388 lines
14 KiB
Python
388 lines
14 KiB
Python
import numpy as np
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from skimage.measure import LineModelND, CircleModel, EllipseModel, ransac
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from skimage.transform import AffineTransform
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from skimage.measure.fit import _dynamic_max_trials
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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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assert_array_less, xfail, arch32)
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def test_line_model_invalid_input():
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with testing.raises(ValueError):
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LineModelND().estimate(np.empty((1, 3)))
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def test_line_model_predict():
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model = LineModelND()
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model.params = ((0, 0), (1, 1))
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x = np.arange(-10, 10)
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y = model.predict_y(x)
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assert_almost_equal(x, model.predict_x(y))
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def test_line_model_nd_invalid_input():
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with testing.raises(ValueError):
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LineModelND().predict_x(np.zeros(1))
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with testing.raises(ValueError):
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LineModelND().predict_y(np.zeros(1))
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with testing.raises(ValueError):
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LineModelND().predict_x(np.zeros(1), np.zeros(1))
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with testing.raises(ValueError):
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LineModelND().predict_y(np.zeros(1))
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with testing.raises(ValueError):
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LineModelND().predict_y(np.zeros(1), np.zeros(1))
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with testing.raises(ValueError):
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LineModelND().estimate(np.empty((1, 3)))
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with testing.raises(ValueError):
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LineModelND().residuals(np.empty((1, 3)))
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data = np.empty((1, 2))
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with testing.raises(ValueError):
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LineModelND().estimate(data)
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def test_line_model_nd_predict():
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model = LineModelND()
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model.params = (np.array([0, 0]), np.array([0.2, 0.8]))
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x = np.arange(-10, 10)
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y = model.predict_y(x)
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assert_almost_equal(x, model.predict_x(y))
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def test_line_model_nd_estimate():
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# generate original data without noise
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model0 = LineModelND()
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model0.params = (np.array([0, 0, 0], dtype='float'),
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np.array([1, 1, 1], dtype='float')/np.sqrt(3))
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# we scale the unit vector with a factor 10 when generating points on the
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# line in order to compensate for the scale of the random noise
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data0 = (model0.params[0] +
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10 * np.arange(-100, 100)[..., np.newaxis] * model0.params[1])
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# add gaussian noise to data
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random_state = np.random.RandomState(1234)
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data = data0 + random_state.normal(size=data0.shape)
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# estimate parameters of noisy data
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model_est = LineModelND()
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model_est.estimate(data)
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# assert_almost_equal(model_est.residuals(data0), np.zeros(len(data)), 1)
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# test whether estimated parameters are correct
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# we use the following geometric property: two aligned vectors have
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# a cross-product equal to zero
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# test if direction vectors are aligned
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assert_almost_equal(np.linalg.norm(np.cross(model0.params[1],
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model_est.params[1])), 0, 1)
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# test if origins are aligned with the direction
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a = model_est.params[0] - model0.params[0]
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if np.linalg.norm(a) > 0:
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a /= np.linalg.norm(a)
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assert_almost_equal(np.linalg.norm(np.cross(model0.params[1], a)), 0, 1)
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def test_line_model_nd_residuals():
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model = LineModelND()
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model.params = (np.array([0, 0, 0]), np.array([0, 0, 1]))
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assert_equal(abs(model.residuals(np.array([[0, 0, 0]]))), 0)
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assert_equal(abs(model.residuals(np.array([[0, 0, 1]]))), 0)
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assert_equal(abs(model.residuals(np.array([[10, 0, 0]]))), 10)
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# test params argument in model.rediduals
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data = np.array([[10, 0, 0]])
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params = (np.array([0, 0, 0]), np.array([2, 0, 0]))
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assert_equal(abs(model.residuals(data, params=params)), 30)
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def test_line_modelND_under_determined():
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data = np.empty((1, 3))
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with testing.raises(ValueError):
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LineModelND().estimate(data)
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def test_circle_model_invalid_input():
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with testing.raises(ValueError):
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CircleModel().estimate(np.empty((5, 3)))
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def test_circle_model_predict():
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model = CircleModel()
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r = 5
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model.params = (0, 0, r)
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t = np.arange(0, 2 * np.pi, np.pi / 2)
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xy = np.array(((5, 0), (0, 5), (-5, 0), (0, -5)))
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assert_almost_equal(xy, model.predict_xy(t))
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def test_circle_model_estimate():
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# generate original data without noise
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model0 = CircleModel()
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model0.params = (10, 12, 3)
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t = np.linspace(0, 2 * np.pi, 1000)
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data0 = model0.predict_xy(t)
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# add gaussian noise to data
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random_state = np.random.RandomState(1234)
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data = data0 + random_state.normal(size=data0.shape)
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# estimate parameters of noisy data
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model_est = CircleModel()
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model_est.estimate(data)
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# test whether estimated parameters almost equal original parameters
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assert_almost_equal(model0.params, model_est.params, 0)
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def test_circle_model_residuals():
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model = CircleModel()
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model.params = (0, 0, 5)
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assert_almost_equal(abs(model.residuals(np.array([[5, 0]]))), 0)
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assert_almost_equal(abs(model.residuals(np.array([[6, 6]]))),
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np.sqrt(2 * 6**2) - 5)
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assert_almost_equal(abs(model.residuals(np.array([[10, 0]]))), 5)
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def test_ellipse_model_invalid_input():
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with testing.raises(ValueError):
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EllipseModel().estimate(np.empty((5, 3)))
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def test_ellipse_model_predict():
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model = EllipseModel()
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model.params = (0, 0, 5, 10, 0)
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t = np.arange(0, 2 * np.pi, np.pi / 2)
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xy = np.array(((5, 0), (0, 10), (-5, 0), (0, -10)))
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assert_almost_equal(xy, model.predict_xy(t))
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def test_ellipse_model_estimate():
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for angle in range(0, 180, 15):
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rad = np.deg2rad(angle)
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# generate original data without noise
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model0 = EllipseModel()
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model0.params = (10, 20, 15, 25, rad)
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t = np.linspace(0, 2 * np.pi, 100)
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data0 = model0.predict_xy(t)
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# add gaussian noise to data
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random_state = np.random.RandomState(1234)
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data = data0 + random_state.normal(size=data0.shape)
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# estimate parameters of noisy data
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model_est = EllipseModel()
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model_est.estimate(data)
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# test whether estimated parameters almost equal original parameters
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assert_almost_equal(model0.params[:2], model_est.params[:2], 0)
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res = model_est.residuals(data0)
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assert_array_less(res, np.ones(res.shape))
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def test_ellipse_model_estimate_from_data():
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data = np.array([
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[264, 854], [265, 875], [268, 863], [270, 857], [275, 905], [285, 915],
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[305, 925], [324, 934], [335, 764], [336, 915], [345, 925], [345, 945],
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[354, 933], [355, 745], [364, 936], [365, 754], [375, 745], [375, 735],
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[385, 736], [395, 735], [394, 935], [405, 727], [415, 736], [415, 727],
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[425, 727], [426, 929], [435, 735], [444, 933], [445, 735], [455, 724],
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[465, 934], [465, 735], [475, 908], [475, 726], [485, 753], [485, 728],
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[492, 762], [495, 745], [491, 910], [493, 909], [499, 904], [505, 905],
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[504, 747], [515, 743], [516, 752], [524, 855], [525, 844], [525, 885],
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[533, 845], [533, 873], [535, 883], [545, 874], [543, 864], [553, 865],
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[553, 845], [554, 825], [554, 835], [563, 845], [565, 826], [563, 855],
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[563, 795], [565, 735], [573, 778], [572, 815], [574, 804], [575, 665],
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[575, 685], [574, 705], [574, 745], [575, 875], [572, 732], [582, 795],
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[579, 709], [583, 805], [583, 854], [586, 755], [584, 824], [585, 655],
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[581, 718], [586, 844], [585, 915], [587, 905], [594, 824], [593, 855],
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[590, 891], [594, 776], [596, 767], [593, 763], [603, 785], [604, 775],
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[603, 885], [605, 753], [605, 655], [606, 935], [603, 761], [613, 802],
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[613, 945], [613, 965], [615, 693], [617, 665], [623, 962], [624, 972],
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[625, 995], [633, 673], [633, 965], [633, 683], [633, 692], [633, 954],
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[634, 1016], [635, 664], [641, 804], [637, 999], [641, 956], [643, 946],
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[643, 926], [644, 975], [643, 655], [646, 705], [651, 664], [651, 984],
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[647, 665], [651, 715], [651, 725], [651, 734], [647, 809], [651, 825],
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[651, 873], [647, 900], [652, 917], [651, 944], [652, 742], [648, 811],
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[651, 994], [652, 783], [650, 911], [654, 879]])
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# estimate parameters of real data
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model = EllipseModel()
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model.estimate(data)
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# test whether estimated parameters are smaller then 1000, so means stable
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assert_array_less(np.abs(model.params[:4]), np.array([2e3] * 4))
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@xfail(condition=arch32,
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reason=('Known test failure on 32-bit platforms. See links for '
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'details: '
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'https://github.com/scikit-image/scikit-image/issues/3091 '
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'https://github.com/scikit-image/scikit-image/issues/2670'))
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def test_ellipse_model_estimate_failers():
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# estimate parameters of real data
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model = EllipseModel()
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assert not model.estimate(np.ones((5, 2)))
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assert not model.estimate(np.array([[50, 80], [51, 81], [52, 80]]))
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def test_ellipse_model_residuals():
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model = EllipseModel()
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# vertical line through origin
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model.params = (0, 0, 10, 5, 0)
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assert_almost_equal(abs(model.residuals(np.array([[10, 0]]))), 0)
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assert_almost_equal(abs(model.residuals(np.array([[0, 5]]))), 0)
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assert_almost_equal(abs(model.residuals(np.array([[0, 10]]))), 5)
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def test_ransac_shape():
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# generate original data without noise
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model0 = CircleModel()
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model0.params = (10, 12, 3)
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t = np.linspace(0, 2 * np.pi, 1000)
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data0 = model0.predict_xy(t)
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# add some faulty data
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outliers = (10, 30, 200)
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data0[outliers[0], :] = (1000, 1000)
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data0[outliers[1], :] = (-50, 50)
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data0[outliers[2], :] = (-100, -10)
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# estimate parameters of corrupted data
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model_est, inliers = ransac(data0, CircleModel, 3, 5, random_state=1)
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# test whether estimated parameters equal original parameters
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assert_almost_equal(model0.params, model_est.params)
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for outlier in outliers:
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assert outlier not in inliers
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def test_ransac_geometric():
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random_state = np.random.RandomState(1)
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# generate original data without noise
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src = 100 * random_state.random_sample((50, 2))
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model0 = AffineTransform(scale=(0.5, 0.3), rotation=1,
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translation=(10, 20))
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dst = model0(src)
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# add some faulty data
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outliers = (0, 5, 20)
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dst[outliers[0]] = (10000, 10000)
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dst[outliers[1]] = (-100, 100)
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dst[outliers[2]] = (50, 50)
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# estimate parameters of corrupted data
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model_est, inliers = ransac((src, dst), AffineTransform, 2, 20,
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random_state=random_state)
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# test whether estimated parameters equal original parameters
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assert_almost_equal(model0.params, model_est.params)
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assert np.all(np.nonzero(inliers == False)[0] == outliers)
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def test_ransac_is_data_valid():
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def is_data_valid(data):
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return data.shape[0] > 2
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model, inliers = ransac(np.empty((10, 2)), LineModelND, 2, np.inf,
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is_data_valid=is_data_valid, random_state=1)
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assert_equal(model, None)
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assert_equal(inliers, None)
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def test_ransac_is_model_valid():
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def is_model_valid(model, data):
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return False
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model, inliers = ransac(np.empty((10, 2)), LineModelND, 2, np.inf,
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is_model_valid=is_model_valid, random_state=1)
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assert_equal(model, None)
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assert_equal(inliers, None)
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def test_ransac_dynamic_max_trials():
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# Numbers hand-calculated and confirmed on page 119 (Table 4.3) in
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# Hartley, R.~I. and Zisserman, A., 2004,
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# Multiple View Geometry in Computer Vision, Second Edition,
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# Cambridge University Press, ISBN: 0521540518
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# e = 0%, min_samples = X
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assert_equal(_dynamic_max_trials(100, 100, 2, 0.99), 1)
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# e = 5%, min_samples = 2
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assert_equal(_dynamic_max_trials(95, 100, 2, 0.99), 2)
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# e = 10%, min_samples = 2
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assert_equal(_dynamic_max_trials(90, 100, 2, 0.99), 3)
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# e = 30%, min_samples = 2
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assert_equal(_dynamic_max_trials(70, 100, 2, 0.99), 7)
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# e = 50%, min_samples = 2
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assert_equal(_dynamic_max_trials(50, 100, 2, 0.99), 17)
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# e = 5%, min_samples = 8
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assert_equal(_dynamic_max_trials(95, 100, 8, 0.99), 5)
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# e = 10%, min_samples = 8
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assert_equal(_dynamic_max_trials(90, 100, 8, 0.99), 9)
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# e = 30%, min_samples = 8
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assert_equal(_dynamic_max_trials(70, 100, 8, 0.99), 78)
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# e = 50%, min_samples = 8
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assert_equal(_dynamic_max_trials(50, 100, 8, 0.99), 1177)
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# e = 0%, min_samples = 5
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assert_equal(_dynamic_max_trials(1, 100, 5, 0), 0)
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assert_equal(_dynamic_max_trials(1, 100, 5, 1), np.inf)
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def test_ransac_invalid_input():
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# `residual_threshold` must be greater than zero
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with testing.raises(ValueError):
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ransac(np.zeros((10, 2)), None, min_samples=2,
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residual_threshold=-0.5)
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# "`max_trials` must be greater than zero"
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with testing.raises(ValueError):
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ransac(np.zeros((10, 2)), None, min_samples=2,
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residual_threshold=0, max_trials=-1)
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# `stop_probability` must be in range (0, 1)
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with testing.raises(ValueError):
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ransac(np.zeros((10, 2)), None, min_samples=2,
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residual_threshold=0, stop_probability=-1)
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# `stop_probability` must be in range (0, 1)
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with testing.raises(ValueError):
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ransac(np.zeros((10, 2)), None, min_samples=2,
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residual_threshold=0, stop_probability=1.01)
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# `min_samples` as ratio must be in range (0, nb)
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with testing.raises(ValueError):
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ransac(np.zeros((10, 2)), None, min_samples=0,
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residual_threshold=0)
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# `min_samples` as ratio must be in range (0, nb)
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with testing.raises(ValueError):
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ransac(np.zeros((10, 2)), None, min_samples=10,
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residual_threshold=0)
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# `min_samples` must be greater than zero
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with testing.raises(ValueError):
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ransac(np.zeros((10, 2)), None, min_samples=-1,
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residual_threshold=0)
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def test_ransac_sample_duplicates():
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class DummyModel(object):
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"""Dummy model to check for duplicates."""
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def estimate(self, data):
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# Assert that all data points are unique.
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assert_equal(np.unique(data).size, data.size)
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return True
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def residuals(self, data):
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return np.ones(len(data), dtype=np.double)
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# Create dataset with four unique points. Force 10 iterations
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# and check that there are no duplicated data points.
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data = np.arange(4)
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ransac(data, DummyModel, min_samples=3, residual_threshold=0.0,
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max_trials=10)
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