def apply_shifts_dft(src_freq, shifts, diffphase, is_freq = True, border_nan = False):
'''
apply shifts using inverse dft
src_freq: ndarray
if is_freq it is fourier transform image else original image
shifts: shifts to apply
diffphase: comes from the register_translation output
'''
shifts = shifts[::-1]
if not is_freq:
src_freq = np.dstack([np.real(src_freq),np.imag(src_freq)])
src_freq = fftn(src_freq,flags=cv2.DFT_COMPLEX_OUTPUT+cv2.DFT_SCALE)
src_freq = src_freq[:,:,0]+1j*src_freq[:,:,1]
src_freq = np.array(src_freq, dtype=np.complex128, copy=False)
nr,nc = np.shape(src_freq)
Nr = ifftshift(np.arange(-np.fix(old_div(nr,2.)),np.ceil(old_div(nr,2.))))
Nc = ifftshift(np.arange(-np.fix(old_div(nc,2.)),np.ceil(old_div(nc,2.))))
Nr,Nc = np.meshgrid(Nr,Nc)
Greg = src_freq*np.exp(1j*2*np.pi*(-shifts[0]*1.*Nr/nr-shifts[1]*1.*Nc/nc))
Greg = Greg.dot(np.exp(1j*diffphase))
Greg = np.dstack([np.real(Greg),np.imag(Greg)])
new_img = ifftn(Greg)[:,:,0]
if border_nan:
max_w,max_h,min_w,min_h=0,0,0,0
max_h,max_w = np.ceil(np.maximum((max_h,max_w),shifts)).astype(np.int)
min_h,min_w = np.floor(np.minimum((min_h,min_w),shifts)).astype(np.int)
new_img[:max_h,:] = np.nan
if min_h < 0:
new_img[min_h:,:] = np.nan
new_img[:,:max_w] = np.nan
if min_w < 0:
new_img[:,min_w:] = np.nan
return new_img
def register_translation(src_image,
target_image,
upsample_factor=1,
space="real",
shifts_lb=None,
shifts_ub=None,
max_shifts=[3, 3],
**kwargs):
"""
adapted from SIMA (https://github.com/losonczylab) and the
scikit-image (http://scikit-image.org/) package.
Unless otherwise specified by LICENSE.txt files in individual
directories, all code is
Copyright (C) 2011, the scikit-image team
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:
1. Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in
the documentation and/or other materials provided with the
distribution.
3. Neither the name of skimage nor the names of its contributors may be
used to endorse or promote products derived from this software without
specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT,
INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING
IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE.
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"
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.
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).
Raise:
------
NotImplementedError("Error: register_translation only supports "
"subpixel registration for 2D images")
ValueError("Error: images must really be same size for "
"register_translation")
ValueError("Error: register_translation only knows the \"real\" "
"and \"fourier\" values for the ``space`` argument.")
References:
----------
.. [1] Manuel Guizar-Sicairos, Samuel T. Thurman, and James R. Fienup,
"Efficient subpixel image registration algorithms,"
Optics Letters 33, 156-158 (2008).
src_image= filtered_template
target_image=filtered_image
upsample_factor=parameters['upsample_factor']
space="real"
shifts_lb=None
shifts_ub=None
max_shifts=parameters['max_shifts']
"""
# images must be the same shape
if src_image.shape != target_image.shape:
raise ValueError("Error: images must really be same size for "
"register_translation")
# only 2D data makes sense right now
if src_image.ndim != 2 and upsample_factor > 1:
raise NotImplementedError("Error: register_translation only supports "
"subpixel registration for 2D 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':
if opencv:
src_freq_1 = fftn(src_image,
flags=cv2.DFT_COMPLEX_OUTPUT + cv2.DFT_SCALE)
src_freq = src_freq_1[:, :, 0] + 1j * src_freq_1[:, :, 1]
src_freq = np.array(src_freq, dtype=np.complex128, copy=False)
target_freq_1 = fftn(target_image,
flags=cv2.DFT_COMPLEX_OUTPUT + cv2.DFT_SCALE)
target_freq = target_freq_1[:, :, 0] + 1j * target_freq_1[:, :, 1]
target_freq = np.array(target_freq,
dtype=np.complex128,
copy=False)
else:
src_image_cpx = np.array(src_image,
dtype=np.complex128,
copy=False)
target_image_cpx = np.array(target_image,
dtype=np.complex128,
copy=False)
src_freq = np.fft.fftn(src_image_cpx)
target_freq = fftn(target_image_cpx)
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 = src_freq.shape
image_product = src_freq * target_freq.conj()
if opencv:
image_product_cv = np.dstack(
[np.real(image_product),
np.imag(image_product)])
cross_correlation = fftn(image_product_cv,
flags=cv2.DFT_INVERSE + cv2.DFT_SCALE)
cross_correlation = cross_correlation[:, :,
0] + 1j * cross_correlation[:, :,
1]
else:
shape = src_freq.shape
image_product = src_freq * target_freq.conj()
cross_correlation = ifftn(image_product)
# Locate maximum
new_cross_corr = np.abs(cross_correlation)
if (shifts_lb is not None) or (shifts_ub is not None):
if (shifts_lb[0] < 0) and (shifts_ub[0] >= 0):
new_cross_corr[shifts_ub[0]:shifts_lb[0], :] = 0
else:
new_cross_corr[:shifts_lb[0], :] = 0
new_cross_corr[shifts_ub[0]:, :] = 0
if (shifts_lb[1] < 0) and (shifts_ub[1] >= 0):
new_cross_corr[:, shifts_ub[1]:shifts_lb[1]] = 0
else:
new_cross_corr[:, :shifts_lb[1]] = 0
new_cross_corr[:, shifts_ub[1]:] = 0
else:
new_cross_corr[max_shifts[0]:-max_shifts[0], :] = 0
new_cross_corr[:, max_shifts[1]:-max_shifts[1]] = 0
maxima = np.unravel_index(np.argmax(new_cross_corr),
cross_correlation.shape)
midpoints = np.array(
[np.fix(old_div(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:
src_amp = old_div(np.sum(np.abs(src_freq)**2), src_freq.size)
target_amp = old_div(np.sum(np.abs(target_freq)**2), target_freq.size)
CCmax = cross_correlation.max()
# If upsampling > 1, then refine estimate with matrix multiply DFT
else:
# Initial shift estimate in upsampled grid
shifts = old_div(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(old_div(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 + old_div(maxima, upsample_factor)
CCmax = cross_correlation.max()
src_amp = _upsampled_dft(src_freq * src_freq.conj(), 1,
upsample_factor)[0, 0]
src_amp /= normalization
target_amp = _upsampled_dft(target_freq * target_freq.conj(), 1,
upsample_factor)[0, 0]
target_amp /= normalization
# If its only one row or column the shift along that dimension has no
# effect. We set to zero.
for dim in range(src_freq.ndim):
if shape[dim] == 1:
shifts[dim] = 0
return shifts, src_freq, _compute_phasediff(CCmax)
def register_translation(src_image, target_image, upsample_factor=1,
space="real", shifts_lb = None, shifts_ub = None, max_shifts = (10,10)):
"""
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"
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.
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).
"""
# images must be the same shape
if src_image.shape != target_image.shape:
raise ValueError("Error: images must be same size for "
"register_translation")
# only 2D data makes sense right now
if src_image.ndim != 2 and upsample_factor > 1:
raise NotImplementedError("Error: register_translation only supports "
"subpixel registration for 2D 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':
if opencv:
src_freq_1 = fftn(src_image,flags=cv2.DFT_COMPLEX_OUTPUT+cv2.DFT_SCALE)
src_freq = src_freq_1[:,:,0]+1j*src_freq_1[:,:,1]
src_freq = np.array(src_freq, dtype=np.complex128, copy=False)
target_freq_1 = fftn(target_image,flags=cv2.DFT_COMPLEX_OUTPUT+cv2.DFT_SCALE)
target_freq = target_freq_1[:,:,0]+1j*target_freq_1[:,:,1]
target_freq = np.array(target_freq , dtype=np.complex128, copy=False)
else:
src_image_cpx = np.array(src_image, dtype=np.complex128, copy=False)
target_image_cpx = np.array(target_image, dtype=np.complex128, copy=False)
src_freq = np.fft.fftn(src_image_cpx)
target_freq = fftn(target_image_cpx)
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 = src_freq.shape
image_product = src_freq * target_freq.conj()
if opencv:
image_product_cv = np.dstack([np.real(image_product),np.imag(image_product)])
cross_correlation = fftn(image_product_cv,flags=cv2.DFT_INVERSE+cv2.DFT_SCALE)
cross_correlation = cross_correlation[:,:,0]+1j*cross_correlation[:,:,1]
else:
shape = src_freq.shape
image_product = src_freq * target_freq.conj()
cross_correlation = ifftn(image_product)
# Locate maximum
new_cross_corr = np.abs(cross_correlation)
if (shifts_lb is not None) or (shifts_ub is not None):
if (shifts_lb[0]<0) and (shifts_ub[0]>=0):
new_cross_corr[shifts_ub[0]:shifts_lb[0],:] = 0
else:
new_cross_corr[:shifts_lb[0],:] = 0
new_cross_corr[shifts_ub[0]:,:] = 0
if (shifts_lb[1]<0) and (shifts_ub[1]>=0):
new_cross_corr[:,shifts_ub[1]:shifts_lb[1]] = 0
else:
new_cross_corr[:,:shifts_lb[1]] = 0
new_cross_corr[:,shifts_ub[1]:] = 0
else:
new_cross_corr[max_shifts[0]:-max_shifts[0],:] = 0
new_cross_corr[:,max_shifts[1]:-max_shifts[1]] = 0
# pl.cla()
# ranges = np.percentile(np.abs(cross_correlation),[1,99.99])
# pl.subplot(1,2,1)
# pl.imshow( np.abs(cross_correlation),interpolation = 'none',vmin = ranges[0],vmax = ranges[1])
# pl.pause(.1)
# pl.subplot(1,2,2)
# pl.imshow(new_cross_corr,interpolation = 'none',vmin = ranges[0],vmax = ranges[1])
# pl.pause(1)
maxima = np.unravel_index(np.argmax(new_cross_corr),
cross_correlation.shape)
midpoints = np.array([np.fix(old_div(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:
src_amp = old_div(np.sum(np.abs(src_freq) ** 2), src_freq.size)
target_amp = old_div(np.sum(np.abs(target_freq) ** 2), target_freq.size)
CCmax = cross_correlation.max()
# If upsampling > 1, then refine estimate with matrix multiply DFT
else:
# Initial shift estimate in upsampled grid
shifts = old_div(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(old_div(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 + old_div(maxima, upsample_factor)
CCmax = cross_correlation.max()
src_amp = _upsampled_dft(src_freq * src_freq.conj(),
1, upsample_factor)[0, 0]
src_amp /= normalization
target_amp = _upsampled_dft(target_freq * target_freq.conj(),
1, upsample_factor)[0, 0]
target_amp /= normalization
# If its only one row or column the shift along that dimension has no
# effect. We set to zero.
for dim in range(src_freq.ndim):
if shape[dim] == 1:
shifts[dim] = 0
return shifts, src_freq,_compute_phasediff(CCmax) #, _compute_error(CCmax, src_amp, target_amp),\
