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 affineHomographyBlocks(coordinate_list):
"""Generate affine homography blocks which can be used to solve for homography coordinates."""
# Store dtype and backend
dtype = yp.getDatatype(coordinate_list)
backend = yp.getBackend(coordinate_list)
# Convert coordinates to numpy array
coordinate_list = yp.asarray(yp.real(coordinate_list),
dtype='float32',
backend='numpy')
# Ensure coordinate_list is a list of lists
if yp.ndim(coordinate_list) == 1:
coordinate_list = np.asarray([coordinate_list])
# Determine the number of elements in a coordinate
axis_count = yp.shape(coordinate_list)[1]
# Loop over positions and concatenate to array
coordinate_blocks = []
for coordinate in coordinate_list:
block = np.append(coordinate, 1)
coordinate_blocks.append(np.kron(np.eye(len(coordinate)), block))
# Convert to initial datatype and backend
coordinate_blocks = yp.asarray(np.concatenate(coordinate_blocks), dtype,
backend)
return coordinate_blocks
def _loadImage(image_label, shape, dtype=None, backend=None, **kwargs):
# Determine backend and dtype
backend = backend if backend is not None else yp.config.default_backend
dtype = dtype if dtype is not None else yp.config.default_dtype
# Load image
image = np.asarray(
imageio.imread(test_images_directory + '/' +
_image_dict[image_label]['filename']))
# Process color channel
if yp.ndim(image) > 2:
color_processing_mode = kwargs.get('color_channel', 'average')
if color_processing_mode == 'average':
image = np.mean(image, 2)
elif color_processing_mode == None:
pass
else:
assert type(color_processing_mode) in [np.int, int]
image = image[:, :, int(color_processing_mode)]
# Resize image if requested
if shape is not None:
# Warn if the measurement will be band-limited in the frequency domain
if any([image.shape[i] < shape[i] for i in range(len(shape))]):
print(
'WARNING : Raw image size (%d x %d) is smaller than requested size (%d x %d). Resolution will be lower than bandwidth of image.'
% (image.shape[0], image.shape[1], shape[0], shape[1]))
# Perform resize operation
image = resize(image,
shape,
mode=kwargs.get('reshape_mode', 'constant'),
preserve_range=True,
anti_aliasing=kwargs.get('anti_aliasing',
False)).astype(np.float)
return yp.cast(image, dtype, backend)
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
def ConvolutionOld(kernel,
dtype=None,
backend=None,
normalize=False,
mode='circular',
label='C',
pad_value='mean',
pad_size=None,
fft_backend=None,
inverse_regularizer=0,
center=False,
inner_operator=None,
force_full_convolution=False):
"""Convolution linear operator"""
# Get temporary kernel to account for inner_operator size
_kernel = kernel if inner_operator is None else inner_operator * kernel
# Check number of dimensions
N = _kernel.shape
dim_count = len(N)
assert dim_count == ndim(_kernel)
# Get kernel backend
if backend is None:
backend = getBackend(kernel)
else:
# Convert kernel to provided backend
kernel = asbackend(kernel, backend)
# Get kernel dtype
if dtype is None:
dtype = getDatatype(kernel)
else:
kernel = astype(kernel, dtype)
# Determine if the kernel is a shifted delta function - if so, return a
# shift operator masked as a convolution
position_list = tuple([
tuple(np.asarray(pos) - np.asarray(shape(_kernel)) // 2)
for pos in where(_kernel != 0.0)
])
mode = 'discrete' if len(
position_list) == 1 and not force_full_convolution else mode
# Discrete convolution
if mode == 'discrete':
# Create shift operator, or identity operator if there is no shift.
if all([pos == 0.0 for pos in position_list[0]]):
op = Identity(N)
else:
op = Shift(N, position_list[0])
loc = where(_kernel != 0)[0]
# If the kernel is not binary, normalize to the correct value
if scalar(_kernel[loc[0], loc[1]]) != 1.0:
op *= scalar(_kernel[loc[0], loc[1]])
# Update label to indicate this is a shift-based convolution
label += '_{shift}'
# Normalize if desired
if normalize:
op *= 1 / np.sqrt(np.size(kernel))
elif mode in ['windowed', 'circular']:
# The only difference between circular and non-circular convolution is
# the pad size. We'll define this first, then define the convolution in
# a common framework.
if mode == 'circular':
# Pad kernel to effecient size
N_pad = list(N)
for ind, d in enumerate(N):
if next_fast_len(d) != d:
N_pad[ind] = next_fast_len(d)
crop_start = [0] * len(N_pad)
elif mode == 'windowed':
if pad_size is None:
# Determine support of kernel
kernel_support_roi = boundingBox(kernel, return_roi=True)
N_pad_raw = (np.asarray(N) +
np.asarray(kernel_support_roi.size).tolist())
N_pad = [next_fast_len(sz) for sz in N_pad_raw]
# Create pad and crop operator
crop_start = [(N_pad[dim] - N[dim]) // 2
for dim in range(len(N))]
else:
if type(pad_size) not in (list, tuple, np.ndarray):
pad_size = (pad_size, pad_size)
N_pad = (pad_size[0] + N[0], pad_size[1] + N[1])
crop_start = None
# Create pad operator
P = Pad(N,
N_pad,
pad_value=pad_value,
pad_start=crop_start,
backend=backend,
dtype=dtype)
# Create F.T. operator
F = FourierTransform(N_pad,
dtype=dtype,
backend=backend,
normalize=normalize,
fft_backend=fft_backend,
pad=False,
center=center)
# Optionally create FFTShift operator
if not center:
FFTS = FFTShift(N_pad, dtype=dtype, backend=backend)
else:
FFTS = Identity(N_pad, dtype=dtype, backend=backend)
# Diagonalize kernel
K = Diagonalize(kernel,
inner_operator=F * FFTS * P,
inverse_regularizer=inverse_regularizer,
label=label)
# Generate composite op
op = P.H * F.H * K * F * P
# Define inversion function
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
# Set inverse function
op._inverse = types.MethodType(_inverse, op)
else:
raise ValueError(
'Convolution mode %s is not defined! Valid options are "circular" and "windowed"'
% mode)
# Append type to label
if '_' not in label:
label += '_{' + mode + '}'
# Set label
op.label = label
# Set inverse_regularizer
op.inverse_regularizer = inverse_regularizer
# Set latex to be just label
def repr_latex(latex_input=None):
if latex_input is None:
return op.label
else:
return op.label + ' \\times ' + latex_input
op.repr_latex = repr_latex
return op
def Registration(array_to_register_to,
dtype=None,
backend=None,
label='R',
inner_operator=None,
center=False,
axes=None,
debug=False):
"""Registeration operator for input x and operator input."""
# Configure backend and datatype
backend = backend if backend is not None else config.default_backend
dtype = dtype if dtype is not None else config.default_dtype
_shape = shape(
array_to_register_to) if inner_operator is None else inner_operator.M
axes = axes if axes is not None else tuple(
range(ndim(array_to_register_to)))
# Create sub-operators
PR = PhaseRamp(_shape, dtype, backend, center=center, axes=axes)
F = FourierTransform(_shape, dtype, backend, center=center, axes=axes)
X = Diagonalize(-1 * array_to_register_to,
dtype,
backend,
inner_operator=F * inner_operator,
label='x')
_R = X * PR
# Compute Fourier Transform of array to register to
array_to_register_to_f = F * array_to_register_to
# Define inverse
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())))
# Define operator name
repr_str = 'Registration'
# Create a new operator from phase ramp
R = Operator(
_R.shape,
_R.dtype,
_R.backend,
repr_str=repr_str,
label=label,
forward=_R.forward, # Don't provide adjoint, implies nonlinear
gradient=_R._gradient,
inverse=_inverse,
cost=_R.cost,
convex=_R.convex,
smooth=True,
set_arguments_function=X._set_argument_function,
get_arguments_function=X._get_argument_function,
inverse_regularizer=_R.inverse_regularizer,
repr_latex=_R.repr_latex)
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')
# Return operator with prepended inverse Fourier Transform
op = F.H * R
# Set the show_xc in this operator, since it is removed by multiplication
op.show_xc = show_xc
# Set the set and get argument functions
op._setArgumentsFunction = R._set_argument_function
op._getArgumentsFunction = R._get_argument_function
# Return result
return op