_equal(tform.inverse(src), [[0, 1, 0], [0, 1, -1], [0, 1, -1]]) def test_essential_matrix_init(): tform = EssentialMatrixTransform(rotation=np.eye(3), translation=np.array([0, 0, 1])) assert_equal(tform.params, np.array([0, -1, 0, 1, 0, 0, 0, 0, 0]).reshape(3, 3)) def test_essential_matrix_estimation(): src = np.array([1.839035, 1.924743, 0.543582, 0.375221, 0.473240, 0.142522, 0.964910, 0.598376, 0.102388, 0.140092, 15.994343, 9.622164, 0.285901, 0.430055, 0.091150, 0.254594]).reshape(-1, 2) dst = np.array([1.002114, 1.129644, 1.521742, 1.846002, 1.084332, 0.275134, 0.293328, 0.588992, 0.839509, 0.087290, 1.779735, 1.116857, 0.878616, 0.602447, 0.642616, 1.028681]).reshape(-1, 2) tform = estimate_transform('essential', src, dst) # Reference values obtained using COLMAP SfM library. tform_ref = np.array([[-0.0811666, 0.255449, -0.0478999], [-0.192392, -0.0531675, 0.119547], [0.177784, -0.22008, -0.015203]]) assert_almost_equal(tform.params, tform_ref, 6) def test_essential_matrix_forward(): tform = EssentialMatrixTransform(rotation=np.eye(3), translation=np.array([1, 0, 0])) src = np.array([[0, 0], [0, 1], [1, 1]]) assert_almost_equal(tform(src), [[0, -1, 0], [0, -1, 1], [0, -1, 1]]) def test_essential_matrix_inverse(): tform = EssentialMatrixTransform(rotation=np.eye(3), translation=np.array([1, 0, 0])) src = np.array([[0, 0], [0, 1], [1, 1]]) assert_almost_equal(tform.inverse(src), [[0, 1, 0], [0, 1, -1], [0, 1, -1]]) def test_essential_matrix_residuals(): tform = EssentialMatrixTransform(rotation=np.eye(3), translation=np.array([1, 0, 0])) src = np.array([[0, 0], [0, 0], [0, 0]]) dst = np.array([[2, 0], [2, 1], [2, 2]]) assert_almost_equal(tform.residuals(src, dst)**2, [0, 0.5, 2]) def test_projective_estimation(): # exact solution tform = estimate_transform('projective', SRC[:4, :], DST[:4, :]) assert_almost_equal(tform(SRC[:4, :]), DST[:4, :]) # over-determined tform2 = estimate_transform('projective', SRC, DST) assert_almost_equal(tform2.inverse(tform2(SRC)), SRC) # via estimate method tform3 = ProjectiveTransform() assert tform3.estimate(SRC, DST) assert_almost_equal(tform3.params, tform2.params) def test_projective_weighted_estimation(): # Exact solution with same points, and unity weights tform = estimate_transform('projective', SRC[:4, :], DST[:4, :]) tform_w = estimate_transform('projective', SRC[:4, :], DST[:4, :], np.ones(4)) assert_almost_equal(tform.params, tform_w.params) # Over-determined solution with same points, and unity weights tform = estimate_transform('projective', SRC, DST) tform_w = estimate_transform('projective', SRC, DST, np.ones(SRC.shape[0])) assert_almost_equal(tform.params, tform_w.params) # Repeating a point, but setting its weight small, should give nearly # the same result. point_weights = np.ones(SRC.shape[0] + 1) point_weights[0] = 1.0e-15 tform1 = estimate_transform('projective', SRC, DST) tform2 = estimate_transform('projective', SRC[np.arange(-1, SRC.shape[0]), :], DST[np.arange(-1, SRC.shape[0]), :], point_weights) assert_almost_equal(tform1.params, tform2.params, decimal=3) def test_projective_init(): tform = estimate_transform('projective', SRC, DST) # init with transformation matrix tform2 = ProjectiveTransform(tform.params) assert_almost_equal(tform2.params, tform.params) def test_polynomial_estimation(): # over-determined tform = estimate_transform('polynomial', SRC, DST, order=10) assert_almost_equal(tform(SRC), DST, 6) # via estimate method tform2 = PolynomialTransform() assert tform2.estimate(SRC, DST, order=10) assert_almost_equal(tform2.params, tform.params) def test_polynomial_weighted_estimation(): # Over-determined solution with same points, and unity weights tform = estimate_transform('polynomial', SRC, DST, order=10) tform_w = estimate_transform('polynomial', SRC, DST, order=10, weights=np.ones(SRC.shape[0])) assert_almost_equal(tform.params, tform_w.params) # Repeating a point, but setting its weight small, should give nearly # the same result. point_weights = np.ones(SRC.shape[0] + 1) point_weights[0] = 1.0e-15 tform1 = estimate_transform('polynomial', SRC, DST, order=10) tform2 = estimate_transform('polynomial', SRC[np.arange(-1, SRC.shape[0]), :], DST[np.arange(-1, SRC.shape[0]), :], order=10, weights=point_weights) assert_almost_equal(tform1.params, tform2.params, decimal=4) def test_polynomial_init(): tform = estimate_transform('polynomial', SRC, DST, order=10) # init with transformation parameters tform2 = PolynomialTransform(tform.params) assert_almost_equal(tform2.params, tform.params) def test_polynomial_default_order(): tform = estimate_transform('polynomial', SRC, DST) tform2 = estimate_transform('polynomial', SRC, DST, order=2) assert_almost_equal(tform2.params, tform.params) def test_polynomial_inverse(): with pytest.raises(Exception): PolynomialTransform().inverse(0) def test_union(): tform1 = SimilarityTransform(scale=0.1, rotation=0.3) tform2 = SimilarityTransform(scale=0.1, rotation=0.9) tform3 = SimilarityTransform(scale=0.1 ** 2, rotation=0.3 + 0.9) tform = tform1 + tform2 assert_almost_equal(tform.params, tform3.params) tform1 = AffineTransform(scale=(0.1, 0.1), rotation=0.3) tform2 = SimilarityTransform(scale=0.1, rotation=0.9) tform3 = SimilarityTransform(scale=0.1 ** 2, rotation=0.3 + 0.9) tform = tform1 + tform2 assert_almost_equal(tform.params, tform3.params) assert tform.__class__ == ProjectiveTransform tform = AffineTransform(scale=(0.1, 0.1), rotation=0.3) assert_almost_equal((tform + tform.inverse).params, np.eye(3)) tform1 = SimilarityTransform(scale=0.1, rotation=0.3) tform2 = SimilarityTransform(scale=0.1, rotation=0.9) tform3 = SimilarityTransform(scale=0.1 * 1/0.1, rotation=0.3 - 0.9) tform = tform1 + tform2.inverse assert_almost_equal(tform.params, tform3.params) def test_union_differing_types(): tform1 = SimilarityTransform() tform2 = PolynomialTransform() with pytest.raises(TypeError): tform1.__add__(tform2) def test_geometric_tform(): tform = GeometricTransform() with pytest.raises(NotImplementedError): tform(0) with pytest.raises(NotImplementedError): tform.inverse(0) with pytest.raises(NotImplementedError): tform.__add__(0) # See gh-3926 for discussion details for i in range(20): # Generate random Homography H = np.random.rand(3, 3) * 100 H[2, H[2] == 0] += np.finfo(float).eps H /= H[2, 2] # Craft some src coords src = np.array([ [(H[2, 1] + 1) / -H[2, 0], 1], [1, (H[2, 0] + 1) / -H[2, 1]], [1, 1], ]) # Prior to gh-3926, under the above circumstances, # destination coordinates could be returned with nan/inf values. tform = ProjectiveTransform(H) # Construct the transform dst = tform(src) # Obtain the dst coords # Ensure dst coords are finite numeric values assert(np.isfinite(dst).all()) def test_invalid_input(): with pytest.raises(ValueError): ProjectiveTransform(np.zeros((2, 3))) with pytest.raises(ValueError): AffineTransform(np.zeros((2, 3))) with pytest.raises(ValueError): SimilarityTransform(np.zeros((2, 3))) with pytest.raises(ValueError): EuclideanTransform(np.zeros((2, 3))) with pytest.raises(ValueError): AffineTransform(matrix=np.zeros((2, 3)), scale=1) with pytest.raises(ValueError): SimilarityTransform(matrix=np.zeros((2, 3)), scale=1) with pytest.raises(ValueError): EuclideanTransform( matrix=np.zeros((2, 3)), translation=(0, 0)) with pytest.raises(ValueError): PolynomialTransform(np.zeros((3, 3))) with pytest.raises(ValueError): FundamentalMatrixTransform(matrix=np.zeros((3, 2))) with pytest.raises(ValueError): EssentialMatrixTransform(matrix=np.zeros((3, 2))) with pytest.raises(ValueError): EssentialMatrixTransform(rotation=np.zeros((3, 2))) with pytest.raises(ValueError): EssentialMatrixTransform( rotation=np.zeros((3, 3))) with pytest.raises(ValueError): EssentialMatrixTransform( rotation=np.eye(3)) with pytest.raises(ValueError): EssentialMatrixTransform(rotation=np.eye(3), translation=np.zeros((2,))) with pytest.raises(ValueError): EssentialMatrixTransform(rotation=np.eye(3), translation=np.zeros((2,))) with pytest.raises(ValueError): EssentialMatrixTransform( rotation=np.eye(3), translation=np.zeros((3,))) def test_degenerate(): src = dst = np.zeros((10, 2)) tform = SimilarityTransform() assert not tform.estimate(src, dst) assert np.all(np.isnan(tform.params)) tform = EuclideanTransform() assert not tform.estimate(src, dst) assert np.all(np.isnan(tform.params)) tform = AffineTransform() assert not tform.estimate(src, dst) assert np.all(np.isnan(tform.params)) tform = ProjectiveTransform() assert not tform.estimate(src, dst) assert np.all(np.isnan(tform.params)) # See gh-3926 for discussion details tform = ProjectiveTransform() for i in range(20): # Some random coordinates src = np.random.rand(4, 2) * 100 dst = np.random.rand(4, 2) * 100 # Degenerate the case by arranging points on a single line src[:, 1] = np.random.rand() # Prior to gh-3926, under the above circumstances, # a transform could be returned with nan values. assert(not tform.estimate(src, dst) or np.isfinite(tform.params).all()) src = np.array([[0, 2, 0], [0, 2, 0], [0, 4, 0]]) dst = np.array([[0, 1, 0], [0, 1, 0], [0, 3, 0]]) tform = AffineTransform() assert not tform.estimate(src, dst) # Prior to gh-6207, the above would set the parameters as the identity. assert np.all(np.isnan(tform.params)) # The tesselation on the following points produces one degenerate affine # warp within PiecewiseAffineTransform. src = np.asarray([ [0, 192, 256], [0, 256, 256], [5, 0, 192], [5, 64, 0], [5, 64, 64], [5, 64, 256], [5, 192, 192], [5, 256, 256], [0, 192, 256], ]) dst = np.asarray([ [0, 142, 206], [0, 206, 206], [5, -50, 142], [5, 14, 0], [5, 14, 64], [5, 14, 206], [5, 142, 142], [5, 206, 206], [0, 142, 206], ]) tform = PiecewiseAffineTransform() assert not tform.estimate(src, dst) assert np.all(np.isnan(tform.affines[4].params)) # degenerate affine for idx, affine in enumerate(tform.affines): if idx != 4: assert not np.all(np.isnan(affine.params)) for affine in tform.inverse_affines: assert not np.all(np.isnan(affine.params)) def test_normalize_degenerate_points(): """Return nan matrix *of appropriate size* when point is repeated.""" pts = np.array([[73.42834308, 94.2977623 ],] * 3) mat, pts_tf = _center_and_normalize_points(pts) assert np.all(np.isnan(mat)) assert np.all(np.isnan(pts_tf)) assert mat.shape == (3, 3) assert pts_tf.shape == pts.shape def test_projective_repr(): tform = ProjectiveTransform() want = re.escape(textwrap.dedent( ''' ') # Hack the escaped regex to allow whitespace before each number for # compatibility with different numpy versions. want = want.replace('0\\.', ' *0\\.') want = want.replace('1\\.', ' *1\\.') assert re.match(want, repr(tform)) def test_projective_str(): tform = ProjectiveTransform() want = re.escape(textwrap.dedent( ''' ''').strip()) # Hack the escaped regex to allow whitespace before each number for # compatibility with different numpy versions. want = want.replace('0\\.', ' *0\\.') want = want.replace('1\\.', ' *1\\.') print(want) assert re.match(want, str(tform)) def _assert_least_squares(tf, src, dst): baseline = np.sum((tf(src) - dst) ** 2) for i in range(tf.params.size): for update in [0.001, -0.001]: params = np.copy(tf.params) params.flat[i] += update new_tf = tf.__class__(matrix=params) new_ssq = np.sum((new_tf(src) - dst) ** 2) assert new_ssq > baseline def test_estimate_affine_3d(): ndim = 3 src = np.random.random((25, ndim)) * 2 ** np.arange(7, 7 + ndim) matrix = np.array( [[4.8, 0.1, 0.2, 25], [0.0, 1.0, 0.1, 30], [0.0, 0.0, 1.0, -2], [0.0, 0.0, 0.0, 1.]] ) tf = AffineTransform(matrix=matrix) dst = tf(src) dst_noisy = dst + np.random.random((25, ndim)) tf2 = AffineTransform(dimensionality=ndim) assert tf2.estimate(src, dst_noisy) # we check rot/scale/etc more tightly than translation because translation # estimation is on the 1 pixel scale assert_almost_equal(tf2.params[:, :-1], matrix[:, :-1], decimal=2) assert_almost_equal(tf2.params[:, -1], matrix[:, -1], decimal=0) _assert_least_squares(tf2, src, dst_noisy) def test_fundamental_3d_not_implemented(): with pytest.raises(NotImplementedError): _ = FundamentalMatrixTransform(dimensionality=3) with pytest.raises(NotImplementedError): _ = FundamentalMatrixTransform(np.eye(4)) def test_array_protocol(): mat = np.eye(4) tf = ProjectiveTransform(mat) assert_equal(np.array(tf), mat) assert_equal(np.array(tf, dtype=int), mat.astype(int)) def test_affine_transform_from_linearized_parameters(): mat = np.concatenate( (np.random.random((3, 4)), np.eye(4)[-1:]), axis=0 ) v = mat[:-1].ravel() mat_from_v = _affine_matrix_from_vector(v) tf = AffineTransform(matrix=mat_from_v) assert_equal(np.array(tf), mat) # incorrect number of parameters with pytest.raises(ValueError): _ = _affine_matrix_from_vector(v[:-1]) with pytest.raises(ValueError): _ = AffineTransform(matrix=v[:-1]) def test_affine_params_nD_error(): with pytest.raises(ValueError): _ = AffineTransform(scale=5, dimensionality=3) def test_euler_rotation(): v = [0, 10, 0] angles = np.radians([90, 45, 45]) expected = [-5, -5, 7.1] R = _euler_rotation_matrix(angles) assert_almost_equal(R @ v, expected, decimal=1) def test_euclidean_param_defaults(): # 2D rotation is 0 when only translation is given tf = EuclideanTransform(translation=(5, 5)) assert np.array(tf)[0, 1] == 0 # off diagonals are 0 when only translation is given tf = EuclideanTransform(translation=(4, 5, 9), dimensionality=3) assert_equal(np.array(tf)[[0, 0, 1, 1, 2, 2], [1, 2, 0, 2, 0, 1]], 0) with pytest.raises(ValueError): # specifying parameters for D>3 is not supported _ = EuclideanTransform(translation=(5, 6, 7, 8), dimensionality=4) with pytest.raises(ValueError): # incorrect number of angles for given dimensionality _ = EuclideanTransform(rotation=(4, 8), dimensionality=3) # translation is 0 when rotation is given tf = EuclideanTransform(rotation=np.pi * np.arange(3), dimensionality=3) assert_equal(np.array(tf)[:-1, 3], 0) def test_similarity_transform_params(): with pytest.raises(ValueError): _ = SimilarityTransform(translation=(4, 5, 6, 7), dimensionality=4) tf = SimilarityTransform(scale=4, dimensionality=3) assert_equal(tf([[1, 1, 1]]), [[4, 4, 4]]) def test_euler_angle_consistency(): angles = np.random.random((3,)) * 2 * np.pi - np.pi euclid = EuclideanTransform(rotation=angles, dimensionality=3) similar = SimilarityTransform(rotation=angles, dimensionality=3) assert_array_almost_equal(euclid, similar) def test_2D_only_implementations(): with pytest.raises(NotImplementedError): _ = PolynomialTransform(dimensionality=3) tf = AffineTransform(dimensionality=3) with pytest.raises(NotImplementedError): _ = tf.rotation with pytest.raises(NotImplementedError): _ = tf.shear