def precision_subpixel(): shift, error, diffphase = register_translation(image, offset_image, 100) fig, (ax1, ax2, ax3) = plt.subplots(ncols=3, figsize=(8, 3)) ax1.imshow(image) ax1.set_axis_off() ax1.set_title('Reference image') ax2.imshow(offset_image.real) ax2.set_axis_off() ax2.set_title('Offset image') # Calculate the upsampled DFT, again to show what the algorithm is doing # behind the scenes. Constants correspond to calculated values in routine. # See source code for details. cc_image = _upsampled_dft(image_product, 150, 100, (shift * 100) + 75).conj() ax3.imshow(cc_image.real) ax3.set_axis_off() ax3.set_title("Supersampled XC sub-area") print("Detected subpixel offset (y, x):") print(shift) plt.show()
def testCudaUpsampleFFT(self): # ==============Test cuda version upsampling dft========================== raw_data = np.arange(1024 * 1024).reshape(1024, 1024) raw_data_cu = cp.arange(1024 * 1024).reshape(1024, 1024) # print(_upsampled_dft(raw_data, raw_data.shape)) # print(_upsampled_dft_cu(raw_data_cu, raw_data_cu.shape)) import time print(raw_data_cu.device) t0 = time.time() a = _upsampled_dft_cu(raw_data_cu, raw_data_cu.shape) t1 = time.time() b = _upsampled_dft(raw_data, raw_data.shape) t2 = time.time() print(t1 - t0, 's ', t2 - t1, 's') from numpy.testing import assert_allclose assert_array_almost_equal(a, b)
def estimate_image_shift(ref, image, roi=None, sobel=True, medfilter=True, hanning=True, plot=False, dtype='float', normalize_corr=False, sub_pixel_factor=1, return_maxval=True): """Estimate the shift in a image using phase correlation This method can only estimate the shift by comparing bidimensional features that should not change the position in the given axis. To decrease the memory usage, the time of computation and the accuracy of the results it is convenient to select a region of interest by setting the roi keyword. Parameters ---------- ref : 2D numpy.ndarray Reference image image : 2D numpy.ndarray Image to register roi : tuple of ints (top, bottom, left, right) Define the region of interest sobel : bool apply a sobel filter for edge enhancement medfilter : bool apply a median filter for noise reduction hanning : bool Apply a 2d hanning filter plot : bool or matplotlib.Figure If True, plots the images after applying the filters and the phase correlation. If a figure instance, the images will be plotted to the given figure. reference : 'current' or 'cascade' If 'current' (default) the image at the current coordinates is taken as reference. If 'cascade' each image is aligned with the previous one. dtype : str or dtype Typecode or data-type in which the calculations must be performed. normalize_corr : bool If True use phase correlation instead of standard correlation sub_pixel_factor : float Estimate shifts with a sub-pixel accuracy of 1/sub_pixel_factor parts of a pixel. Default is 1, i.e. no sub-pixel accuracy. Returns ------- shifts: np.array containing the estimate shifts max_value : float The maximum value of the correlation Notes ----- The statistical analysis approach to the translation estimation when using reference='stat' roughly follows [*]_ . If you use it please cite their article. References ---------- .. [*] Bernhard Schaffer, Werner Grogger and Gerald Kothleitner. “Automated Spatial Drift Correction for EFTEM Image Series.” Ultramicroscopy 102, no. 1 (December 2004): 27–36. """ ref, image = da.compute(ref, image) # Make a copy of the images to avoid modifying them ref = ref.copy().astype(dtype) image = image.copy().astype(dtype) if roi is not None: top, bottom, left, right = roi else: top, bottom, left, right = [ None, ] * 4 # Select region of interest ref = ref[top:bottom, left:right] image = image[top:bottom, left:right] # Apply filters for im in (ref, image): if hanning is True: im *= hanning2d(*im.shape) if medfilter is True: # This is faster than sp.signal.med_filt, # which was the previous implementation. # The size is fixed at 3 to be consistent # with the previous implementation. im[:] = sp.ndimage.median_filter(im, size=3) if sobel is True: im[:] = sobel_filter(im) # If sub-pixel alignment not being done, use faster real-valued fft real_only = (sub_pixel_factor == 1) phase_correlation, image_product = fft_correlation( ref, image, normalize=normalize_corr, real_only=real_only) # Estimate the shift by getting the coordinates of the maximum argmax = np.unravel_index(np.argmax(phase_correlation), phase_correlation.shape) threshold = (phase_correlation.shape[0] / 2 - 1, phase_correlation.shape[1] / 2 - 1) shift0 = argmax[0] if argmax[0] < threshold[0] else \ argmax[0] - phase_correlation.shape[0] shift1 = argmax[1] if argmax[1] < threshold[1] else \ argmax[1] - phase_correlation.shape[1] max_val = phase_correlation.real.max() shifts = np.array((shift0, shift1)) # The following code is more or less copied from # skimage.feature.register_feature, to gain access to the maximum value: if sub_pixel_factor != 1: # Initial shift estimate in upsampled grid shifts = np.round(shifts * sub_pixel_factor) / sub_pixel_factor upsampled_region_size = np.ceil(sub_pixel_factor * 1.5) # Center of output array at dftshift + 1 dftshift = np.fix(upsampled_region_size / 2.0) sub_pixel_factor = np.array(sub_pixel_factor, dtype=np.float64) normalization = (image_product.size * sub_pixel_factor**2) # Matrix multiply DFT around the current shift estimate sample_region_offset = dftshift - shifts * sub_pixel_factor correlation = _upsampled_dft(image_product.conj(), upsampled_region_size, sub_pixel_factor, sample_region_offset).conj() correlation /= normalization # Locate maximum and map back to original pixel grid maxima = np.array(np.unravel_index(np.argmax(np.abs(correlation)), correlation.shape), dtype=np.float64) maxima -= dftshift shifts = shifts + maxima / sub_pixel_factor max_val = correlation.real.max() # Plot on demand if plot is True or isinstance(plot, plt.Figure): if isinstance(plot, plt.Figure): fig = plot axarr = plot.axes if len(axarr) < 3: for i in range(3): fig.add_subplot(1, 3, i + 1) axarr = fig.axes else: fig, axarr = plt.subplots(1, 3) full_plot = len(axarr[0].images) == 0 if full_plot: axarr[0].set_title('Reference') axarr[1].set_title('Image') axarr[2].set_title('Phase correlation') axarr[0].imshow(ref) axarr[1].imshow(image) d = (np.array(phase_correlation.shape) - 1) // 2 extent = [-d[1], d[1], -d[0], d[0]] axarr[2].imshow(np.fft.fftshift(phase_correlation), extent=extent) plt.show() else: axarr[0].images[0].set_data(ref) axarr[1].images[0].set_data(image) axarr[2].images[0].set_data(np.fft.fftshift(phase_correlation)) # TODO: Renormalize images fig.canvas.draw_idle() # Liberate the memory. It is specially necessary if it is a # memory map del ref del image if return_maxval: return -shifts, max_val else: return -shifts
print("Detected pixel offset (y, x): {}".format(shift)) # subpixel precision shift, error, diffphase = register_translation(image, offset_image, 100) fig = plt.figure(figsize=(8, 3)) ax1 = plt.subplot(1, 3, 1, adjustable='box-forced') ax2 = plt.subplot(1, 3, 2, sharex=ax1, sharey=ax1, adjustable='box-forced') ax3 = plt.subplot(1, 3, 3) ax1.imshow(image, cmap='gray') ax1.set_axis_off() ax1.set_title('Reference image') ax2.imshow(offset_image.real, cmap='gray') ax2.set_axis_off() ax2.set_title('Offset image') # Calculate the upsampled DFT, again to show what the algorithm is doing # behind the scenes. Constants correspond to calculated values in routine. # See source code for details. cc_image = _upsampled_dft(image_product, 150, 100, (shift * 100) + 75).conj() ax3.imshow(cc_image.real) ax3.set_axis_off() ax3.set_title("Supersampled XC sub-area") plt.show() print("Detected subpixel offset (y, x): {}".format(shift))
def guizar_multiframe(corr_sum, upsample_factor=100, np=np): """ Efficient subpixel image translation registration by cross-correlation. Modified and simplified version of register_translation from skimage Args: corr_sum (ndarray): correlated and summed input frame groups upsample_factor (int): Upsampling factor Returns: shifts : ndarray """ shape = corr_sum[0].shape d = [] for time_diff, cross_correlation in enumerate(corr_sum, 1): # Locate maximum maxima = np.unravel_index(np.argmax(np.abs(cross_correlation)), cross_correlation.shape) 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] # Initial shift estimate in upsampled grid shifts = np.around(shifts * upsample_factor) / upsample_factor # cast cupy.ndarray -> int upsampled_region_size = int(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(), np.fft.ifftn(cross_correlation).conj(), upsampled_region_size, upsample_factor, sample_region_offset).conj() # cross_correlation /= normalization # Locate maximum and map back to original pixel grid maxima = np.unravel_index(np.argmax(np.abs(cross_correlation)), cross_correlation.shape) CCmax = cross_correlation[maxima] maxima = np.array(maxima, dtype=np.float64) - dftshift shifts = shifts + maxima / upsample_factor d.append(np.array((shifts[1], -shifts[0])) / time_diff) weights = np.arange(1, len(corr_sum) + 1)**2 # FIXME weights[-2:] = 0 weights = weights / weights.sum() d = np.array(d) guizar_error = np.sum(d * weights[:, np.newaxis], axis=0) return guizar_error, d
def test_mismatch_offsets_size(): with pytest.raises(ValueError): _upsampled_dft(np.ones((4, 4)), 3, axis_offsets=[3, 2, 1, 4])
def test_mismatch_upsampled_region_size(): with pytest.raises(ValueError): _upsampled_dft( np.ones((4, 4)), upsampled_region_size=[3, 2, 1, 4])
print("Detected pixel offset (y, x): {}".format(shift)) # subpixel precision shift, error, diffphase = register_translation(image, offset_image, 100) fig = plt.figure(figsize=(8, 3)) ax1 = plt.subplot(1, 3, 1) ax2 = plt.subplot(1, 3, 2, sharex=ax1, sharey=ax1) ax3 = plt.subplot(1, 3, 3) ax1.imshow(image, cmap='gray') ax1.set_axis_off() ax1.set_title('Reference image') ax2.imshow(offset_image.real, cmap='gray') ax2.set_axis_off() ax2.set_title('Offset image') # Calculate the upsampled DFT, again to show what the algorithm is doing # behind the scenes. Constants correspond to calculated values in routine. # See source code for details. cc_image = _upsampled_dft(image_product, 150, 100, (shift*100)+75).conj() ax3.imshow(cc_image.real) ax3.set_axis_off() ax3.set_title("Supersampled XC sub-area") plt.show() print("Detected subpixel offset (y, x): {}".format(shift))
def register_translation(frames, upsample_factor=1, time_diff=20): """ Efficient subpixel image translation registration by cross-correlation. Parameters ---------- frames (ndarray): input frames upsample_factor (int): 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) time_diff (int): frame separation when computing correlation 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) 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` """ freq = np.fft.fftn(frames, axes=(1, 2)) # Whole-pixel shift - Compute cross-correlation by an IFFT # shape = src_freq.shape shape = freq[0].shape # image_product = src_freq * target_freq.conj() image_products = freq[:-time_diff] * freq[time_diff:].conj() image_product = np.sum(image_products, axis=0) cross_correlation = np.fft.ifftn(image_product) # Locate maximum maxima = np.unravel_index(np.argmax(np.abs(cross_correlation)), cross_correlation.shape) 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] # 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.unravel_index(np.argmax(np.abs(cross_correlation)), cross_correlation.shape) CCmax = cross_correlation[maxima] maxima = np.array(maxima, dtype=np.float64) - dftshift shifts = shifts + maxima / upsample_factor return shifts
for i in range(ncells): cells.append( Cell(np.array(minpos[i]), minang[i], minlen[i], minrad[i], minintensity)) plt.figure(figsize=(24, 8)) for f in range( startframe, startframe + nframes, ): data = dataall[f, :, :] w, h = data.shape # Upsample image by scale fim = fft2(data) data = np.real( _upsampled_dft(fim, (w * scale, h * scale), upsample_factor=scale)[::-1, ::-1]) data = gaussian(data, 1.) data = crop_data(data) data = (data - data.min()) / (data.max() - data.min()) #data = data/data.max() print("max data = ", data.max()) print("data shape =", data.shape) minerr = 1e12 for i in range(1): cells, err = simulated_anneal(cells, data, nt=800 * len(cells)) cells = split_cells(data, cells, minlen=5.) #cells,err = minimizer(cells, data) print("error = ", err) if err < minerr: mincells = deepcopy(cells)
def estimate_image_shift(ref, image, roi=None, sobel=True, medfilter=True, hanning=True, plot=False, dtype='float', normalize_corr=False, sub_pixel_factor=1, return_maxval=True): """Estimate the shift in a image using phase correlation This method can only estimate the shift by comparing bidimensional features that should not change the position in the given axis. To decrease the memory usage, the time of computation and the accuracy of the results it is convenient to select a region of interest by setting the roi keyword. Parameters ---------- ref : 2D numpy.ndarray Reference image image : 2D numpy.ndarray Image to register roi : tuple of ints (top, bottom, left, right) Define the region of interest sobel : bool apply a sobel filter for edge enhancement medfilter : bool apply a median filter for noise reduction hanning : bool Apply a 2d hanning filter plot : bool | matplotlib.Figure If True, plots the images after applying the filters and the phase correlation. If a figure instance, the images will be plotted to the given figure. reference : 'current' | 'cascade' If 'current' (default) the image at the current coordinates is taken as reference. If 'cascade' each image is aligned with the previous one. dtype : str or dtype Typecode or data-type in which the calculations must be performed. normalize_corr : bool If True use phase correlation instead of standard correlation sub_pixel_factor : float Estimate shifts with a sub-pixel accuracy of 1/sub_pixel_factor parts of a pixel. Default is 1, i.e. no sub-pixel accuracy. Returns ------- shifts: np.array containing the estimate shifts max_value : float The maximum value of the correlation Notes ----- The statistical analysis approach to the translation estimation when using `reference`='stat' roughly follows [1]_ . If you use it please cite their article. References ---------- .. [1] Bernhard Schaffer, Werner Grogger and Gerald Kothleitner. “Automated Spatial Drift Correction for EFTEM Image Series.” Ultramicroscopy 102, no. 1 (December 2004): 27–36. """ ref, image = da.compute(ref, image) # Make a copy of the images to avoid modifying them ref = ref.copy().astype(dtype) image = image.copy().astype(dtype) if roi is not None: top, bottom, left, right = roi else: top, bottom, left, right = [None, ] * 4 # Select region of interest ref = ref[top:bottom, left:right] image = image[top:bottom, left:right] # Apply filters for im in (ref, image): if hanning is True: im *= hanning2d(*im.shape) if medfilter is True: im[:] = sp.signal.medfilt(im) if sobel is True: im[:] = sobel_filter(im) phase_correlation, image_product = fft_correlation( ref, image, normalize=normalize_corr) # Estimate the shift by getting the coordinates of the maximum argmax = np.unravel_index(np.argmax(phase_correlation), phase_correlation.shape) threshold = (phase_correlation.shape[0] / 2 - 1, phase_correlation.shape[1] / 2 - 1) shift0 = argmax[0] if argmax[0] < threshold[0] else \ argmax[0] - phase_correlation.shape[0] shift1 = argmax[1] if argmax[1] < threshold[1] else \ argmax[1] - phase_correlation.shape[1] max_val = phase_correlation.real.max() shifts = np.array((shift0, shift1)) # The following code is more or less copied from # skimage.feature.register_feature, to gain access to the maximum value: if sub_pixel_factor != 1: # Initial shift estimate in upsampled grid shifts = np.round(shifts * sub_pixel_factor) / sub_pixel_factor upsampled_region_size = np.ceil(sub_pixel_factor * 1.5) # Center of output array at dftshift + 1 dftshift = np.fix(upsampled_region_size / 2.0) sub_pixel_factor = np.array(sub_pixel_factor, dtype=np.float64) normalization = (image_product.size * sub_pixel_factor ** 2) # Matrix multiply DFT around the current shift estimate sample_region_offset = dftshift - shifts * sub_pixel_factor correlation = _upsampled_dft(image_product.conj(), upsampled_region_size, sub_pixel_factor, sample_region_offset).conj() correlation /= normalization # Locate maximum and map back to original pixel grid maxima = np.array(np.unravel_index( np.argmax(np.abs(correlation)), correlation.shape), dtype=np.float64) maxima -= dftshift shifts = shifts + maxima / sub_pixel_factor max_val = correlation.real.max() # Plot on demand if plot is True or isinstance(plot, plt.Figure): if isinstance(plot, plt.Figure): fig = plot axarr = plot.axes if len(axarr) < 3: for i in range(3): fig.add_subplot(1, 3, i + 1) axarr = fig.axes else: fig, axarr = plt.subplots(1, 3) full_plot = len(axarr[0].images) == 0 if full_plot: axarr[0].set_title('Reference') axarr[1].set_title('Image') axarr[2].set_title('Phase correlation') axarr[0].imshow(ref) axarr[1].imshow(image) d = (np.array(phase_correlation.shape) - 1) // 2 extent = [-d[1], d[1], -d[0], d[0]] axarr[2].imshow(np.fft.fftshift(phase_correlation), extent=extent) plt.show() else: axarr[0].images[0].set_data(ref) axarr[1].images[0].set_data(image) axarr[2].images[0].set_data(np.fft.fftshift(phase_correlation)) # TODO: Renormalize images fig.canvas.draw_idle() # Liberate the memory. It is specially necessary if it is a # memory map del ref del image if return_maxval: return -shifts, max_val else: return -shifts
def register_translation_hybrid(src_image, target_image, exponent=1, upsample_factor=1, space="real"): """ Efficient subpixel image translation registration by hybrid-correlation (cross and phase). Exponent = 1 -> cross correlation, exponent = 0 -> phase correlation. Closer to zero is more precise but more susceptible to noise. This code gives the same precision as the FFT upsampled 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``. exponent: float, optional Power to which amplitude contribution to correlation is raised. exponent = 0: Phase correlation exponent = 1: Cross correlation 0 < exponent < 1 = Hybrid 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': src_image = np.array(src_image, dtype=np.complex128, copy=False) target_image = np.array(target_image, dtype=np.complex128, copy=False) src_freq = np.fft.fftn(src_image) target_freq = np.fft.fftn(target_image) else: raise ValueError("Error: register_translation only knows the \"real\" " "and \"fourier\" values for the ``space`` argument.") # Whole-pixel shift - Compute hybrid-correlation by an IFFT shape = src_freq.shape image_product = src_freq * target_freq.conj() amplitude = np.abs(image_product) phase = np.angle(image_product) total_fourier = amplitude**exponent * np.exp(phase * 1j) correlation = np.fft.ifftn(total_fourier) # Locate maximum maxima = np.unravel_index(np.argmax(np.abs(correlation)), correlation.shape) 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: src_amp = np.sum(np.abs(src_freq)**2) / src_freq.size target_amp = np.sum(np.abs(target_freq)**2) / target_freq.size CCmax = correlation.max() # If upsampling > 1, then refine estimate with matrix multiply DFT else: # 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 correlation = _upsampled_dft(total_fourier.conj(), upsampled_region_size, upsample_factor, sample_region_offset).conj() correlation /= normalization # Locate maximum and map back to original pixel grid maxima = np.array(np.unravel_index(np.argmax(np.abs(correlation)), correlation.shape), dtype=np.float64) maxima -= dftshift shifts = shifts + maxima / upsample_factor CCmax = 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, _compute_error(CCmax, src_amp, target_amp),\ _compute_phasediff(CCmax)
errors = [] for noise_level in noisy_list: offset, error, diffphase = register_translation(noise_level[0], noise_level[1], 100) offsets.append(offset) errors.append(error) correlations = [] for noise_level, offset in zip(noisy_list, offsets): image_product = np.fft.fft2(noise_level[0]) * np.fft.fft2( noise_level[1]).conj() # preview the correlation map computed by register_translation coarse_correlation = np.fft.fftshift(np.fft.ifft2(image_product)) # preview the correlation map computed by register_translation fine_correlation = _upsampled_dft(image_product, image_product.shape[0], 100, (offset * 100) + image_product.shape[0] // 2).conj() correlations.append([coarse_correlation, fine_correlation]) correlations = np.array(correlations) # %% plot ----- plt = plotter4d(noisy_list, title='Original and shifted images at various noise levels', colorbar=False, row_labels=max_photon_count_list, column_labels=['original', 'shifted'], sup_ylabel='max photon count', figsize=(4.5, 10), cmap='gist_heat') plt.savefig('images.png', dpi=300)