def _iteration_function(self, x, iteration_number, step_size): if iteration_number == 0: self.r = self.y - self.A * x self.p = self.r else: # Helper variables Ap = self.A * self.p pAp = yp.sum(yp.real((yp.conj(self.p) * Ap))) r2 = yp.sum(yp.real((yp.conj(self.r) * self.r))) # Update alpha alpha = r2 / pAp # Update x x += alpha * self.p # Update r self.r -= alpha * Ap # Update beta beta = yp.sum(yp.real((yp.conj(self.r) * self.r))) / r2 # Update p self.p = self.r + beta * self.p return (x)
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 _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 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 CrossCorrelation(kernel, mode='circular', dtype=None, backend=None, label='X', pad_value=0, axis=None, pad_convolution=True, pad_fft=True, invalid_support_value=1, fft_backend=None): # Flip kernel kernel = iFt(conj(Ft(kernel))) # Call Convolution return Convolution(kernel, mode=mode, dtype=dtype, backend=backend, label=label, pad_value=pad_value, axis=None, pad_convolution=pad_convolution, pad_fft=pad_fft, invalid_support_value=invalid_support_value, fft_backend=fft_backend)
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 _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 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 _forward(self, x, y): y[:] = 0.5 * sum(conj(x) * (x - self.denoiser(x)))