def test_butterworth_2D_realfft(high_pass):
"""Filtering a real-valued array is equivalent to filtering a
complex-valued array where the imaginary part is zero.
"""
im = np.random.randn(32, 64)
kwargs = dict(cutoff_frequency_ratio=0.20, high_pass=high_pass)
filtered_real = butterworth(im, **kwargs)
filtered_cplx = butterworth(im.astype(np.complex128), **kwargs)
assert_allclose(filtered_real, filtered_cplx.real)
def test_butterworth_2D(high_pass):
# rough check of high-pass vs. low-pass behavior via relative energy
im = np.random.randn(64, 128)
filtered = butterworth(
im,
cutoff_frequency_ratio=0.20,
high_pass=high_pass,
)
# Compute the energy at the outer edges of the Fourier domain
# before and after filtering.
im_fft = _fft_centered(im)
im_fft = np.real(im_fft * np.conj(im_fft))
filtered_fft = _fft_centered(filtered)
filtered_fft = np.real(filtered_fft * np.conj(filtered_fft))
outer_mask = np.ones(im.shape, dtype=bool)
outer_mask[4:-4, 4:-4] = 0
abs_filt_outer = filtered_fft[outer_mask].mean()
abs_im_outer = im_fft[outer_mask].mean()
# Compute energy near the center of the Fourier domain
inner_sl = tuple(slice(s // 2 - 4, s // 2 + 4) for s in im.shape)
abs_filt_inner = filtered_fft[inner_sl].mean()
abs_im_inner = im_fft[inner_sl].mean()
if high_pass:
assert abs_filt_outer > 0.9 * abs_im_outer
assert abs_filt_inner < 0.1 * abs_im_inner
else:
assert abs_filt_outer < 0.1 * abs_im_outer
assert abs_filt_inner > 0.9 * abs_im_inner
def get_filtered(image, cutoffs, squared_butterworth=True, order=3.0, npad=0):
"""Lowpass and highpass butterworth filtering at all specified cutoffs.
Parameters
----------
image : ndarray
The image to be filtered.
cutoffs : sequence of int
Both lowpass and highpass filtering will be performed for each cutoff
frequency in `cutoffs`.
squared_butterworth : bool, optional
Whether the traditional Butterworth filter or its square is used.
order : float, optional
The order of the Butterworth filter
Returns
-------
lowpass_filtered : list of ndarray
List of images lowpass filtered at the frequencies in `cutoffs`.
highpass_filtered : list of ndarray
List of images highpass filtered at the frequencies in `cutoffs`.
"""
lowpass_filtered = []
highpass_filtered = []
for cutoff in cutoffs:
lowpass_filtered.append(
filters.butterworth(
image,
cutoff_frequency_ratio=cutoff,
order=order,
high_pass=False,
squared_butterworth=squared_butterworth,
npad=npad,
))
highpass_filtered.append(
filters.butterworth(
image,
cutoff_frequency_ratio=cutoff,
order=order,
high_pass=True,
squared_butterworth=squared_butterworth,
npad=npad,
))
return lowpass_filtered, highpass_filtered
def test_butterworth_2D_realfft(high_pass, dtype):
"""Filtering a real-valued array is equivalent to filtering a
complex-valued array where the imaginary part is zero.
"""
im = np.random.randn(32, 64).astype(dtype)
kwargs = dict(cutoff_frequency_ratio=0.20, high_pass=high_pass)
expected_dtype = _supported_float_type(im.dtype)
filtered_real = butterworth(im, **kwargs)
assert filtered_real.dtype == expected_dtype
cplx_dtype = np.promote_types(im.dtype, np.complex64)
filtered_cplx = butterworth(im.astype(cplx_dtype), **kwargs)
assert filtered_cplx.real.dtype == expected_dtype
if expected_dtype == np.float64:
rtol = atol = 1e-13
else:
rtol = atol = 1e-5
assert_allclose(filtered_real, filtered_cplx.real, rtol=rtol, atol=atol)
def test_butterworth_correctness_bw():
small = coins()[180:190, 260:270]
filtered = butterworth(small, cutoff_frequency_ratio=0.2)
correct = np.array([
[
28.63019362, -17.69023786, 26.95346957, 20.57423019, -15.1933463,
-28.05828136, -35.25135674, -25.70376951, -43.37121955,
-16.87688457
],
[
4.62077869, 36.5726672, 28.41926375, -22.86436829, -25.32375274,
-19.94182623, -2.9666164, 6.62250413, 3.55910886, -33.15358921
],
[
25.00377084, 34.2948942, -15.13862785, -15.34354183, -12.68722526,
12.82729905, 5.21622357, 11.41087761, 16.33690526, -50.39790969
],
[
72.62331496, -14.7924709, -22.14868895, -7.47854864, 9.66784721,
24.37625693, 12.5479457, -1.38194367, 2.40079497, -26.61141413
],
[
21.85962078, -56.73932031, -14.82425429, 4.10524297, -19.16561768,
-48.19021687, 5.0258744, 28.82432166, 0.66992097, 9.8378842
],
[
-54.93417679, -5.12037233, 19.2956981, 38.56431593, 27.95408908,
-3.53103389, 23.75329532, -6.92615359, -8.50823024, 7.05743093
],
[
-30.51016624, -9.99691211, -7.1080672, 23.67643315, 1.61919726,
12.94103905, -29.08141699, -11.56937511, 22.70988847, 32.04063285
],
[
-7.51780937, -30.27899181, -2.57782655, -1.58947887, -2.13564576,
-11.34039302, 1.59165041, 14.39173421, -14.15148821, -2.21664717
],
[
14.81167298, -3.75274782, 18.41459894, 15.80334075, -19.7477109,
-3.68619619, -2.9513036, -10.17325791, 18.32438702, 18.68003971
],
[
-50.53430811, 12.14152989, 17.69341877, 9.1858496, 12.1470914,
1.45865179, 61.08961357, 29.76775029, -11.04603619, 24.18621404
],
])
assert_allclose(filtered, correct)
def test_butterworth_4D_channel(chan, dtype):
im = np.zeros((3, 4, 5, 6), dtype=dtype)
filtered = butterworth(im, channel_axis=chan)
assert filtered.shape == im.shape
def test_butterworth_4D_zeros():
im = np.zeros((3, 4, 5, 6))
filtered = butterworth(im)
assert filtered.shape == im.shape
assert_array_equal(im, filtered)
def test_butterworth_correctness_rgb():
small = astronaut()[135:145, 205:215]
filtered = butterworth(small,
cutoff_frequency_ratio=0.3,
high_pass=True,
channel_axis=-1)
correct = np.array([
[
[-5.30292781e-01, 2.17985072e+00, 2.86622486e+00],
[6.39360740e+00, 9.30643715e+00, 8.61226660e+00],
[5.47978436e+00, 1.03641402e+01, 1.02940329e+01],
[8.88312002e+00, 7.29681652e+00, 8.16021235e+00],
[4.67693778e+00, 6.33135145e-01, -2.51296407e+00],
[3.21039522e+00, -9.14893931e-01, -2.11543661e+00],
[4.61985125e-02, -6.10682453e+00, -1.72837650e+00],
[-4.59492989e+00, -7.35887525e+00, -1.03532871e+01],
[-3.67859542e+00, -4.36371621e+00, -5.67371459e+00],
[-4.38264080e+00, -6.08362280e+00, -9.20394882e+00],
],
[
[-2.46191390e+00, -2.10996960e+00, -1.41287606e+00],
[4.87042304e-01, 4.70686760e-01, 2.90817746e+00],
[9.33095004e-01, -2.11867564e-01, 3.10917925e+00],
[-2.35660768e+00, -1.35043153e+00, -2.67062162e+00],
[-1.22363424e+00, 1.11155488e-01, 1.25392954e+00],
[-1.05667680e+00, 1.58195605e-01, 6.11873557e-01],
[-4.12128910e+00, -3.55994486e+00, -8.75303054e+00],
[2.47171790e+00, 2.70762582e+00, 5.69543552e+00],
[6.97042504e-01, -2.24173305e+00, 3.26477871e-01],
[5.00195333e-01, -2.66024743e+00, -1.87479563e+00],
],
[
[-4.40136260e+00, -4.02254309e+00, -4.89246563e+00],
[-4.64563864e+00, -6.21442755e+00, -9.31399553e+00],
[-2.11532959e+00, -2.58844609e+00, -4.20629743e+00],
[-3.40862389e+00, -3.29511853e+00, -4.78220207e+00],
[-8.06768327e-01, -4.01651211e+00, -2.84783939e+00],
[1.72379068e+00, 1.00930709e+00, 2.57575911e+00],
[-2.13771052e+00, -1.75564076e+00, -2.88676819e+00],
[-2.72015191e-01, -1.61610409e-01, 2.15906305e+00],
[-3.80356741e+00, -7.30201675e-01, -3.79800352e+00],
[1.43534281e-01, -2.95121861e+00, -2.67070135e+00],
],
[[1.03480271e+00, 6.34545011e+00, 3.53610283e+00],
[7.44740677e+00, 9.97350707e+00, 1.25152734e+01],
[3.10493189e+00, 5.15553793e+00, 6.48354940e+00],
[-7.89260096e-01, 3.04573015e-01, -1.43829810e+00],
[-1.46298411e+00, 1.23095495e+00, -1.33983509e+00],
[2.82986807e+00, 2.80546223e+00, 6.39492794e+00],
[-9.15293187e-01, 2.88688464e+00, -9.69417480e-01],
[4.50217964e+00, 2.90410068e+00, 5.39107589e+00],
[-5.71608069e-01, 1.78198962e+00, -3.72062011e-01],
[7.43870617e+00, 8.78780364e+00, 9.91142612e+00]],
[
[-1.01243616e+01, -1.46725955e+01, -1.63691866e+01],
[1.06512445e+01, 7.84699418e+00, 1.05428678e+01],
[4.75343829e+00, 6.11329861e+00, 2.81633365e+00],
[7.78936796e+00, 9.63684277e+00, 1.21495065e+01],
[5.19238043e+00, 5.38165743e+00, 8.03025884e+00],
[1.67424214e+00, 2.25530135e+00, 2.44161390e-01],
[-3.18012002e-01, 1.99405335e+00, -4.33960644e-01],
[-1.21700957e+00, -2.65973900e+00, -6.31515766e-01],
[-4.87805104e+00, -5.55289609e+00, -8.50052504e+00],
[1.43493808e+01, 1.77252074e+01, 1.92810954e+01],
],
[
[-4.21712178e+01, -4.47409535e+01, -4.16375264e+01],
[1.18585381e+00, 1.33732681e+00, -1.45927283e+00],
[-4.83275742e+00, -7.14344851e+00, -7.59812923e+00],
[-7.13716513e+00, -1.10025632e+01, -1.16111397e+01],
[-5.00275373e+00, -4.20410732e+00, -4.93030043e+00],
[1.98421851e+00, 2.68393141e+00, 3.14898078e+00],
[1.97471502e+00, -2.11937555e+00, 2.04674150e+00],
[3.42916035e+00, 4.98808524e+00, 6.74436447e+00],
[-3.29035900e-01, -9.88239773e-01, 2.38909382e-02],
[2.58646940e+01, 2.40294324e+01, 2.64535438e+01],
],
[
[-2.72408341e+01, -2.51637965e+01, -2.95566971e+01],
[4.83667855e+00, 5.63749968e+00, 6.97366639e+00],
[6.18182884e+00, 2.89519333e+00, 6.15697112e+00],
[-1.03326540e+00, -4.04702873e+00, -5.50872246e+00],
[-6.92401355e+00, -8.99374166e+00, -9.43201766e+00],
[-7.24967366e+00, -1.16225741e+01, -1.26385982e+01],
[-7.79470220e+00, -9.36143025e+00, -7.13686778e+00],
[-1.22393834e+01, -1.24094588e+01, -1.70498337e+01],
[-4.65034860e+00, -3.93071471e+00, -4.65788605e+00],
[2.47461715e+01, 2.46389560e+01, 3.11843915e+01],
],
[
[1.22510987e+00, -3.30423292e+00, -1.02785428e+01],
[-2.41285934e+01, -1.60883211e+01, -1.97064909e+01],
[9.77242420e+00, 1.80847757e+01, 2.01088714e+01],
[1.21335913e+01, 1.16812821e+01, 1.20531919e+01],
[-1.64052514e+00, -4.45404672e+00, -3.83103216e+00],
[9.97519545e-01, -6.32678881e+00, -4.89843180e-01],
[1.07464325e+01, 2.62880708e+01, 1.74691665e+01],
[2.31869805e+00, 1.91935135e+00, -9.65612833e-01],
[-9.23026361e+00, -1.75138706e+01, -1.39243019e+01],
[4.60784836e+00, 5.60845273e+00, 5.28255564e+00],
],
[
[9.68795318e+00, 2.78851276e+00, 5.45620353e+00],
[-1.02076906e+01, -1.47926224e+01, -1.43257049e+01],
[-2.17025353e+00, 6.23446752e+00, 5.21771748e+00],
[1.57074742e+01, 2.17163634e+01, 2.55600809e+01],
[7.03884578e+00, 1.29273058e+01, 7.50960315e+00],
[-6.69896692e+00, -1.83433042e+01, -1.60702492e+01],
[7.44877725e+00, 1.28971365e+01, 1.10234666e+01],
[5.25663607e+00, 9.80648891e+00, 1.22955858e+01],
[-7.44903684e+00, -1.92670342e+01, -1.68232131e+01],
[1.25609220e+01, 2.09808909e+01, 2.21425299e+01],
],
[
[2.87825597e+00, 3.37945227e+00, 3.05777360e+00],
[1.18858884e+00, -5.27430874e+00, -6.96009863e+00],
[-7.55910235e+00, -2.12068126e+01, -2.06925790e+01],
[-1.47217788e+01, -1.45626702e+01, -1.56493571e+01],
[-5.60886203e+00, 8.81908697e-01, 5.47367282e+00],
[-1.00478644e+01, -8.01471176e+00, -7.45670458e+00],
[3.61521638e+00, 8.99194959e+00, 4.93826323e+00],
[7.87025438e+00, 1.34804191e+01, 1.96899695e+01],
[-5.50012037e+00, -6.40490471e+00, -1.17265188e+01],
[6.17010624e+00, 1.56199152e+01, 1.79889524e+01],
],
])
assert_allclose(filtered, correct)
def test_butterworth_2D_zeros_dtypes(dtype):
im = np.zeros((4, 4), dtype=dtype)
filtered = butterworth(im)
assert filtered.shape == im.shape
assert filtered.dtype == _supported_float_type(dtype)
assert_array_equal(im, filtered)
def test_butterworth_invalid_cutoff(cutoff):
with pytest.raises(ValueError):
butterworth(np.ones((4, 4)), cutoff_frequency_ratio=cutoff)