def test_base(self):
assert np.abs(bops.norm(self.x_np_ones) -
bops.norm(self.x_ocl_ones)) < 1e-8
assert np.abs(
np.linalg.norm(self.x_np_ones) - bops.norm(self.x_ocl_ones)) < 1e-8
assert np.sum(
np.abs(
bops.angle(self.x_np_randn) -
np.asarray(bops.angle(self.x_ocl_randn)))) < 1e-4
assert np.sum(
np.abs(
bops.abs(self.x_np_randn) -
np.asarray(bops.abs(self.x_ocl_randn)))) < 1e-4
assert np.sum(
np.abs(
bops.exp(self.x_np_randn) -
np.asarray(bops.exp(self.x_ocl_randn)))) < 1e-4
assert np.sum(
np.abs(
bops.conj(self.x_np_randn) -
np.asarray(bops.conj(self.x_ocl_randn)))) < 1e-4
assert np.sum(
np.abs(
bops.flip(self.x_np_randn) -
np.asarray(bops.flip(self.x_ocl_randn)))) < 1e-4
assert np.sum(
np.abs(
bops.transpose(self.x_np_randn) -
np.asarray(bops.transpose(self.x_ocl_randn)))) < 1e-4
assert np.sum(np.abs(self.A_np - np.asarray(self.A_ocl))) < 1e-4
assert np.sum(
np.abs(self.x_np_randn - np.asarray(self.x_ocl_randn))) < 1e-4
def test_operator_fourier_transform(self):
# Define "true" FFTs
Ft = lambda x: np.fft.fftshift(np.fft.fft2(np.fft.fftshift(x, axes=(0, 1)), axes=(0, 1), norm='ortho'), axes=(0, 1))
iFt = lambda x: np.fft.fftshift(np.fft.ifft2(np.fft.fftshift(x, axes=(0, 1)), axes=(0, 1), norm='ortho'), axes=(0, 1))
eps_fft = yp.precision(self.x, for_sum=True)
if global_backend == 'numpy':
fft_backends = ['scipy', 'numpy']
else:
fft_backends = ['af']
for fft_backend in fft_backends:
# Create Operator
F = ops.FourierTransform(image_size, dtype=global_dtype, axes=(0, 1), fft_backend=fft_backend, center=True, backend=global_backend)
# Check forward model
assert yp.sumb(yp.abs(Ft(self.x).reshape(image_size) - yp.changeBackend(F * self.x, 'numpy').reshape(image_size))) < eps_fft, '%f' % yp.sumb(yp.abs(Ft(x).reshape(image_size) - yp.changeBackend(F * vec(self.x), 'numpy').reshape(image_size)))
assert yp.sumb(yp.abs(iFt(self.x).reshape(image_size) - yp.changeBackend((F.H * self.x), 'numpy').reshape(image_size))) < eps_fft
# Check reciprocity
assert yp.sumb(yp.abs(F * F.H * self.x - self.x)) < eps_fft, "%.4e" % yp.sumb(yp.abs(F * F.H * vec(self.x) - vec(self.x)))
# Check Gradient
F.gradient_check()
def test_intensity(self):
I = ops.Intensity(image_size)
# Check forward operator
assert yp.sumb(yp.abs((yp.abs(yp.changeBackend(self.x, 'numpy')) ** 2) - yp.changeBackend(I * self.x, 'numpy'))) < eps
# Check gradient
I.gradient_check()
def psnr(signal, noise_roi=None, signal_roi=None):
""" Calculate the peak signal to noise ratio (SNR) of a signal """
# Reference: https://en.wikipedia.org/wiki/Signal-to-noise_ratio
# Calculate full power of signal
signal_power = yp.sum(yp.abs(signal)**2) if signal_roi is None else yp.sum(
yp.abs(signal[noise_roi.slice])**2)
# Calculate noise standard deviation, using ROI if provided
signal_var = yp.std(signal)**2 if noise_roi is None else yp.std(
signal[noise_roi.slice])**2
return yp.log10(signal_power / signal_var)
def _inverse(x, y):
"""Inverse using phase correlation."""
# Extract two arrays to correlate
xf_1 = array_to_register_to_f
xf_2 = x
# Compute normalized cross-correlation
phasor = (conj(xf_1) * xf_2) / abs(conj(xf_1) * xf_2)
phasor[isnan(phasor)] = 0
# Convert phasor to delta function
delta = F.H * phasor
# If axes is defined, return only one axis
if len(axes) != ndim(x) or any(
[ax != index for (ax, index) in zip(axes, range(len(axes)))]):
axes_not_used = [
index for index in range(ndim(x)) if index not in axes
]
delta = squeeze(sum(delta, axes=axes_not_used))
if debug:
import matplotlib.pyplot as plt
plt.figure(figsize=(12, 3))
plt.subplot(131)
plt.imshow(abs(F.H * xf_1))
plt.subplot(132)
plt.imshow(abs(F.H * xf_2))
plt.subplot(133)
if ndim(delta) > 1:
plt.imshow(abs(delta))
else:
plt.plot(abs(delta))
# Calculate maximum and return
if not center:
y[:] = reshape(asarray(argmax(delta)), shape(y))
else:
y[:] = reshape(
asarray(argmax(delta)) - asarray(delta.shape) / 2, shape(y))
# Deal with negative values
sizes = reshape(asarray([_shape[ax] for ax in axes]), shape(y))
mask = y[:] > sizes / 2
y[:] -= mask * sizes
if debug:
plt.title(
str(np.real(np.asarray(argmax(delta))).tolist()) + ' ' +
str(np.abs(np.asarray(y).ravel())))
def test_operator_matrix_multiply(self):
matrix_size = (10,10)
m = yp.rand(matrix_size, global_dtype, global_backend)
xm = yp.rand(matrix_size[1], global_dtype, global_backend)
M = ops.MatrixMultiply(m)
# Check Forward operator
assert yp.sumb(yp.abs(yp.vec(yp.changeBackend(M * xm, 'numpy')) - yp.vec(yp.changeBackend(m, 'numpy').dot(yp.changeBackend(xm, 'numpy'))))) < eps, "%f" % yp.sumb(yp.abs(yp.changeBackend(M * xm, 'numpy') - yp.changeBackend(m, 'numpy').dot(yp.changeBackend(xm, 'numpy'))[:, np.newaxis]))
# Check Adjoint
assert yp.sumb(yp.abs(yp.vec(yp.changeBackend(M.H * xm, 'numpy')) - yp.vec(np.conj(yp.changeBackend(m, 'numpy').T).dot(yp.changeBackend(xm, 'numpy'))))) < eps, "%f" % yp.sumb(yp.abs(yp.changeBackend(M.H * xm, 'numpy') - np.conj(yp.changeBackend(m, 'numpy').T).dot(yp.changeBackend(xm, 'numpy'))[:, np.newaxis]))
# Check gradient
M.gradient_check()
def cnr(signal, noise_roi=None, signal_roi=None):
""" Calculate the imaging contrast to noise ratio (CNR) of an image """
# Reference: https://en.wikipedia.org/wiki/Contrast-to-noise_ratio
# Calculate signal mean, using ROI if provided
signal_contrast = yp.abs(yp.max(signal) -
yp.min(signal)) if signal_roi is None else yp.abs(
yp.max(signal[noise_roi.slice]) -
yp.min(signal[noise_roi.slice]))
# Calculate noise standard deviation, using ROI if provided
signal_std = yp.std(signal) if noise_roi is None else np.std(
signal[noise_roi.slice])
return (signal_contrast / signal_std)
def otf(shape,
camera_pixel_size,
illumination_wavelength,
objective_numerical_aperture,
center=True,
dtype=None,
backend=None):
# Generate pupil
p = pupil(shape,
camera_pixel_size,
illumination_wavelength,
objective_numerical_aperture,
center,
dtype=dtype,
backend=backend)
# Generate OTF
otf = iFt(Ft(p) * yp.conj(Ft(p)))
# Normalize
otf /= yp.max(yp.abs(otf))
# Center
if center:
return otf
else:
return yp.fft.ifftshift(otf)
def show_xc(x, figsize=(11, 3)):
xf_1 = F * _R.arguments[0]
xf_2 = F * x
# Compute normalized cross-correlation
phasor = (conj(xf_1) * xf_2) / abs(conj(xf_1) * xf_2)
import matplotlib.pyplot as plt
import llops as yp
plt.figure(figsize=figsize)
plt.subplot(121)
plt.imshow(yp.angle(phasor))
plt.title('Phase of Frequency domain')
plt.subplot(122)
plt.imshow(yp.abs(yp.iFt(phasor)))
plt.title('Amplitude of Object domain')
def test_operator_flip(self):
''' Flip Operator '''
flip_axis = 0
L = ops.Flip(image_size, axis=flip_axis)
# Check forward operator
assert yp.sumb(yp.abs(L * self.x - yp.flip(self.x, flip_axis))) < eps, "%f" % yp.sumb(yp.abs(L * self.x - vec(yp.flip(self.x, flip_axis))))
# Check gradient
L.gradient_check()
def test_operator_crop_non_centered(self):
''' Non-centered Crop Operator '''
# Generate Crop Operator
crop_size = (image_size[0] // 2, image_size[1] // 2)
crop_start = (6, 6)
CR = ops.Crop(image_size, crop_size, pad_value=0, dtype=global_dtype, backend=global_backend, crop_start=crop_start)
# Check forward operator
y_1 = yp.changeBackend(CR * self.x, 'numpy')
y_2 = yp.changeBackend(yp.crop(self.x, crop_size, crop_start), 'numpy')
assert yp.sumb(yp.abs(y_1 - y_2)) < eps
# Check Adjoint Operator
pad_size = [int((image_size[i] - crop_size[i]) / 2) for i in range(len(image_size))]
y_3 = yp.pad(yp.crop(self.x, crop_size, crop_start), image_size, crop_start, pad_value=0)
y_4 = yp.reshape(CR.H * CR * self.x, image_size)
assert yp.sumb(yp.abs(y_3 - y_4)) < eps
# Check gradient
CR.gradient_check()
def test_operator_crop(self):
''' Crop Operator '''
# Generate Crop Operator
crop_size = (image_size[0] // 2, image_size[1] // 2)
CR = ops.Crop(image_size, crop_size, pad_value=0, dtype=global_dtype, backend=global_backend)
# Check forward operator
crop_start = tuple(np.asarray(image_size) // 2 - np.asarray(crop_size) // 2)
y_1 = yp.changeBackend(CR * self.x, 'numpy')
y_2 = yp.changeBackend(yp.crop(self.x, crop_size, crop_start), 'numpy')
assert yp.sumb(yp.abs(y_1 - y_2)) < eps
# Check Adjoint Operator
pad_size = [int((image_size[i] - crop_size[i]) / 2) for i in range(len(image_size))]
y_3 = yp.pad(yp.crop(self.x, crop_size, crop_start), image_size, crop_start, pad_value=0)
y_4 = CR.H * CR * self.x
assert yp.sumb(yp.abs(y_3 - y_4)) < eps
# Check gradient
CR.gradient_check()
def propKernelFresnelFourier(shape,
pixel_size,
wavelength,
prop_distance,
angle_deg=None,
RI=1.0):
'''
Creates a fresnel propagation kernel in the Fourier Domain
:param shape: :class:`list, tuple, np.array`
Shape of sensor plane (pixels)
:param pixel_size: :class:`float`
Pixel size of sensor in spatial units
:param wavelength: :class:`float`
Detection wavelength in spatial units
:param prop_distance: :class:`float`
Propagation distance in spatial units
:param angle_deg: :class:`tuple, list, np.array`
Propagation angle, degrees
:param RI: :class:`float`
Refractive index of medium
'''
assert len(
shape) == 2, "Propigation kernel size should be two dimensional!"
# Determine propagation angle and spatial frequency
angle = len(shape) * [0.0] if angle_deg is None else np.deg2rad(angle_deg)
fy_illu, fx_illu = [RI * np.sin(a) / wavelength for a in angle]
# Generate coordinate system
fylin = _genLin(shape[0], 1 / pixel_size / shape[0])
fxlin = _genLin(shape[1], 1 / pixel_size / shape[1])
# Calculate wavenunmber
k = (2.0 * np.pi / wavelength) * RI
prop_kernel = yp.exp(1j * k * yp.abs(prop_distance)) * yp.exp(
-1j * np.pi * wavelength * yp.abs(prop_distance) *
((fxlin[np.newaxis, :] - fx_illu)**2 +
(fylin[:, np.newaxis] - fy_illu)**2))
return prop_kernel if prop_distance >= 0 else prop_kernel.conj()
def test_operator_wavelet(self):
''' Wavelet Transform Operator '''
import pywt
wavelet_list = ['db1', 'haar', 'rbio1.1', 'bior1.1', 'bior4.4', 'sym12']
for wavelet_test in wavelet_list:
# Wavelet Transform
W = ops.WaveletTransform(image_size, wavelet_type=wavelet_test, use_cycle_spinning=False)
# Check forward operation
coeffs = pywt.wavedecn(self.x, wavelet=wavelet_test)
x_wavelet, coeff_slices = pywt.coeffs_to_array(coeffs)
assert yp.sumb(yp.abs(yp.changeBackend(W * self.x, 'numpy') - x_wavelet)) < eps, "Difference %.6e"
# Check inverse operation
coeffs_from_arr = pywt.array_to_coeffs(x_wavelet, coeff_slices)
cam_recon = pywt.waverecn(coeffs_from_arr, wavelet=wavelet_test)
assert yp.sumb(yp.abs(W.H * W * self.x - self.x)) < 1e-2
# Ensure that the wavelet transform isn't just identity (weird bug)
if W.shape[1] is yp.size(self.x):
assert yp.sumb(yp.abs(W * yp.vec(self.x) - yp.vec(self.x))) > 1e-2, "%s" % wavelet_test
def _forward(self, x, y):
fill(self._forward_y, 0)
# Take finite differences
for dim in range(len(self.shape)):
self._forward_y += abs(roll(x, 1, axis=dim) - x)
# Normalize
self._forward_y[:] = sqrt(self._forward_y)
# Return sum
y[:] = sum(self._forward_y)
def propKernelRayleighSpatial(shape, pixel_size, wavelength, prop_distance):
# Generate coordinate system
ylin, xlin = yp.grid(shape, pixel_size)
kb = 2 * np.pi / wavelength
R2 = prop_distance**2 + xlin[np.newaxis, :]**2 + ylin[:, np.newaxis]**2
R = yp.sqrt(R2)
prop_kernel = yp.abs(prop_distance) * kb / (2j * np.pi) * yp.exp(
1j * kb * R) * (1 + 1j / (kb * R)) / R2
return prop_kernel if prop_distance >= 0 else prop_kernel.conj()
def test_operator_shift(self):
''' Shift Operator '''
# Normal shift
shift = (0, 10) # should be y, x
T = ops.Shift(image_size, shift)
def shift_func(x, shift):
x = yp.changeBackend(self.x, 'numpy')
for ax, sh in enumerate(shift):
x = np.roll(self.x, int(sh), axis=ax)
return(x)
# Check Forward Operator
y_1 = yp.changeBackend(T * self.x, 'numpy')
y_2 = shift_func(yp.changeBackend(self.x, 'numpy'), shift)
assert yp.sumb(yp.abs(y_1 - y_2)) < eps
# Check Adjoint Operator
assert yp.sumb(yp.abs(T.H * T * self.x - self.x)) < eps
# Check gradient
T.gradient_check()
def calcDnfFromKernel(x):
if len(x) == 0:
return 0
else:
# Normalize
x = x / yp.scalar(yp.sum(x))
# Take fourier transform intensity
x_fft = yp.Ft(x)
sigma_x = yp.abs(x_fft) ** 2
# Calculate DNF
return np.sqrt(1 / len(x) * np.sum(1 / sigma_x))
def test_operator_stacking_linear(self):
# Create list of operators
op_list_linear = [
ops.FourierTransform(image_size, dtype=global_dtype, backend=global_backend),
ops.Identity(image_size, dtype=global_dtype, backend=global_backend),
ops.Exponential(image_size, dtype=global_dtype, backend=global_backend)
]
# Horizontally stacked operators
H_l = ops.Hstack(op_list_linear)
# Vertically stack x for forward operator
x_np = yp.changeBackend(self.x, 'numpy')
x3 = yp.changeBackend(np.vstack((x_np, x_np, x_np)), global_backend)
# Check forward operation
y2 = yp.zeros(op_list_linear[0].N, op_list_linear[0].dtype, op_list_linear[0].backend)
for op in op_list_linear:
y2 = y2 + op * self.x
assert yp.sumb(yp.abs(yp.changeBackend(H_l(x3) - y2, 'numpy'))) < eps, "%.4e" % yp.sumb(yp.abs(H_l(x3) - y2))
# Check gradient
H_l.gradient_check()
# Create vertically stacked operator
V_l = ops.Vstack(op_list_linear)
# Check forward operator
y3 = np.empty((0,image_size[1]), dtype=yp.getNativeDatatype(global_dtype, 'numpy'))
for index, op in enumerate(op_list_linear):
y3 = np.append(y3, (op * self.x), axis=0)
y3 = yp.changeBackend(y3, global_backend)
assert yp.sumb(yp.abs(V_l * self.x - y3)) < eps, "%.4e" % yp.sumb(yp.abs(V_l * vec(x) - y3))
# Check gradient
V_l.gradient_check()
def test_operator_sum(self):
''' Element-wise Sum Operator '''
axis_to_sum = (0,1)
Σ = ops.Sum(image_size, axes=axis_to_sum)
# Check forward operator
y_1 = yp.changeBackend(Σ * self.x, 'numpy')
y_2 = yp.sumb(yp.changeBackend(self.x, 'numpy'), axes=axis_to_sum)
assert yp.abs(yp.sumb(y_1 - y_2)) < eps
# Check adjoint operator
y_3 = yp.changeBackend(Σ.H * Σ * self.x, 'numpy')
reps = [1, ] * len(image_size)
axes = list(range(len(image_size))) if axis_to_sum is 'all' else axis_to_sum
scale = 1
for axis in axes:
reps[axis] = image_size[axis]
scale *= 1 / image_size[axis]
y_4 = yp.tile(y_2, reps) * scale
assert yp.sumb(yp.abs(y_3 - y_4)) < eps
# Check gradient
Σ.gradient_check(eps=1)
def _inverse(self, x, y):
# Get current kernel
kernel_f = F * FFTS * P * kernel
# Invert and create operator
kernel_f_inv = conj(kernel_f) / (abs(kernel_f)**2 +
self.inverse_regularizer)
K_inverse = Diagonalize(kernel_f_inv,
backend=backend,
dtype=dtype,
label=label)
# Set output
y[:] = P.H * F.H * K_inverse * F * P * x
def propKernelRayleightFourier(shape, pixel_size, wavelength, prop_distance):
# Generate coordinate system
fylin, fxlin = yp.grid(shape, 1 / pixel_size / np.asarray(shape))
# Generate Squared Coordinate System
fy2 = (fylin**2)[:, np.newaxis]
fx2 = (fxlin**2)[np.newaxis, :]
fz2 = 1 / wavelength**2 - fy2 - fx2
fz = np.lib.scimath.sqrt(fz2)
prop_kernel = yp.exp(2j * np.pi * fz * yp.abs(prop_distance))
return prop_kernel if prop_distance >= 0 else np.conj(prop_kernel)
def dnfFromConvolutionKernel(h):
"""Calculate the deconvolution noise factor (DNF) of N-dimensional
convolution operator, given it's kernel."""
if len(h) == 0:
return 0
else:
# Normalize
h = copy.deepcopy(h) / yp.scalar(yp.sum(h))
# Take fourier transform intensity
h_fft = yp.Ft(h)
sigma_h = yp.abs(h_fft)**2
# Calculate DNF
return np.sqrt(1 / len(h) * np.sum(1 / sigma_h))
def test_operator_exponential(self):
L2 = ops.L2Norm(image_size)
F = ops.FourierTransform(image_size)
EXP = ops.Exponential(image_size)
# Forward model
assert yp.sumb(yp.abs(yp.changeBackend(EXP * self.x, 'numpy') - np.exp(yp.changeBackend(self.x, 'numpy')))) < eps
# Check gradient
EXP.gradient_check()
# Generate composite operator
D = ops.Diagonalize(self.h)
L2 = ops.L2Norm(image_size)
EXP_COMP = L2 * F * EXP
EXP_COMP.gradient_check()
EXP_COMP_2 = L2 * F * EXP * D
EXP_COMP_2.gradient_check()
def add(signal, type='gaussian', **kwargs):
""" Add noise to a measurement"""
if type == 'gaussian':
snr = kwargs.get('snr', 1.0)
signal_mean = yp.abs(yp.mean(signal))
noise_gaussian = np.random.normal(0, signal_mean / snr,
yp.shape(signal))
return signal + noise_gaussian
elif type == 'poisson':
noise_poisson = np.random.poisson(np.real(signal))
return signal + noise_poisson
elif type == 'saltpepper' or type == 'saltandpepper':
salt_pepper_ratio = kwargs.get('ratio', 0.5)
salt_pepper_saturation = kwargs.get('saturation', 0.004)
output = yp.changeBackend(signal, 'numpy')
# Salt mode
num_salt = np.ceil(salt_pepper_saturation * signal.size *
salt_pepper_ratio)
coords = [
np.random.randint(0, i - 1, int(num_salt)) for i in signal.shape
]
output[tuple(coords)] = 1
# Pepper mode
num_pepper = np.ceil(salt_pepper_saturation * signal.size *
(1. - salt_pepper_ratio))
coords = [
np.random.randint(0, i - 1, int(num_pepper)) for i in signal.shape
]
output[tuple(coords)] = 0
return yp.cast_like(output, signal)
elif type == 'speckle':
noise_speckle = yp.randn(signal.shape)
return signal + signal * noise_speckle
def test_operator_phase_ramp(self):
eps_phase_ramp = 1e-4
shift = yp.changeBackend(np.asarray((-5,3)).astype(yp.getNativeDatatype(global_dtype, 'numpy')), global_backend)
# Generate phase ramp
R = ops.PhaseRamp(image_size)
r = R * shift
F = ops.FourierTransform(image_size, dtype=global_dtype, normalize=False, backend=global_backend)
D_R = ops.Diagonalize(r, dtype=global_dtype)
S_R = F.H * D_R * F
# Pixel-wise shift operator
S = ops.Shift(image_size, shift)
# Check that phase ramp is shifting by correct amount
assert yp.sumb(yp.abs(yp.changeBackend(S_R * self.x, 'numpy') - yp.changeBackend(S * self.x, 'numpy'))) < 1e-3
# Check gradient of phase ramp convolution
S_R.gradient_check()
# Check gradient of phase ramp
R.gradient_check(eps=1e-1)
def blur_vectors(self, dtype=None, backend=None, debug=False,
use_phase_ramp=False, corrections={}):
"""
This function generates the object size, image size, and blur kernels from
a libwallerlab dataset object.
Args:
dataset: An io.Dataset object
dtype [np.float32]: Which datatype to use for kernel generation (All numpy datatypes supported)
Returns:
object_size: The object size this dataset can recover
image_size: The computed image size of the dataset
blur_kernel_list: A dictionary of blur kernels lists, one key per color channel.
"""
# Assign dataset
dataset = self
# Get corrections from metadata
if len(corrections) is 0 and 'blur_vector' in self.metadata.calibration:
corrections = dataset.metadata.calibration['blur_vector']
# Get datatype and backends
dtype = dtype if dtype is not None else yp.config.default_dtype
backend = backend if backend is not None else yp.config.default_backend
# Calculate effective pixel size if necessaey
if dataset.metadata.system.eff_pixel_size_um is None:
dataset.metadata.system.eff_pixel_size_um = dataset.metadata.camera.pixel_size_um / \
(dataset.metadata.objective.mag * dataset.metadata.system.mag)
# Recover and store position and illumination list
blur_vector_roi_list = []
position_list, illumination_list = [], []
frame_segment_map = []
for frame_index in range(dataset.shape[0]):
frame_state = dataset.frame_state_list[frame_index]
# Store which segment this measurement uses
frame_segment_map.append(frame_state['position']['common']['linear_segment_index'])
# Extract list of illumination values for each time point
if 'illumination' in frame_state:
illumination_list_frame = []
if type(frame_state['illumination']) is str:
illum_state_list = self._frame_state_list[0]['illumination']['states']
else:
illum_state_list = frame_state['illumination']['states']
for time_point in illum_state_list:
illumination_list_time_point = []
for illumination in time_point:
illumination_list_time_point.append(
{'index': illumination['index'], 'value': illumination['value']})
illumination_list_frame.append(illumination_list_time_point)
else:
raise ValueError('Frame %d does not contain illumination information' % frame_index)
# Extract list of positions for each time point
if 'position' in frame_state:
position_list_frame = []
for time_point in frame_state['position']['states']:
position_list_time_point = []
for position in time_point:
if 'units' in position['value']:
if position['value']['units'] == 'mm':
ps_um = dataset.metadata.system.eff_pixel_size_um
position_list_time_point.append(
[1000 * position['value']['y'] / ps_um, 1000 * position['value']['x'] / ps_um])
elif position['value']['units'] == 'um':
position_list_time_point.append(
[position['value']['y'] / ps_um, position['value']['x'] / ps_um])
elif position['value']['units'] == 'pixels':
position_list_time_point.append([position['value']['y'], position['value']['x']])
else:
raise ValueError('Invalid units %s for position in frame %d' %
(position['value']['units'], frame_index))
else:
# print('WARNING: Could not find posiiton units in metadata, assuming mm')
ps_um = dataset.metadata.system.eff_pixel_size_um
position_list_time_point.append(
[1000 * position['value']['y'] / ps_um, 1000 * position['value']['x'] / ps_um])
position_list_frame.append(position_list_time_point[0]) # Assuming single time point for now.
# Define positions and position indicies used
positions_used, position_indicies_used = [], []
for index, pos in enumerate(position_list_frame):
for color in illumination_list_frame[index][0]['value']:
if any([illumination_list_frame[index][0]['value'][color] > 0 for color in illumination_list_frame[index][0]['value']]):
position_indicies_used.append(index)
positions_used.append(pos)
# Generate ROI for this blur vector
from htdeblur.blurkernel import getPositionListBoundingBox
blur_vector_roi = getPositionListBoundingBox(positions_used)
# Append to list
blur_vector_roi_list.append(blur_vector_roi)
# Crop illumination list to values within the support used
illumination_list.append([illumination_list_frame[index] for index in range(min(position_indicies_used), max(position_indicies_used) + 1)])
# Store corresponding positions
position_list.append(positions_used)
# Apply kernel scaling or compression if necessary
if 'scale' in corrections:
# We need to use phase-ramp based kernel generation if we modify the positions
use_phase_ramp = True
# Modify position list
for index in range(len(position_list)):
_positions = np.asarray(position_list[index])
for scale_correction in corrections['scale']:
factor, axis = corrections['scale']['factor'], corrections['scale']['axis']
_positions[:, axis] = ((_positions[:, axis] - yp.min(_positions[:, axis])) * factor + yp.min(_positions[:, axis]))
position_list[index] = _positions.tolist()
# Synthesize blur vectors
blur_vector_list = []
for frame_index in range(dataset.shape[0]):
# Generate blur vectors
if use_phase_ramp:
from llops.operators import PhaseRamp
kernel_shape = [yp.fft.next_fast_len(max(sh, 1)) for sh in blur_vector_roi_list[frame_index].shape]
offset = yp.cast([sh // 2 + st for (sh, st) in zip(kernel_shape, blur_vector_roi_list[frame_index].start)], 'complex32', dataset.backend)
# Create phase ramp and calculate offset
R = PhaseRamp(kernel_shape, dtype='complex32', backend=dataset.backend)
# Generate blur vector
blur_vector = yp.zeros(R.M, dtype='complex32', backend=dataset.backend)
for pos, illum in zip(position_list[frame_index], illumination_list[frame_index]):
pos = yp.cast(pos, dtype=dataset.dtype, backend=dataset.backend)
blur_vector += (R * (yp.cast(pos - offset, 'complex32')))
# Take inverse Fourier Transform
blur_vector = yp.abs(yp.cast(yp.iFt(blur_vector)), 0.0)
if position_list[frame_index][0][-1] > position_list[frame_index][0][0]:
blur_vector = yp.flip(blur_vector)
else:
blur_vector = yp.asarray([illum[0]['value']['w'] for illum in illumination_list[frame_index]],
dtype=dtype, backend=backend)
# Normalize illuminaiton vectors
blur_vector /= yp.scalar(yp.sum(blur_vector))
# Append to list
blur_vector_list.append(blur_vector)
# Return
return blur_vector_list, blur_vector_roi_list
def registerImage(image0,
image1,
method='xc',
axis=None,
preprocess_methods=['reflect'],
debug=False,
**kwargs):
# Perform preprocessing
if len(preprocess_methods) > 0:
image0, image1 = _preprocessForRegistration(image0, image1,
preprocess_methods,
**kwargs)
# Parameter on whether we can trust our registration
trust_ratio = 1.0
if method in ['xc' or 'cross_correlation']:
# Get energy ratio threshold
trust_threshold = kwargs.get('energy_ratio_threshold', 1.5)
# Pad arrays for optimal speed
pad_size = tuple(
[sp.fftpack.next_fast_len(s) for s in yp.shape(image0)])
# Perform padding
if pad_size is not yp.shape(image0):
image0 = yp.pad(image0, pad_size, pad_value='edge', center=True)
image1 = yp.pad(image1, pad_size, pad_value='edge', center=True)
# Take F.T. of measurements
src_freq, target_freq = yp.Ft(image0, axes=axis), yp.Ft(image1,
axes=axis)
# Whole-pixel shift - Compute cross-correlation by an IFFT
image_product = src_freq * yp.conj(target_freq)
# image_product /= abs(src_freq * yp.conj(target_freq))
cross_correlation = yp.iFt(image_product, center=False, axes=axis)
# Take sum along axis if we're doing 1D
if axis is not None:
axis_to_sum = list(range(yp.ndim(image1)))
del axis_to_sum[axis]
cross_correlation = yp.sum(cross_correlation, axis=axis_to_sum)
# Locate maximum
shape = yp.shape(src_freq)
maxima = yp.argmax(yp.abs(cross_correlation))
midpoints = np.array([np.fix(axis_size / 2) for axis_size in shape])
shifts = np.array(maxima, dtype=np.float64)
shifts[shifts > midpoints] -= np.array(shape)[shifts > midpoints]
# If its only one row or column the shift along that dimension has no
# effect. We set to zero.
for dim in range(yp.ndim(src_freq)):
if shape[dim] == 1:
shifts[dim] = 0
# If energy ratio is too small, set all shifts to zero
trust_metric = yp.scalar(
yp.max(yp.abs(cross_correlation)**2) /
yp.mean(yp.abs(cross_correlation)**2))
# Determine if this registraition can be trusted
trust_ratio = trust_metric / trust_threshold
elif method == 'orb':
# Get user-defined mean_residual_threshold if given
trust_threshold = kwargs.get('mean_residual_threshold', 40.0)
# Get user-defined mean_residual_threshold if given
orb_feature_threshold = kwargs.get('orb_feature_threshold', 25)
match_count = 0
fast_threshold = 0.05
while match_count < orb_feature_threshold:
descriptor_extractor = ORB(n_keypoints=500,
fast_n=9,
harris_k=0.1,
fast_threshold=fast_threshold)
# Extract keypoints from first frame
descriptor_extractor.detect_and_extract(
np.asarray(image0).astype(np.double))
keypoints0 = descriptor_extractor.keypoints
descriptors0 = descriptor_extractor.descriptors
# Extract keypoints from second frame
descriptor_extractor.detect_and_extract(
np.asarray(image1).astype(np.double))
keypoints1 = descriptor_extractor.keypoints
descriptors1 = descriptor_extractor.descriptors
# Set match count
match_count = min(len(keypoints0), len(keypoints1))
fast_threshold -= 0.01
if fast_threshold == 0:
raise RuntimeError(
'Could not find any keypoints (even after shrinking fast threshold).'
)
# Match descriptors
matches = match_descriptors(descriptors0,
descriptors1,
cross_check=True)
# Filter descriptors to axes (if provided)
if axis is not None:
matches_filtered = []
for (index_0, index_1) in matches:
point_0 = keypoints0[index_0, :]
point_1 = keypoints1[index_1, :]
unit_vec = point_0 - point_1
unit_vec /= np.linalg.norm(unit_vec)
if yp.abs(unit_vec[axis]) > 0.99:
matches_filtered.append((index_0, index_1))
matches_filtered = np.asarray(matches_filtered)
else:
matches_filtered = matches
# Robustly estimate affine transform model with RANSAC
model_robust, inliers = ransac((keypoints0[matches_filtered[:, 0]],
keypoints1[matches_filtered[:, 1]]),
EuclideanTransform,
min_samples=3,
residual_threshold=2,
max_trials=100)
# Note that model_robust has a translation property, but this doesn't
# seem to be as numerically stable as simply averaging the difference
# between the coordinates along the desired axis.
# Apply match filter
matches_filtered = matches_filtered[inliers, :]
# Process keypoints
if yp.shape(matches_filtered)[0] > 0:
# Compute shifts
difference = keypoints0[matches_filtered[:, 0]] - keypoints1[
matches_filtered[:, 1]]
shifts = (yp.sum(difference, axis=0) / yp.shape(difference)[0])
shifts = np.round(shifts[0])
# Filter to axis mask
if axis is not None:
_shifts = [0, 0]
_shifts[axis] = shifts[axis]
shifts = _shifts
# Calculate residuals
residuals = yp.sqrt(
yp.sum(
yp.abs(keypoints0[matches_filtered[:, 0]] +
np.asarray(shifts) -
keypoints1[matches_filtered[:, 1]])**2))
# Define a trust metric
trust_metric = residuals / yp.shape(
keypoints0[matches_filtered[:, 0]])[0]
# Determine if this registration can be trusted
trust_ratio = 1 / (trust_metric / trust_threshold)
print('===')
print(trust_ratio)
print(trust_threshold)
print(trust_metric)
print(shifts)
else:
trust_metric = 1e10
trust_ratio = 0.0
shifts = np.asarray([0, 0])
elif method == 'optimize':
# Create Operators
L2 = ops.L2Norm(yp.shape(image0), dtype='complex64')
R = ops.PhaseRamp(yp.shape(image0), dtype='complex64')
REAL = ops.RealFilter((2, 1), dtype='complex64')
# Take Fourier Transforms of images
image0_f, image1_f = yp.astype(yp.Ft(image0), 'complex64'), yp.astype(
yp.Ft(image1), 'complex64')
# Diagonalize one of the images
D = ops.Diagonalize(image0_f)
# Form objective
objective = L2 * (D * R * REAL - image1_f)
# Solve objective
solver = ops.solvers.GradientDescent(objective)
shifts = solver.solve(iteration_count=1000, step_size=1e-8)
# Convert to numpy array, take real part, and round.
shifts = yp.round(yp.real(yp.asbackend(shifts, 'numpy')))
# Flip shift axes (x,y to y, x)
shifts = np.fliplr(shifts)
# TODO: Trust metric and trust_threshold
trust_threshold = 1
trust_ratio = 1.0
else:
raise ValueError('Invalid Registration Method %s' % method)
# Mark whether or not this measurement is of good quality
if not trust_ratio > 1:
if debug:
print('Ignoring shift with trust metric %g (threshold is %g)' %
(trust_metric, trust_threshold))
shifts = yp.zeros_like(np.asarray(shifts)).tolist()
# Show debugging figures if requested
if debug:
import matplotlib.pyplot as plt
plt.figure(figsize=(6, 5))
plt.subplot(131)
plt.imshow(yp.abs(image0))
plt.axis('off')
plt.subplot(132)
plt.imshow(yp.abs(image1))
plt.title('Trust ratio: %g' % (trust_ratio))
plt.axis('off')
plt.subplot(133)
if method in ['xc' or 'cross_correlation']:
if axis is not None:
plt.plot(yp.abs(yp.squeeze(cross_correlation)))
else:
plt.imshow(yp.abs(yp.fftshift(cross_correlation)))
else:
plot_matches(plt.gca(), yp.real(image0), yp.real(image1),
keypoints0, keypoints1, matches_filtered)
plt.title(str(shifts))
plt.axis('off')
# Return
return shifts, trust_ratio
def register_translation(src_image,
target_image,
upsample_factor=1,
energy_ratio_threshold=2,
space="real"):
"""
Efficient subpixel image translation registration by cross-correlation.
This code gives the same precision as the FFT upsampled cross-correlation
in a fraction of the computation time and with reduced memory requirements.
It obtains an initial estimate of the cross-correlation peak by an FFT and
then refines the shift estimation by upsampling the DFT only in a small
neighborhood of that estimate by means of a matrix-multiply DFT.
Parameters
----------
src_image : ndarray
Reference image.
target_image : ndarray
Image to register. Must be same dimensionality as ``src_image``.
upsample_factor : int, optional
Upsampling factor. Images will be registered to within
``1 / upsample_factor`` of a pixel. For example
``upsample_factor == 20`` means the images will be registered
within 1/20th of a pixel. Default is 1 (no upsampling)
space : string, one of "real" or "fourier", optional
Defines how the algorithm interprets input data. "real" means data
will be FFT'd to compute the correlation, while "fourier" data will
bypass FFT of input data. Case insensitive.
return_error : bool, optional
Returns error and phase difference if on,
otherwise only shifts are returned
Returns
-------
shifts : ndarray
Shift vector (in pixels) required to register ``target_image`` with
``src_image``. Axis ordering is consistent with numpy (e.g. Z, Y, X)
error : float
Translation invariant normalized RMS error between ``src_image`` and
``target_image``.
phasediff : float
Global phase difference between the two images (should be
zero if images are non-negative).
References
----------
.. [1] Manuel Guizar-Sicairos, Samuel T. Thurman, and James R. Fienup,
"Efficient subpixel image registration algorithms,"
Optics Letters 33, 156-158 (2008). :DOI:`10.1364/OL.33.000156`
.. [2] James R. Fienup, "Invariant error metrics for image reconstruction"
Optics Letters 36, 8352-8357 (1997). :DOI:`10.1364/AO.36.008352`
"""
# images must be the same shape
if yp.shape(src_image) != yp.shape(target_image):
raise ValueError("Error: images must be same size for "
"register_translation")
# only 2D data makes sense right now
if yp.ndim(src_image) > 3 and upsample_factor > 1:
raise NotImplementedError("Error: register_translation only supports "
"subpixel registration for 2D and 3D images")
# assume complex data is already in Fourier space
if space.lower() == 'fourier':
src_freq = src_image
target_freq = target_image
# real data needs to be fft'd.
elif space.lower() == 'real':
src_freq = yp.Ft(src_image)
target_freq = yp.Ft(target_image)
else:
raise ValueError("Error: register_translation only knows the \"real\" "
"and \"fourier\" values for the ``space`` argument.")
# Whole-pixel shift - Compute cross-correlation by an IFFT
shape = yp.shape(src_freq)
image_product = src_freq * yp.conj(target_freq)
cross_correlation = yp.iFt(image_product, center=False)
# Locate maximum
maxima = yp.argmax(yp.abs(cross_correlation))
midpoints = np.array([np.fix(axis_size / 2) for axis_size in shape])
shifts = np.array(maxima, dtype=np.float64)
shifts[shifts > midpoints] -= np.array(shape)[shifts > midpoints]
# if upsample_factor > 1:
# # Initial shift estimate in upsampled grid
# shifts = np.round(shifts * upsample_factor) / upsample_factor
# upsampled_region_size = np.ceil(upsample_factor * 1.5)
# # Center of output array at dftshift + 1
# dftshift = np.fix(upsampled_region_size / 2.0)
# upsample_factor = np.array(upsample_factor, dtype=np.float64)
# normalization = (src_freq.size * upsample_factor ** 2)
# # Matrix multiply DFT around the current shift estimate
# sample_region_offset = dftshift - shifts*upsample_factor
# cross_correlation = _upsampled_dft(image_product.conj(),
# upsampled_region_size,
# upsample_factor,
# sample_region_offset).conj()
# cross_correlation /= normalization
# # Locate maximum and map back to original pixel grid
# maxima = np.array(np.unravel_index(
# np.argmax(np.abs(cross_correlation)),
# cross_correlation.shape),
# dtype=np.float64)
# maxima -= dftshift
#
# shifts = shifts + maxima / upsample_factor
# If its only one row or column the shift along that dimension has no
# effect. We set to zero.
for dim in range(yp.ndim(src_freq)):
if shape[dim] == 1:
shifts[dim] = 0
# If energy ratio is too small, set all shifts to zero
energy_ratio = yp.max(yp.abs(cross_correlation)**2) / yp.sum(
yp.abs(cross_correlation)**2) * yp.prod(yp.shape(cross_correlation))
if energy_ratio < energy_ratio_threshold:
print('Ignoring shift with energy ratio %g (threshold is %g)' %
(energy_ratio, energy_ratio_threshold))
shifts = yp.zeros_like(shifts)
return shifts
