524 lines
18 KiB
Python
524 lines
18 KiB
Python
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import numpy as np
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import re
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from skimage.transform._geometric import GeometricTransform
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from skimage.transform import (estimate_transform, matrix_transform,
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EuclideanTransform, SimilarityTransform,
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AffineTransform, FundamentalMatrixTransform,
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EssentialMatrixTransform, ProjectiveTransform,
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PolynomialTransform, PiecewiseAffineTransform)
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from skimage._shared import testing
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from skimage._shared.testing import assert_equal, assert_almost_equal
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import textwrap
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SRC = np.array([
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[-12.3705, -10.5075],
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[-10.7865, 15.4305],
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[8.6985, 10.8675],
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[11.4975, -9.5715],
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[7.8435, 7.4835],
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[-5.3325, 6.5025],
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[6.7905, -6.3765],
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[-6.1695, -0.8235],
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])
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DST = np.array([
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[0, 0],
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[0, 5800],
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[4900, 5800],
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[4900, 0],
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[4479, 4580],
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[1176, 3660],
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[3754, 790],
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[1024, 1931],
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])
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def test_estimate_transform():
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for tform in ('euclidean', 'similarity', 'affine', 'projective',
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'polynomial'):
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estimate_transform(tform, SRC[:2, :], DST[:2, :])
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with testing.raises(ValueError):
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estimate_transform('foobar', SRC[:2, :], DST[:2, :])
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def test_matrix_transform():
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tform = AffineTransform(scale=(0.1, 0.5), rotation=2)
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assert_equal(tform(SRC), matrix_transform(SRC, tform.params))
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def test_euclidean_estimation():
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# exact solution
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tform = estimate_transform('euclidean', SRC[:2, :], SRC[:2, :] + 10)
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assert_almost_equal(tform(SRC[:2, :]), SRC[:2, :] + 10)
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assert_almost_equal(tform.params[0, 0], tform.params[1, 1])
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assert_almost_equal(tform.params[0, 1], - tform.params[1, 0])
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# over-determined
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tform2 = estimate_transform('euclidean', SRC, DST)
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assert_almost_equal(tform2.inverse(tform2(SRC)), SRC)
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assert_almost_equal(tform2.params[0, 0], tform2.params[1, 1])
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assert_almost_equal(tform2.params[0, 1], - tform2.params[1, 0])
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# via estimate method
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tform3 = EuclideanTransform()
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tform3.estimate(SRC, DST)
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assert_almost_equal(tform3.params, tform2.params)
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def test_euclidean_init():
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# init with implicit parameters
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rotation = 1
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translation = (1, 1)
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tform = EuclideanTransform(rotation=rotation, translation=translation)
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assert_almost_equal(tform.rotation, rotation)
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assert_almost_equal(tform.translation, translation)
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# init with transformation matrix
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tform2 = EuclideanTransform(tform.params)
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assert_almost_equal(tform2.rotation, rotation)
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assert_almost_equal(tform2.translation, translation)
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# test special case for scale if rotation=0
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rotation = 0
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translation = (1, 1)
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tform = EuclideanTransform(rotation=rotation, translation=translation)
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assert_almost_equal(tform.rotation, rotation)
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assert_almost_equal(tform.translation, translation)
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# test special case for scale if rotation=90deg
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rotation = np.pi / 2
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translation = (1, 1)
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tform = EuclideanTransform(rotation=rotation, translation=translation)
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assert_almost_equal(tform.rotation, rotation)
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assert_almost_equal(tform.translation, translation)
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def test_similarity_estimation():
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# exact solution
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tform = estimate_transform('similarity', SRC[:2, :], DST[:2, :])
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assert_almost_equal(tform(SRC[:2, :]), DST[:2, :])
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assert_almost_equal(tform.params[0, 0], tform.params[1, 1])
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assert_almost_equal(tform.params[0, 1], - tform.params[1, 0])
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# over-determined
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tform2 = estimate_transform('similarity', SRC, DST)
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assert_almost_equal(tform2.inverse(tform2(SRC)), SRC)
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assert_almost_equal(tform2.params[0, 0], tform2.params[1, 1])
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assert_almost_equal(tform2.params[0, 1], - tform2.params[1, 0])
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# via estimate method
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tform3 = SimilarityTransform()
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tform3.estimate(SRC, DST)
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assert_almost_equal(tform3.params, tform2.params)
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def test_similarity_init():
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# init with implicit parameters
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scale = 0.1
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rotation = 1
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translation = (1, 1)
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tform = SimilarityTransform(scale=scale, rotation=rotation,
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translation=translation)
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assert_almost_equal(tform.scale, scale)
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assert_almost_equal(tform.rotation, rotation)
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assert_almost_equal(tform.translation, translation)
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# init with transformation matrix
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tform2 = SimilarityTransform(tform.params)
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assert_almost_equal(tform2.scale, scale)
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assert_almost_equal(tform2.rotation, rotation)
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assert_almost_equal(tform2.translation, translation)
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# test special case for scale if rotation=0
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scale = 0.1
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rotation = 0
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translation = (1, 1)
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tform = SimilarityTransform(scale=scale, rotation=rotation,
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translation=translation)
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assert_almost_equal(tform.scale, scale)
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assert_almost_equal(tform.rotation, rotation)
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assert_almost_equal(tform.translation, translation)
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# test special case for scale if rotation=90deg
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scale = 0.1
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rotation = np.pi / 2
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translation = (1, 1)
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tform = SimilarityTransform(scale=scale, rotation=rotation,
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translation=translation)
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assert_almost_equal(tform.scale, scale)
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assert_almost_equal(tform.rotation, rotation)
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assert_almost_equal(tform.translation, translation)
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# test special case for scale where the rotation isn't exactly 90deg,
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# but very close
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scale = 1.0
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rotation = np.pi / 2
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translation = (0, 0)
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params = np.array([[0, -1, 1.33226763e-15],
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[1, 2.22044605e-16, -1.33226763e-15],
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[0, 0, 1]])
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tform = SimilarityTransform(params)
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assert_almost_equal(tform.scale, scale)
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assert_almost_equal(tform.rotation, rotation)
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assert_almost_equal(tform.translation, translation)
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def test_affine_estimation():
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# exact solution
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tform = estimate_transform('affine', SRC[:3, :], DST[:3, :])
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assert_almost_equal(tform(SRC[:3, :]), DST[:3, :])
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# over-determined
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tform2 = estimate_transform('affine', SRC, DST)
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assert_almost_equal(tform2.inverse(tform2(SRC)), SRC)
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# via estimate method
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tform3 = AffineTransform()
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tform3.estimate(SRC, DST)
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assert_almost_equal(tform3.params, tform2.params)
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def test_affine_init():
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# init with implicit parameters
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scale = (0.1, 0.13)
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rotation = 1
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shear = 0.1
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translation = (1, 1)
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tform = AffineTransform(scale=scale, rotation=rotation, shear=shear,
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translation=translation)
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assert_almost_equal(tform.scale, scale)
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assert_almost_equal(tform.rotation, rotation)
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assert_almost_equal(tform.shear, shear)
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assert_almost_equal(tform.translation, translation)
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# init with transformation matrix
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tform2 = AffineTransform(tform.params)
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assert_almost_equal(tform2.scale, scale)
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assert_almost_equal(tform2.rotation, rotation)
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assert_almost_equal(tform2.shear, shear)
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assert_almost_equal(tform2.translation, translation)
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# scalar vs. tuple scale arguments
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assert_almost_equal(AffineTransform(scale=0.5).scale, AffineTransform(scale=(0.5, 0.5)).scale)
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def test_piecewise_affine():
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tform = PiecewiseAffineTransform()
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tform.estimate(SRC, DST)
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# make sure each single affine transform is exactly estimated
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assert_almost_equal(tform(SRC), DST)
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assert_almost_equal(tform.inverse(DST), SRC)
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def test_fundamental_matrix_estimation():
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src = np.array([1.839035, 1.924743, 0.543582, 0.375221,
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0.473240, 0.142522, 0.964910, 0.598376,
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0.102388, 0.140092, 15.994343, 9.622164,
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0.285901, 0.430055, 0.091150, 0.254594]).reshape(-1, 2)
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dst = np.array([1.002114, 1.129644, 1.521742, 1.846002,
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1.084332, 0.275134, 0.293328, 0.588992,
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0.839509, 0.087290, 1.779735, 1.116857,
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0.878616, 0.602447, 0.642616, 1.028681]).reshape(-1, 2)
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tform = estimate_transform('fundamental', src, dst)
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# Reference values obtained using COLMAP SfM library.
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tform_ref = np.array([[-0.217859, 0.419282, -0.0343075],
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[-0.0717941, 0.0451643, 0.0216073],
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[0.248062, -0.429478, 0.0221019]])
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assert_almost_equal(tform.params, tform_ref, 6)
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def test_fundamental_matrix_residuals():
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essential_matrix_tform = EssentialMatrixTransform(
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rotation=np.eye(3), translation=np.array([1, 0, 0]))
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tform = FundamentalMatrixTransform()
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tform.params = essential_matrix_tform.params
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src = np.array([[0, 0], [0, 0], [0, 0]])
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dst = np.array([[2, 0], [2, 1], [2, 2]])
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assert_almost_equal(tform.residuals(src, dst)**2, [0, 0.5, 2])
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def test_fundamental_matrix_forward():
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essential_matrix_tform = EssentialMatrixTransform(
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rotation=np.eye(3), translation=np.array([1, 0, 0]))
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tform = FundamentalMatrixTransform()
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tform.params = essential_matrix_tform.params
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src = np.array([[0, 0], [0, 1], [1, 1]])
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assert_almost_equal(tform(src), [[0, -1, 0], [0, -1, 1], [0, -1, 1]])
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def test_fundamental_matrix_inverse():
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essential_matrix_tform = EssentialMatrixTransform(
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rotation=np.eye(3), translation=np.array([1, 0, 0]))
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tform = FundamentalMatrixTransform()
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tform.params = essential_matrix_tform.params
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src = np.array([[0, 0], [0, 1], [1, 1]])
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assert_almost_equal(tform.inverse(src),
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[[0, 1, 0], [0, 1, -1], [0, 1, -1]])
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def test_essential_matrix_init():
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tform = EssentialMatrixTransform(rotation=np.eye(3),
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translation=np.array([0, 0, 1]))
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assert_equal(tform.params,
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np.array([0, -1, 0, 1, 0, 0, 0, 0, 0]).reshape(3, 3))
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def test_essential_matrix_estimation():
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src = np.array([1.839035, 1.924743, 0.543582, 0.375221,
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0.473240, 0.142522, 0.964910, 0.598376,
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0.102388, 0.140092, 15.994343, 9.622164,
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0.285901, 0.430055, 0.091150, 0.254594]).reshape(-1, 2)
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dst = np.array([1.002114, 1.129644, 1.521742, 1.846002,
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1.084332, 0.275134, 0.293328, 0.588992,
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0.839509, 0.087290, 1.779735, 1.116857,
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0.878616, 0.602447, 0.642616, 1.028681]).reshape(-1, 2)
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tform = estimate_transform('essential', src, dst)
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# Reference values obtained using COLMAP SfM library.
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tform_ref = np.array([[-0.0811666, 0.255449, -0.0478999],
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[-0.192392, -0.0531675, 0.119547],
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[0.177784, -0.22008, -0.015203]])
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assert_almost_equal(tform.params, tform_ref, 6)
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def test_essential_matrix_forward():
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tform = EssentialMatrixTransform(rotation=np.eye(3),
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translation=np.array([1, 0, 0]))
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src = np.array([[0, 0], [0, 1], [1, 1]])
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assert_almost_equal(tform(src), [[0, -1, 0], [0, -1, 1], [0, -1, 1]])
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def test_essential_matrix_inverse():
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tform = EssentialMatrixTransform(rotation=np.eye(3),
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translation=np.array([1, 0, 0]))
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src = np.array([[0, 0], [0, 1], [1, 1]])
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assert_almost_equal(tform.inverse(src),
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[[0, 1, 0], [0, 1, -1], [0, 1, -1]])
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def test_essential_matrix_residuals():
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tform = EssentialMatrixTransform(rotation=np.eye(3),
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translation=np.array([1, 0, 0]))
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src = np.array([[0, 0], [0, 0], [0, 0]])
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dst = np.array([[2, 0], [2, 1], [2, 2]])
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assert_almost_equal(tform.residuals(src, dst)**2, [0, 0.5, 2])
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def test_projective_estimation():
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# exact solution
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tform = estimate_transform('projective', SRC[:4, :], DST[:4, :])
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assert_almost_equal(tform(SRC[:4, :]), DST[:4, :])
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# over-determined
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tform2 = estimate_transform('projective', SRC, DST)
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assert_almost_equal(tform2.inverse(tform2(SRC)), SRC)
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# via estimate method
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tform3 = ProjectiveTransform()
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tform3.estimate(SRC, DST)
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assert_almost_equal(tform3.params, tform2.params)
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def test_projective_init():
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tform = estimate_transform('projective', SRC, DST)
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# init with transformation matrix
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tform2 = ProjectiveTransform(tform.params)
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assert_almost_equal(tform2.params, tform.params)
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def test_polynomial_estimation():
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# over-determined
|
||
|
|
tform = estimate_transform('polynomial', SRC, DST, order=10)
|
||
|
|
assert_almost_equal(tform(SRC), DST, 6)
|
||
|
|
|
||
|
|
# via estimate method
|
||
|
|
tform2 = PolynomialTransform()
|
||
|
|
tform2.estimate(SRC, DST, order=10)
|
||
|
|
assert_almost_equal(tform2.params, tform.params)
|
||
|
|
|
||
|
|
|
||
|
|
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 testing.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 testing.raises(TypeError):
|
||
|
|
tform1.__add__(tform2)
|
||
|
|
|
||
|
|
|
||
|
|
def test_geometric_tform():
|
||
|
|
tform = GeometricTransform()
|
||
|
|
with testing.raises(NotImplementedError):
|
||
|
|
tform(0)
|
||
|
|
with testing.raises(NotImplementedError):
|
||
|
|
tform.inverse(0)
|
||
|
|
with testing.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 testing.raises(ValueError):
|
||
|
|
ProjectiveTransform(np.zeros((2, 3)))
|
||
|
|
with testing.raises(ValueError):
|
||
|
|
AffineTransform(np.zeros((2, 3)))
|
||
|
|
with testing.raises(ValueError):
|
||
|
|
SimilarityTransform(np.zeros((2, 3)))
|
||
|
|
with testing.raises(ValueError):
|
||
|
|
EuclideanTransform(np.zeros((2, 3)))
|
||
|
|
with testing.raises(ValueError):
|
||
|
|
AffineTransform(matrix=np.zeros((2, 3)), scale=1)
|
||
|
|
with testing.raises(ValueError):
|
||
|
|
SimilarityTransform(matrix=np.zeros((2, 3)), scale=1)
|
||
|
|
with testing.raises(ValueError):
|
||
|
|
EuclideanTransform(
|
||
|
|
matrix=np.zeros((2, 3)), translation=(0, 0))
|
||
|
|
with testing.raises(ValueError):
|
||
|
|
PolynomialTransform(np.zeros((3, 3)))
|
||
|
|
with testing.raises(ValueError):
|
||
|
|
FundamentalMatrixTransform(matrix=np.zeros((3, 2)))
|
||
|
|
with testing.raises(ValueError):
|
||
|
|
EssentialMatrixTransform(matrix=np.zeros((3, 2)))
|
||
|
|
|
||
|
|
with testing.raises(ValueError):
|
||
|
|
EssentialMatrixTransform(rotation=np.zeros((3, 2)))
|
||
|
|
with testing.raises(ValueError):
|
||
|
|
EssentialMatrixTransform(
|
||
|
|
rotation=np.zeros((3, 3)))
|
||
|
|
with testing.raises(ValueError):
|
||
|
|
EssentialMatrixTransform(
|
||
|
|
rotation=np.eye(3))
|
||
|
|
with testing.raises(ValueError):
|
||
|
|
EssentialMatrixTransform(rotation=np.eye(3),
|
||
|
|
translation=np.zeros((2,)))
|
||
|
|
with testing.raises(ValueError):
|
||
|
|
EssentialMatrixTransform(rotation=np.eye(3),
|
||
|
|
translation=np.zeros((2,)))
|
||
|
|
with testing.raises(ValueError):
|
||
|
|
EssentialMatrixTransform(
|
||
|
|
rotation=np.eye(3), translation=np.zeros((3,)))
|
||
|
|
|
||
|
|
|
||
|
|
def test_degenerate():
|
||
|
|
src = dst = np.zeros((10, 2))
|
||
|
|
|
||
|
|
tform = SimilarityTransform()
|
||
|
|
tform.estimate(src, dst)
|
||
|
|
assert np.all(np.isnan(tform.params))
|
||
|
|
|
||
|
|
tform = AffineTransform()
|
||
|
|
tform.estimate(src, dst)
|
||
|
|
assert np.all(np.isnan(tform.params))
|
||
|
|
|
||
|
|
tform = ProjectiveTransform()
|
||
|
|
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())
|
||
|
|
|
||
|
|
|
||
|
|
def test_projective_repr():
|
||
|
|
tform = ProjectiveTransform()
|
||
|
|
want = re.escape(textwrap.dedent(
|
||
|
|
'''
|
||
|
|
<ProjectiveTransform(matrix=
|
||
|
|
[[1., 0., 0.],
|
||
|
|
[0., 1., 0.],
|
||
|
|
[0., 0., 1.]]) at
|
||
|
|
''').strip()) + ' 0x[a-f0-9]+' + re.escape('>')
|
||
|
|
# 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(
|
||
|
|
'''
|
||
|
|
<ProjectiveTransform(matrix=
|
||
|
|
[[1., 0., 0.],
|
||
|
|
[0., 1., 0.],
|
||
|
|
[0., 0., 1.]])>
|
||
|
|
''').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))
|