From 0d61d8b3fa94d9703bde65c625fc0b8631d97cfc Mon Sep 17 00:00:00 2001 From: Jamil Zakirov Date: Sun, 21 Jun 2020 15:50:57 +0300 Subject: [PATCH 1/8] feature/fsim: PyTorch implementation of FSIM --- photosynthesis_metrics/fsim.py | 402 +++++++++++++++++++++++++++++++++ 1 file changed, 402 insertions(+) create mode 100644 photosynthesis_metrics/fsim.py diff --git a/photosynthesis_metrics/fsim.py b/photosynthesis_metrics/fsim.py new file mode 100644 index 00000000..3e352826 --- /dev/null +++ b/photosynthesis_metrics/fsim.py @@ -0,0 +1,402 @@ +import math + +import torch +from typing import Union, Tuple + +from photosynthesis_metrics.utils import _adjust_dimensions, _validate_input + + +def fsim(x: torch.Tensor, y: torch.Tensor, + reduction: str = 'mean', + data_range: Union[int, float] = 1.0, + chromatic: bool = True) -> torch.Tensor: + r"""Compute Feature Similarity Index Measure for a batch of images. + + + Args: + x: Batch of predicted images with shape (batch_size x channels x H x W) + y: Batch of target images with shape (batch_size x channels x H x W) + + data_range: Value range of input images (usually 1.0 or 255). Default: 1.0 + chromatic: Flag to compute FSIMc, which also takes into account chromatic components + + Returns: + FSIM: Index of similarity betwen two images. Usually in [0, 1] interval. + Can be bigger than 1 for predicted images with higher contrast than original one. + Note: + This implementation is based on original authors MATLAB code. + https://www4.comp.polyu.edu.hk/~cslzhang/IQA/FSIM/FSIM.htm + + """ + + _validate_input(input_tensors=(x, y), allow_5d=False) + x, y = _adjust_dimensions(input_tensors=(x, y)) + + # Scale to [0., 1.] range + x = x / float(data_range) + y = y / float(data_range) + + # Rescale to [0, 255] range, because all constant are calculated for this factor + x = x * 255 + y = y * 255 + + # Apply average pooling + kernel_size = max(1, min(x.shape[-2:]) // 256) + x = torch.nn.functional.avg_pool2d(x, kernel_size, stride=2) + y = torch.nn.functional.avg_pool2d(y, kernel_size, stride=2) + + num_channels = x.size(1) + + # Convert RGB to YIQ color space https://en.wikipedia.org/wiki/YIQ + if num_channels == 3: + yiq_weights = torch.tensor([ + [0.229, 0.587, 0.114], + [0.5959, -0.2746, -0.3213], + [0.2115, -0.5227, 0.3112]]).t().to(x) + x = torch.matmul(x.permute(0, 2, 3, 1), yiq_weights).permute(0, 3, 1, 2) + y = torch.matmul(y.permute(0, 2, 3, 1), yiq_weights).permute(0, 3, 1, 2) + + x_Y = x[:, : 1, :, :] + y_Y = y[:, : 1, :, :] + + x_I = x[:, 1: 2, :, :] + y_I = y[:, 1: 2, :, :] + x_Q = x[:, 2:, :, :] + y_Q = y[:, 2:, :, :] + + else: + x_Y = x + y_Y = y + + # Compute phase congruency maps + PCx = _phase_congruency(x_Y) + PCy = _phase_congruency(y_Y) + + # Gradient maps + kernel = torch.stack([_scharr_filter(), _scharr_filter().transpose(-1, -2)]).to(x) + grad_x = torch.nn.functional.conv2d(x_Y, kernel, padding=1) + grad_y = torch.nn.functional.conv2d(y_Y, kernel, padding=1) + + grad_map_x = torch.sqrt(torch.sum(grad_x ** 2, dim=-3, keepdim=True)) + grad_map_y = torch.sqrt(torch.sum(grad_y ** 2, dim=-3, keepdim=True)) + + # Constants from paper + T1, T2, T3, T4, lmbda = 0.85, 160, 200, 200, 0.03 + + # Compute FSIM + PC = (2.0 * PCx * PCy + T1) / (PCx ** 2 + PCy ** 2 + T1) + GM = (2.0 * grad_map_x * grad_map_y + T2) / (grad_map_x ** 2 + grad_map_y ** 2 + T2) + PCmax = torch.where(PCx > PCy, PCx, PCy) + + score = GM * PC * PCmax + + if chromatic: + S_I = (2 * x_I * y_I + T3) / (x_I ** 2 + y_I ** 2 + T3) + S_Q = (2 * x_Q * y_Q + T4) / (x_Q ** 2 + y_Q ** 2 + T4) + print(score.shape, S_I.shape, S_Q.shape) + score = score * (S_I * S_Q) ** lmbda + + result = score.sum(dim=[2, 3]) / PCmax.sum(dim=[2, 3]) + + if reduction == 'none': + return result + + return {'mean': result.mean, + 'sum': result.sum + }[reduction](dim=0) + + +def _scharr_filter() -> torch.Tensor: + """Utility function that returns a normalized 3x3 Scharr kernel in X direction + Return: + kernel: Tensor with shape 1x3x3""" + kernel = torch.tensor([[[-3., 0., 3.], [-10., 0., 10.], [-3., 0., 3.]]]) / 16 + return kernel + + +def _construct_filters(x: torch.Tensor, scales: int = 4, orientations: int = 4, + min_length: int = 6, mult: int = 2, sigma_f: float = 0.55, + delta_theta: float = 1.2, k: float = 2.0): + """Creates stack of filters used for computation of phase congruensy maps + + Args: + x: Tensor with shape Bx1xHxW + scales: Number of wavelets + orientations: Number of filter orientations + min_length: Wavelength of smallest scale filter + mult: Scaling factor between successive filters + sigma_f: Ratio of the standard deviation of the Gaussian + describing the log Gabor filter's transfer function + in the frequency domain to the filter center frequency. + delta_theta: Ratio of angular interval between filter orientations + and the standard deviation of the angular Gaussian function + used to construct filters in the freq. plane. + k: No of standard deviations of the noise energy beyond the mean + at which we set the noise threshold point, below which phase + congruency values get penalized. + """ + B, _, H, W = x.shape + + # Calculate the standard deviation of the angular Gaussian function + # used to construct filters in the freq. plane. + theta_sigma = math.pi / (orientations * delta_theta) + + # Pre-compute some stuff to speed up filter construction + grid_x, grid_y = _get_meshgrid((H, W)) + radius = torch.sqrt(grid_x ** 2 + grid_y ** 2) + theta = torch.atan2(-grid_y, grid_x).t() + + # Quadrant shift radius and theta so that filters are constructed with 0 frequency at the corners. + # Get rid of the 0 radius value at the 0 frequency point (now at top-left corner) + # so that taking the log of the radius will not cause trouble. + radius = ifftshift(radius) + theta = ifftshift(theta) + radius[0, 0] = 1 + + sintheta = torch.sin(theta) + costheta = torch.cos(theta) + + # Filters are constructed in terms of two components. + # 1) The radial component, which controls the frequency band that the filter responds to + # 2) The angular component, which controls the orientation that the filter responds to. + # The two components are multiplied together to construct the overall filter. + + # First construct a low-pass filter that is as large as possible, yet falls + # away to zero at the boundaries. All log Gabor filters are multiplied by + # this to ensure no extra frequencies at the 'corners' of the FFT are + # incorporated as this seems to upset the normalisation process when + lp = _lowpassfilter(size=(H, W), cutoff=.45, n=15) + + # Construct the radial filter components... + logGabor = [] + for s in range(scales): + wavelength = min_length * mult ** s + fo = 1.0 / wavelength # Centre frequency of filter. + gabor_filter = torch.exp((- torch.log(radius / fo) ** 2) / (2 * math.log(sigma_f) ** 2)) + gabor_filter = gabor_filter * lp + gabor_filter[0, 0] = 0 + logGabor.append(gabor_filter) + + # Then construct the angular filter components... + spread = [] + for o in range(orientations): + angl = o * math.pi / orientations + + # For each point in the filter matrix calculate the angular distance from + # the specified filter orientation. To overcome the angular wrap-around + # problem sine difference and cosine difference values are first computed + # and then the atan2 function is used to determine angular distance. + ds = sintheta * math.cos(angl) - costheta * math.sin(angl) # Difference in sine. + dc = costheta * math.cos(angl) + sintheta * math.sin(angl) # Difference in cosine. + dtheta = torch.abs(torch.atan2(ds, dc)) + spread.append(torch.exp((- dtheta ** 2) / (2 * theta_sigma ** 2))) + + spread = torch.stack(spread) + logGabor = torch.stack(logGabor) + + # Multiply, add batch dimension and transfer to correct device. + filters = (spread.repeat_interleave(scales, dim=0) * logGabor.repeat(orientations, 1, 1)).unsqueeze(0).to(x) + return filters + + +def _phase_congruency(x: torch.Tensor, scales: int = 4, orientations: int = 4, + min_length: int = 6, mult: int = 2, sigma_f: float = 0.55, + delta_theta: float = 1.2, k: float = 2.0) -> torch.Tensor: + r"""Compute Phase Congruence for a batch of greyscale images + + Args: + x: Tensor with shape Bx1xHxW + levels: Number of wavelet scales + orientations: Number of filter orientations + min_length: Wavelength of smallest scale filter + mult: Scaling factor between successive filters + sigma_f: Ratio of the standard deviation of the Gaussian + describing the log Gabor filter's transfer function + in the frequency domain to the filter center frequency. + delta_theta: Ratio of angular interval between filter orientations + and the standard deviation of the angular Gaussian function + used to construct filters in the freq. plane. + k: No of standard deviations of the noise energy beyond the mean + at which we set the noise threshold point, below which phase + congruency values get penalized. + """ + EPS = 1e-4 + + B, _, H, W = x.shape + + # Fourier transform + imagefft = torch.rfft(x, 2, onesided=False) + + filters = _construct_filters(x, scales, orientations, min_length, mult, sigma_f, delta_theta, k) + + filters_ifft = torch.ifft(torch.stack([filters, torch.zeros_like(filters)], dim=-1), 2)[..., 0] * math.sqrt(H * W) + + # Convolve image with even and odd filters + E0 = torch.ifft(imagefft * filters.unsqueeze(-1), 2).view(B, orientations, scales, H, W, 2) + + # Amplitude of even & odd filter response. An = sqrt(real^2 + imag^2) + An = torch.sqrt(torch.sum(E0 ** 2, dim=-1)) + + # Take filter at scale 0 and sum spatially + # Record mean squared filter value at smallest scale. + # This is used for noise estimation. + EM_n = (filters.view(1, orientations, scales, H, W)[:, :, :1, ...] ** 2).sum(dim=[-2, -1], keepdims=True) + + # Sum of amplitude responses + sumAn = An.sum(dim=2, keepdims=True) + + # Sum of even filter convolution results. + sumE = E0[..., 0].sum(dim=2, keepdims=True) + + # Sum of odd filter convolution results. + sumO = E0[..., 1].sum(dim=2, keepdims=True) + + # Get weighted mean filter response vector, this gives the weighted mean phase angle. + XEnergy = torch.sqrt(sumE ** 2 + sumO ** 2) + EPS + + MeanE = sumE / XEnergy + MeanO = sumO / XEnergy + + # Now calculate An(cos(phase_deviation) - | sin(phase_deviation)) | by + # using dot and cross products between the weighted mean filter response + # vector and the individual filter response vectors at each scale. + # This quantity is phase congruency multiplied by An, which we call energy. + + # Extract even and odd convolution results. + E = E0[..., 0] + O = E0[..., 1] + + Energy = (E * MeanE + O * MeanO - torch.abs(E * MeanO - O * MeanE)).sum(dim=2, keepdim=True) + + # Compensate for noise + # We estimate the noise power from the energy squared response at the + # smallest scale. If the noise is Gaussian the energy squared will have a + # Chi-squared 2DOF pdf. We calculate the median energy squared response + # as this is a robust statistic. From this we estimate the mean. + # The estimate of noise power is obtained by dividing the mean squared + # energy value by the mean squared filter value + + absE0 = torch.sqrt(torch.sum(E0[:, :, :1, ...] ** 2, dim=-1)).reshape(B, orientations, 1, 1, H * W) + medianE2n = torch.median(absE0 ** 2, dim=-1, keepdims=True).values + + meanE2n = - medianE2n / math.log(0.5) + + # Estimate of noise power. + noisePower = meanE2n / EM_n + + # Now estimate the total energy^2 due to noise + # Estimate for sum(An^2) + sum(Ai.*Aj.*(cphi.*cphj + sphi.*sphj)) + filters_ifft = filters_ifft.view(1, orientations, scales, H, W) + + EstSumAn2 = torch.sum(filters_ifft ** 2, dim=-3, keepdim=True) + + EstSumAiAj = torch.zeros(B, orientations, 1, H, W).to(x) + for s in range(scales - 1): + EstSumAiAj = EstSumAiAj + (filters_ifft[:, :, s: s + 1] * filters_ifft[:, :, s + 1:]).sum(dim=-3, keepdim=True) + + sumEstSumAn2 = torch.sum(EstSumAn2, dim=[-1, -2], keepdim=True) + sumEstSumAiAj = torch.sum(EstSumAiAj, dim=[-1, -2], keepdim=True) + + EstNoiseEnergy2 = 2 * noisePower * sumEstSumAn2 + 4 * noisePower * sumEstSumAiAj + + # Rayleigh parameter + tau = torch.sqrt(EstNoiseEnergy2 / 2) + + # Expected value of noise energy + EstNoiseEnergy = tau * math.sqrt(math.pi / 2) + EstNoiseEnergySigma = torch.sqrt((2 - math.pi / 2) * tau ** 2) + + # Noise threshold + T = EstNoiseEnergy + k * EstNoiseEnergySigma + + # The estimated noise effect calculated above is only valid for the PC_1 measure. + # The PC_2 measure does not lend itself readily to the same analysis. However + # empirically it seems that the noise effect is overestimated roughly by a factor + # of 1.7 for the filter parameters used here. + + # Empirical rescaling of the estimated noise effect to suit the PC_2 phase congruency measure + T = T / 1.7 + + # Apply noise threshold + Energy = torch.max(Energy - T, torch.zeros_like(T)) + + EnergyAll = Energy.sum(dim=1, keepdims=True) + + sumAn = An.sum(dim=2, keepdims=True) + + AnAll = sumAn.sum(dim=1, keepdims=True) + + ResultPC = (EnergyAll / AnAll).view(B, 1, H, W) + return ResultPC + + +def _get_meshgrid(size): + if size[0] % 2: + # Odd + x = torch.range(-(size[0] - 1) / 2, (size[0] - 1) / 2) / (size[0] - 1) + else: + # Even + x = torch.range(- size[0] / 2, size[0] / 2 - 1) / size[0] + + if size[1] % 2: + # Odd + y = torch.range(-(size[1] - 1) / 2, (size[1] - 1) / 2) / (size[1] - 1) + else: + # Even + y = torch.range(- size[1] / 2, size[1] / 2 - 1) / size[1] + return torch.meshgrid(x, y) + + +def _lowpassfilter(size: Union[int, Tuple[int, int]], cutoff: float, n: int) -> torch.Tensor: + r""" + Constructs a low-pass Butterworth filter. + Args: + size: Tuple with heigth and width of filter to construct + cutoff: Cutoff frequency of the filter in (0, 0.5() + n: Filter order. Higher `n` means sharper transition. + Note that `n` is doubled so that it is always an even integer. + + Returns: + f = 1 / (1 + w/cutoff) ^ 2n + + Note: + The frequency origin of the returned filter is at the corners. + + """ + + assert (cutoff >= 0) and (cutoff <= 0.5), "Cutoff frequency must be between 0 and 0.5" + assert n > 1, "n must be an integer >= 1" + + grid_x, grid_y = _get_meshgrid(size) + + # A matrix with every pixel = radius relative to centre. + radius = torch.sqrt(grid_x ** 2 + grid_y ** 2) + + return ifftshift(1. / (1.0 + (radius / cutoff) ** (2 * n))) + + +def ifftshift(x, dim=None): + """ + Similar to np.fft.ifftshift but applies to PyTorch Tensors + """ + dim = tuple(range(x.dim())) + shift = [(dim + 1) // 2 for dim in x.shape] + + return roll(x, shift, dim) + + +def roll(x, shift, dim): + """ + Similar to np.roll but applies to PyTorch Tensors + """ + if isinstance(shift, (tuple, list)): + assert len(shift) == len(dim) + for s, d in zip(shift, dim): + x = roll(x, s, d) + return x + shift = shift % x.size(dim) + if shift == 0: + return x + left = x.narrow(dim, 0, x.size(dim) - shift) + right = x.narrow(dim, x.size(dim) - shift, shift) + return torch.cat((right, left), dim=dim) From d00145c1e62a4ec40d403d4539ca50944b98a546 Mon Sep 17 00:00:00 2001 From: Jamil Zakirov Date: Sun, 21 Jun 2020 16:29:58 +0300 Subject: [PATCH 2/8] Rename to piq. Small bugfix --- {photosynthesis_metrics => piq}/fsim.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) rename {photosynthesis_metrics => piq}/fsim.py (99%) diff --git a/photosynthesis_metrics/fsim.py b/piq/fsim.py similarity index 99% rename from photosynthesis_metrics/fsim.py rename to piq/fsim.py index 3e352826..d777d364 100644 --- a/photosynthesis_metrics/fsim.py +++ b/piq/fsim.py @@ -144,7 +144,7 @@ def _construct_filters(x: torch.Tensor, scales: int = 4, orientations: int = 4, # Pre-compute some stuff to speed up filter construction grid_x, grid_y = _get_meshgrid((H, W)) radius = torch.sqrt(grid_x ** 2 + grid_y ** 2) - theta = torch.atan2(-grid_y, grid_x).t() + theta = torch.atan2(-grid_y, grid_x) # Quadrant shift radius and theta so that filters are constructed with 0 frequency at the corners. # Get rid of the 0 radius value at the 0 frequency point (now at top-left corner) From 0dc69b292c3ffc9301e24945761450ab9f5d729f Mon Sep 17 00:00:00 2001 From: Jamil Zakirov Date: Sun, 21 Jun 2020 19:33:42 +0300 Subject: [PATCH 3/8] feature/fsim: Big fixes --- piq/fsim.py | 33 +++++++++++++++++---------------- 1 file changed, 17 insertions(+), 16 deletions(-) diff --git a/piq/fsim.py b/piq/fsim.py index d777d364..b33bd34a 100644 --- a/piq/fsim.py +++ b/piq/fsim.py @@ -3,7 +3,7 @@ import torch from typing import Union, Tuple -from photosynthesis_metrics.utils import _adjust_dimensions, _validate_input +from piq.utils import _adjust_dimensions, _validate_input def fsim(x: torch.Tensor, y: torch.Tensor, @@ -41,7 +41,7 @@ def fsim(x: torch.Tensor, y: torch.Tensor, y = y * 255 # Apply average pooling - kernel_size = max(1, min(x.shape[-2:]) // 256) + kernel_size = max(1, round(min(x.shape[-2:]) / 256)) x = torch.nn.functional.avg_pool2d(x, kernel_size, stride=2) y = torch.nn.functional.avg_pool2d(y, kernel_size, stride=2) @@ -50,7 +50,7 @@ def fsim(x: torch.Tensor, y: torch.Tensor, # Convert RGB to YIQ color space https://en.wikipedia.org/wiki/YIQ if num_channels == 3: yiq_weights = torch.tensor([ - [0.229, 0.587, 0.114], + [0.299, 0.587, 0.114], [0.5959, -0.2746, -0.3213], [0.2115, -0.5227, 0.3112]]).t().to(x) x = torch.matmul(x.permute(0, 2, 3, 1), yiq_weights).permute(0, 3, 1, 2) @@ -59,10 +59,10 @@ def fsim(x: torch.Tensor, y: torch.Tensor, x_Y = x[:, : 1, :, :] y_Y = y[:, : 1, :, :] - x_I = x[:, 1: 2, :, :] - y_I = y[:, 1: 2, :, :] - x_Q = x[:, 2:, :, :] - y_Q = y[:, 2:, :, :] + x_I = x[:, 1, :, :] + y_I = y[:, 1, :, :] + x_Q = x[:, 2, :, :] + y_Q = y[:, 2, :, :] else: x_Y = x @@ -77,8 +77,8 @@ def fsim(x: torch.Tensor, y: torch.Tensor, grad_x = torch.nn.functional.conv2d(x_Y, kernel, padding=1) grad_y = torch.nn.functional.conv2d(y_Y, kernel, padding=1) - grad_map_x = torch.sqrt(torch.sum(grad_x ** 2, dim=-3, keepdim=True)) - grad_map_y = torch.sqrt(torch.sum(grad_y ** 2, dim=-3, keepdim=True)) + grad_map_x = torch.sqrt(torch.sum(grad_x ** 2, dim=-3)) + grad_map_y = torch.sqrt(torch.sum(grad_y ** 2, dim=-3)) # Constants from paper T1, T2, T3, T4, lmbda = 0.85, 160, 200, 200, 0.03 @@ -87,16 +87,16 @@ def fsim(x: torch.Tensor, y: torch.Tensor, PC = (2.0 * PCx * PCy + T1) / (PCx ** 2 + PCy ** 2 + T1) GM = (2.0 * grad_map_x * grad_map_y + T2) / (grad_map_x ** 2 + grad_map_y ** 2 + T2) PCmax = torch.where(PCx > PCy, PCx, PCy) - score = GM * PC * PCmax if chromatic: S_I = (2 * x_I * y_I + T3) / (x_I ** 2 + y_I ** 2 + T3) S_Q = (2 * x_Q * y_Q + T4) / (x_Q ** 2 + y_Q ** 2 + T4) - print(score.shape, S_I.shape, S_Q.shape) - score = score * (S_I * S_Q) ** lmbda + score = score * torch.abs(S_I * S_Q) ** lmbda + # Complex gradients will work in PyTorch 1.6.0 + # score = score * torch.real((S_I * S_Q).to(torch.complex64) ** lmbda) - result = score.sum(dim=[2, 3]) / PCmax.sum(dim=[2, 3]) + result = score.sum(dim=[1, 2]) / PCmax.sum(dim=[1, 2]) if reduction == 'none': return result @@ -229,6 +229,7 @@ def _phase_congruency(x: torch.Tensor, scales: int = 4, orientations: int = 4, filters = _construct_filters(x, scales, orientations, min_length, mult, sigma_f, delta_theta, k) + # Note rescaling to match power record ifft2 of filter filters_ifft = torch.ifft(torch.stack([filters, torch.zeros_like(filters)], dim=-1), 2)[..., 0] * math.sqrt(H * W) # Convolve image with even and odd filters @@ -320,13 +321,13 @@ def _phase_congruency(x: torch.Tensor, scales: int = 4, orientations: int = 4, # Apply noise threshold Energy = torch.max(Energy - T, torch.zeros_like(T)) - EnergyAll = Energy.sum(dim=1, keepdims=True) + EnergyAll = Energy.sum(dim=[1, 2]) sumAn = An.sum(dim=2, keepdims=True) - AnAll = sumAn.sum(dim=1, keepdims=True) + AnAll = sumAn.sum(dim=[1, 2]) - ResultPC = (EnergyAll / AnAll).view(B, 1, H, W) + ResultPC = EnergyAll / AnAll return ResultPC From cf3afa12ad342ec46903afa24c10c84f31abae07 Mon Sep 17 00:00:00 2001 From: Emil Zakirov Date: Thu, 2 Jul 2020 01:41:52 +0300 Subject: [PATCH 4/8] feature/fsim: Added docsumentation --- README.md | 29 +++++++++++++++++++++++++++++ 1 file changed, 29 insertions(+) diff --git a/README.md b/README.md index 54df6a50..a93a4a0d 100644 --- a/README.md +++ b/README.md @@ -216,6 +216,35 @@ output.backward()

+ +
+ Feature Similarity Index Measure (FSIM) +

+ + To compute [FSIM ](https://www4.comp.polyu.edu.hk/~cslzhang/IQA/TIP_IQA_FSIM.pdf) as a measure, use lower case function from the library: + ```python + import torch + from piq import fsim + + prediction = torch.rand(3, 3, 256, 256) + target = torch.rand(3, 3, 256, 256) + vsi_index: torch.Tensor = fsim(prediction, target, data_range=1.) + ``` + + In order to use FSIM as a loss function, use corresponding PyTorch module: + ```python + import torch + from piq import FSIMLoss + + loss = FSIMLoss(data_range=1.) + prediction = torch.rand(3, 3, 256, 256, requires_grad=True) + target = torch.rand(3, 3, 256, 256) + output: torch.Tensor = loss(prediction, target) + output.backward() + ``` +

+
+
Blind/Referenceless Image Spatial Quality Evaluator (BRISQUE) From f26d3f5acaa5fd9528bc11578bde627bd769f72b Mon Sep 17 00:00:00 2001 From: Emil Zakirov Date: Thu, 2 Jul 2020 01:47:24 +0300 Subject: [PATCH 5/8] feature/fsim: Lot's of new tests --- tests/assets/I01.BMP | Bin 0 -> 589878 bytes tests/assets/goldhill.gif | Bin 0 -> 262137 bytes tests/assets/goldhill_jpeg.gif | Bin 0 -> 126524 bytes tests/assets/i01_01_5.bmp | Bin 0 -> 589878 bytes tests/test_fsim.py | 116 +++++++++++++++++++++++++++++++++ 5 files changed, 116 insertions(+) create mode 100644 tests/assets/I01.BMP create mode 100644 tests/assets/goldhill.gif create mode 100644 tests/assets/goldhill_jpeg.gif create mode 100644 tests/assets/i01_01_5.bmp create mode 100644 tests/test_fsim.py diff --git a/tests/assets/I01.BMP b/tests/assets/I01.BMP new file mode 100644 index 0000000000000000000000000000000000000000..b5aaf9c7e1939e9b191e0b371b2c283d66122f77 GIT binary patch literal 589878 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zD01h{I{uvqYQ!t}2Cr4fd$qi@vxSq`N-^VTH`U=)DJ(0xeVKhfX#9ud-ODj6MC+TL zZOh6(y|XJ9WJ@;fPe$yv7qhphGClIq=uL=rVy6cF+{9aR8&<-dWQtfNU_2A^v=V`s xgc5~AfUfyvD`Z)7;@l8$Ekr#ENn4@3)2b|6L`PtPAnKLOm20tVDPBno{{Pqr torch.Tensor: + return torch.rand(3, 3, 256, 256) + + +@pytest.fixture(scope='module') +def target() -> torch.Tensor: + return torch.rand(3, 3, 256, 256) + + +@pytest.fixture(scope='module') +def prediction_grey() -> torch.Tensor: + return torch.rand(3, 3, 256, 256) + + +@pytest.fixture(scope='module') +def target_grey() -> torch.Tensor: + return torch.rand(3, 3, 256, 256) + + +# ================== Test function: `fsim` ================== +@pytest.mark.parametrize("chromatic", [False, True]) +def test_fsim_symmetry(prediction: torch.Tensor, target: torch.Tensor, chromatic: bool, device: str) -> None: + measure = fsim(prediction, target, data_range=1., chromatic=chromatic) + reverse_measure = fsim(target, prediction, data_range=1., chromatic=chromatic) + assert (measure == reverse_measure).all(), f'Expect: FSIM(a, b) == FSIM(b, a), got {measure} != {reverse_measure}' + + +@pytest.mark.parametrize( + "x,y,expectation,value", + [ + (torch.rand(4, 3, 128, 128, 2), torch.rand(4, 3, 128, 128, 2), pytest.raises(AssertionError), None), + (torch.randn(4, 3, 128, 128), torch.randn(4, 3, 128, 128), pytest.raises(AssertionError), None), + (torch.zeros(4, 3, 128, 128), torch.zeros(4, 3, 128, 128), raise_nothing(), 1.0), + (torch.ones(4, 3, 128, 128), torch.ones(4, 3, 128, 128), raise_nothing(), 1.0), + (torch.rand(4, 3, 28, 28), torch.rand(4, 3, 28, 28), raise_nothing(), None), + ], +) +def test_fsim_for_special_cases(x: torch.Tensor, y: torch.Tensor, expectation: Any, value: float) -> None: + with expectation: + if value is None: + fsim(x, y) + else: + score = fsim(x, y) + assert torch.isclose(score, torch.tensor(value)), \ + f'Expected loss value to be equal to target value. Got {score} and {value}' + + +def test_fsim_simmular_to_matlab_implementation(): + # Greyscale images + goldhill = torch.tensor(imread('tests/assets/goldhill.gif')) + goldhill_jpeg = torch.tensor(imread('tests/assets/goldhill_jpeg.gif')) + + score = fsim(goldhill_jpeg, goldhill, data_range=255, chromatic=False) + score_baseline = torch.tensor(0.89691) + + assert torch.allclose(score, score_baseline), \ + f'Expected PyTorch score to be equal to MATLAB prediction. Got {score} and {score_baseline}' + + # RGB images + I01 = torch.tensor(imread('tests/assets/I01.BMP')).permute(2, 0, 1) + i1_01_5 = torch.tensor(imread('tests/assets/i01_01_5.bmp')).permute(2, 0, 1) + + score = fsim(i1_01_5, I01, data_range=255, chromatic=False) + score_chromatic = fsim(i1_01_5, I01, data_range=255, chromatic=True) + + # Baseline values are from original MATLAB code + score_baseline = torch.tensor(0.93674) + score_baseline_chromatic = torch.tensor(0.92587) + + assert torch.allclose(score, score_baseline), \ + f'Expected PyTorch score to be equal to MATLAB prediction. Got {score} and {score_baseline}' + assert torch.allclose(score, score_baseline), \ + 'Expected PyTorch chromatic score to be equal to MATLAB prediction.' \ + f'Got {score_chromatic} and {score_baseline_chromatic}' + + +# ================== Test class: `FSIMLoss` ================== +def test_fsim_loss_reduction(prediction: torch.Tensor, target: torch.Tensor) -> None: + loss = FSIMLoss(reduction='mean') + measure = loss(prediction, target) + assert measure.dim() == 0, f'FSIM with `mean` reduction must return 1 number, got {len(measure)}' + + loss = FSIMLoss(reduction='sum') + measure = loss(prediction, target) + assert measure.dim() == 0, f'FSIM with `mean` reduction must return 1 number, got {len(measure)}' + + loss = FSIMLoss(reduction='none') + measure = loss(prediction, target) + assert len(measure) == prediction.size(0), \ + f'FSIM with `none` reduction must have length equal to number of images, got {len(measure)}' + + loss = FSIMLoss(reduction='random string') + with pytest.raises(KeyError): + loss(prediction, target) + + +def test_fsim_loss_computes_grad(prediction: torch.Tensor, target: torch.Tensor, device: str) -> None: + prediction.requires_grad_() + loss_value = FSIMLoss()(prediction, target) + loss_value.backward() + assert prediction.grad is not None, 'Expected non None gradient of leaf variable' From 9bcbc1300423ce9117f3e916ce94b5cddb9ac744 Mon Sep 17 00:00:00 2001 From: Emil Zakirov Date: Thu, 2 Jul 2020 01:49:57 +0300 Subject: [PATCH 6/8] feature/fsim: Changed FSIM logic. --- piq/__init__.py | 1 + piq/fsim.py | 284 +++++++++++++++++++++++++++------------------- piq/functional.py | 72 ++++++++++++ piq/gmsd.py | 27 +---- 4 files changed, 246 insertions(+), 138 deletions(-) create mode 100644 piq/functional.py diff --git a/piq/__init__.py b/piq/__init__.py index 7b47c6a9..62b2b3a1 100644 --- a/piq/__init__.py +++ b/piq/__init__.py @@ -12,3 +12,4 @@ from .brisque import BRISQUELoss, brisque from .perceptual import StyleLoss, ContentLoss, LPIPS from .psnr import psnr +from .fsim import fsim, FSIMLoss \ No newline at end of file diff --git a/piq/fsim.py b/piq/fsim.py index b33bd34a..d4043158 100644 --- a/piq/fsim.py +++ b/piq/fsim.py @@ -1,24 +1,43 @@ +r"""Implemetation of Feature Similarity Index Measure +Code is based on MATLAB version for computations in pixel domain +https://www4.comp.polyu.edu.hk/~cslzhang/IQA/FSIM/Files/FeatureSIM.m +References: + https://www4.comp.polyu.edu.hk/~cslzhang/IQA/TIP_IQA_FSIM.pdf +""" import math +import functools +from typing import Union, Tuple import torch -from typing import Union, Tuple +from torch.nn.modules.loss import _Loss from piq.utils import _adjust_dimensions, _validate_input +from piq.functional import ifftshift, get_meshgrid, similarity_map, gradient_map, scharr_filter -def fsim(x: torch.Tensor, y: torch.Tensor, - reduction: str = 'mean', - data_range: Union[int, float] = 1.0, - chromatic: bool = True) -> torch.Tensor: +def fsim(x: torch.Tensor, y: torch.Tensor, reduction: str = 'mean', + data_range: Union[int, float] = 1.0, chromatic: bool = True, + scales: int = 4, orientations: int = 4, min_length: int = 6, + mult: int = 2, sigma_f: float = 0.55, delta_theta: float = 1.2, + k: float = 2.0) -> torch.Tensor: r"""Compute Feature Similarity Index Measure for a batch of images. Args: x: Batch of predicted images with shape (batch_size x channels x H x W) y: Batch of target images with shape (batch_size x channels x H x W) - data_range: Value range of input images (usually 1.0 or 255). Default: 1.0 chromatic: Flag to compute FSIMc, which also takes into account chromatic components + scales: Number of wavelets used for computation of phase congruensy maps + orientations: Number of filter orientations used for computation of phase congruensy maps + min_length: Wavelength of smallest scale filter + mult: Scaling factor between successive filters + sigma_f: Ratio of the standard deviation of the Gaussian describing the log Gabor filter's + transfer function in the frequency domain to the filter center frequency. + delta_theta: Ratio of angular interval between filter orientations and the standard deviation + of the angular Gaussian function used to construct filters in the frequency plane. + k: No of standard deviations of the noise energy beyond the mean at which we set the noise + threshold point, below which phase congruency values get penalized. Returns: FSIM: Index of similarity betwen two images. Usually in [0, 1] interval. @@ -56,47 +75,52 @@ def fsim(x: torch.Tensor, y: torch.Tensor, x = torch.matmul(x.permute(0, 2, 3, 1), yiq_weights).permute(0, 3, 1, 2) y = torch.matmul(y.permute(0, 2, 3, 1), yiq_weights).permute(0, 3, 1, 2) - x_Y = x[:, : 1, :, :] - y_Y = y[:, : 1, :, :] + x_lum = x[:, : 1, :, :] + y_lum = y[:, : 1, :, :] - x_I = x[:, 1, :, :] - y_I = y[:, 1, :, :] - x_Q = x[:, 2, :, :] - y_Q = y[:, 2, :, :] + x_i = x[:, 1:2, :, :] + y_i = y[:, 1:2, :, :] + x_q = x[:, 2:, :, :] + y_q = y[:, 2:, :, :] else: - x_Y = x - y_Y = y + x_lum = x + y_lum = y # Compute phase congruency maps - PCx = _phase_congruency(x_Y) - PCy = _phase_congruency(y_Y) + pc_x = _phase_congruency( + x_lum, scales=scales, orientations=orientations, + min_length=min_length, mult=mult, sigma_f=sigma_f, + delta_theta=delta_theta, k=k + ) + pc_y = _phase_congruency( + y_lum, scales=scales, orientations=orientations, + min_length=min_length, mult=mult, sigma_f=sigma_f, + delta_theta=delta_theta, k=k + ) # Gradient maps - kernel = torch.stack([_scharr_filter(), _scharr_filter().transpose(-1, -2)]).to(x) - grad_x = torch.nn.functional.conv2d(x_Y, kernel, padding=1) - grad_y = torch.nn.functional.conv2d(y_Y, kernel, padding=1) - - grad_map_x = torch.sqrt(torch.sum(grad_x ** 2, dim=-3)) - grad_map_y = torch.sqrt(torch.sum(grad_y ** 2, dim=-3)) + kernels = torch.stack([scharr_filter(), scharr_filter().transpose(-1, -2)]) + grad_map_x = gradient_map(x_lum, kernels) + grad_map_y = gradient_map(y_lum, kernels) # Constants from paper T1, T2, T3, T4, lmbda = 0.85, 160, 200, 200, 0.03 # Compute FSIM - PC = (2.0 * PCx * PCy + T1) / (PCx ** 2 + PCy ** 2 + T1) - GM = (2.0 * grad_map_x * grad_map_y + T2) / (grad_map_x ** 2 + grad_map_y ** 2 + T2) - PCmax = torch.where(PCx > PCy, PCx, PCy) - score = GM * PC * PCmax + PC = similarity_map(pc_x, pc_y, T1) + GM = similarity_map(grad_map_x, grad_map_y, T2) + pc_max = torch.where(pc_x > pc_y, pc_x, pc_y) + score = GM * PC * pc_max if chromatic: - S_I = (2 * x_I * y_I + T3) / (x_I ** 2 + y_I ** 2 + T3) - S_Q = (2 * x_Q * y_Q + T4) / (x_Q ** 2 + y_Q ** 2 + T4) + S_I = similarity_map(x_i, y_i, T3) + S_Q = similarity_map(x_q, y_q, T4) score = score * torch.abs(S_I * S_Q) ** lmbda # Complex gradients will work in PyTorch 1.6.0 # score = score * torch.real((S_I * S_Q).to(torch.complex64) ** lmbda) - result = score.sum(dim=[1, 2]) / PCmax.sum(dim=[1, 2]) + result = score.sum(dim=[1, 2, 3]) / pc_max.sum(dim=[1, 2, 3]) if reduction == 'none': return result @@ -106,14 +130,6 @@ def fsim(x: torch.Tensor, y: torch.Tensor, }[reduction](dim=0) -def _scharr_filter() -> torch.Tensor: - """Utility function that returns a normalized 3x3 Scharr kernel in X direction - Return: - kernel: Tensor with shape 1x3x3""" - kernel = torch.tensor([[[-3., 0., 3.], [-10., 0., 10.], [-3., 0., 3.]]]) / 16 - return kernel - - def _construct_filters(x: torch.Tensor, scales: int = 4, orientations: int = 4, min_length: int = 6, mult: int = 2, sigma_f: float = 0.55, delta_theta: float = 1.2, k: float = 2.0): @@ -142,7 +158,7 @@ def _construct_filters(x: torch.Tensor, scales: int = 4, orientations: int = 4, theta_sigma = math.pi / (orientations * delta_theta) # Pre-compute some stuff to speed up filter construction - grid_x, grid_y = _get_meshgrid((H, W)) + grid_x, grid_y = get_meshgrid((H, W)) radius = torch.sqrt(grid_x ** 2 + grid_y ** 2) theta = torch.atan2(-grid_y, grid_x) @@ -168,14 +184,14 @@ def _construct_filters(x: torch.Tensor, scales: int = 4, orientations: int = 4, lp = _lowpassfilter(size=(H, W), cutoff=.45, n=15) # Construct the radial filter components... - logGabor = [] + log_gabor = [] for s in range(scales): wavelength = min_length * mult ** s fo = 1.0 / wavelength # Centre frequency of filter. gabor_filter = torch.exp((- torch.log(radius / fo) ** 2) / (2 * math.log(sigma_f) ** 2)) gabor_filter = gabor_filter * lp gabor_filter[0, 0] = 0 - logGabor.append(gabor_filter) + log_gabor.append(gabor_filter) # Then construct the angular filter components... spread = [] @@ -192,10 +208,10 @@ def _construct_filters(x: torch.Tensor, scales: int = 4, orientations: int = 4, spread.append(torch.exp((- dtheta ** 2) / (2 * theta_sigma ** 2))) spread = torch.stack(spread) - logGabor = torch.stack(logGabor) + log_gabor = torch.stack(log_gabor) # Multiply, add batch dimension and transfer to correct device. - filters = (spread.repeat_interleave(scales, dim=0) * logGabor.repeat(orientations, 1, 1)).unsqueeze(0).to(x) + filters = (spread.repeat_interleave(scales, dim=0) * log_gabor.repeat(orientations, 1, 1)).unsqueeze(0).to(x) return filters @@ -219,6 +235,9 @@ def _phase_congruency(x: torch.Tensor, scales: int = 4, orientations: int = 4, k: No of standard deviations of the noise energy beyond the mean at which we set the noise threshold point, below which phase congruency values get penalized. + Returns: + PCmap: Tensor with shape BxHxW + """ EPS = 1e-4 @@ -236,27 +255,24 @@ def _phase_congruency(x: torch.Tensor, scales: int = 4, orientations: int = 4, E0 = torch.ifft(imagefft * filters.unsqueeze(-1), 2).view(B, orientations, scales, H, W, 2) # Amplitude of even & odd filter response. An = sqrt(real^2 + imag^2) - An = torch.sqrt(torch.sum(E0 ** 2, dim=-1)) + an = torch.sqrt(torch.sum(E0 ** 2, dim=-1)) # Take filter at scale 0 and sum spatially # Record mean squared filter value at smallest scale. # This is used for noise estimation. - EM_n = (filters.view(1, orientations, scales, H, W)[:, :, :1, ...] ** 2).sum(dim=[-2, -1], keepdims=True) - - # Sum of amplitude responses - sumAn = An.sum(dim=2, keepdims=True) - + em_n = (filters.view(1, orientations, scales, H, W)[:, :, :1, ...] ** 2).sum(dim=[-2, -1], keepdims=True) + # Sum of even filter convolution results. - sumE = E0[..., 0].sum(dim=2, keepdims=True) + sum_e = E0[..., 0].sum(dim=2, keepdims=True) # Sum of odd filter convolution results. - sumO = E0[..., 1].sum(dim=2, keepdims=True) + sum_o = E0[..., 1].sum(dim=2, keepdims=True) # Get weighted mean filter response vector, this gives the weighted mean phase angle. - XEnergy = torch.sqrt(sumE ** 2 + sumO ** 2) + EPS + x_energy = torch.sqrt(sum_e ** 2 + sum_o ** 2) + EPS - MeanE = sumE / XEnergy - MeanO = sumO / XEnergy + mean_e = sum_e / x_energy + mean_o = sum_o / x_energy # Now calculate An(cos(phase_deviation) - | sin(phase_deviation)) | by # using dot and cross products between the weighted mean filter response @@ -267,7 +283,7 @@ def _phase_congruency(x: torch.Tensor, scales: int = 4, orientations: int = 4, E = E0[..., 0] O = E0[..., 1] - Energy = (E * MeanE + O * MeanO - torch.abs(E * MeanO - O * MeanE)).sum(dim=2, keepdim=True) + energy = (E * mean_e + O * mean_o - torch.abs(E * mean_o - O * mean_e)).sum(dim=2, keepdim=True) # Compensate for noise # We estimate the noise power from the energy squared response at the @@ -277,38 +293,38 @@ def _phase_congruency(x: torch.Tensor, scales: int = 4, orientations: int = 4, # The estimate of noise power is obtained by dividing the mean squared # energy value by the mean squared filter value - absE0 = torch.sqrt(torch.sum(E0[:, :, :1, ...] ** 2, dim=-1)).reshape(B, orientations, 1, 1, H * W) - medianE2n = torch.median(absE0 ** 2, dim=-1, keepdims=True).values + abs_e0 = torch.sqrt(torch.sum(E0[:, :, :1, ...] ** 2, dim=-1)).reshape(B, orientations, 1, 1, H * W) + median_e2n = torch.median(abs_e0 ** 2, dim=-1, keepdims=True).values - meanE2n = - medianE2n / math.log(0.5) + mean_e2n = - median_e2n / math.log(0.5) # Estimate of noise power. - noisePower = meanE2n / EM_n + noisePower = mean_e2n / em_n # Now estimate the total energy^2 due to noise # Estimate for sum(An^2) + sum(Ai.*Aj.*(cphi.*cphj + sphi.*sphj)) filters_ifft = filters_ifft.view(1, orientations, scales, H, W) - EstSumAn2 = torch.sum(filters_ifft ** 2, dim=-3, keepdim=True) + sum_an2 = torch.sum(filters_ifft ** 2, dim=-3, keepdim=True) - EstSumAiAj = torch.zeros(B, orientations, 1, H, W).to(x) + sum_ai_aj = torch.zeros(B, orientations, 1, H, W).to(x) for s in range(scales - 1): - EstSumAiAj = EstSumAiAj + (filters_ifft[:, :, s: s + 1] * filters_ifft[:, :, s + 1:]).sum(dim=-3, keepdim=True) + sum_ai_aj = sum_ai_aj + (filters_ifft[:, :, s: s + 1] * filters_ifft[:, :, s + 1:]).sum(dim=-3, keepdim=True) - sumEstSumAn2 = torch.sum(EstSumAn2, dim=[-1, -2], keepdim=True) - sumEstSumAiAj = torch.sum(EstSumAiAj, dim=[-1, -2], keepdim=True) + sum_an2 = torch.sum(sum_an2, dim=[-1, -2], keepdim=True) + sum_ai_aj = torch.sum(sum_ai_aj, dim=[-1, -2], keepdim=True) - EstNoiseEnergy2 = 2 * noisePower * sumEstSumAn2 + 4 * noisePower * sumEstSumAiAj + noise_energy2 = 2 * noisePower * sum_an2 + 4 * noisePower * sum_ai_aj # Rayleigh parameter - tau = torch.sqrt(EstNoiseEnergy2 / 2) + tau = torch.sqrt(noise_energy2 / 2) # Expected value of noise energy - EstNoiseEnergy = tau * math.sqrt(math.pi / 2) - EstNoiseEnergySigma = torch.sqrt((2 - math.pi / 2) * tau ** 2) + noise_energy = tau * math.sqrt(math.pi / 2) + moise_energy_sigma = torch.sqrt((2 - math.pi / 2) * tau ** 2) # Noise threshold - T = EstNoiseEnergy + k * EstNoiseEnergySigma + T = noise_energy + k * moise_energy_sigma # The estimated noise effect calculated above is only valid for the PC_1 measure. # The PC_2 measure does not lend itself readily to the same analysis. However @@ -319,33 +335,13 @@ def _phase_congruency(x: torch.Tensor, scales: int = 4, orientations: int = 4, T = T / 1.7 # Apply noise threshold - Energy = torch.max(Energy - T, torch.zeros_like(T)) + energy = torch.max(energy - T, torch.zeros_like(T)) - EnergyAll = Energy.sum(dim=[1, 2]) - - sumAn = An.sum(dim=2, keepdims=True) - - AnAll = sumAn.sum(dim=[1, 2]) - - ResultPC = EnergyAll / AnAll - return ResultPC - - -def _get_meshgrid(size): - if size[0] % 2: - # Odd - x = torch.range(-(size[0] - 1) / 2, (size[0] - 1) / 2) / (size[0] - 1) - else: - # Even - x = torch.range(- size[0] / 2, size[0] / 2 - 1) / size[0] - - if size[1] % 2: - # Odd - y = torch.range(-(size[1] - 1) / 2, (size[1] - 1) / 2) / (size[1] - 1) - else: - # Even - y = torch.range(- size[1] / 2, size[1] / 2 - 1) / size[1] - return torch.meshgrid(x, y) + eps = torch.finfo(energy.dtype).eps + energy_all = energy.sum(dim=[1, 2]) + eps + an_all = an.sum(dim=[1, 2]) + eps + result_pc = energy_all / an_all + return result_pc.unsqueeze(1) def _lowpassfilter(size: Union[int, Tuple[int, int]], cutoff: float, n: int) -> torch.Tensor: @@ -368,7 +364,7 @@ def _lowpassfilter(size: Union[int, Tuple[int, int]], cutoff: float, n: int) -> assert (cutoff >= 0) and (cutoff <= 0.5), "Cutoff frequency must be between 0 and 0.5" assert n > 1, "n must be an integer >= 1" - grid_x, grid_y = _get_meshgrid(size) + grid_x, grid_y = get_meshgrid(size) # A matrix with every pixel = radius relative to centre. radius = torch.sqrt(grid_x ** 2 + grid_y ** 2) @@ -376,28 +372,82 @@ def _lowpassfilter(size: Union[int, Tuple[int, int]], cutoff: float, n: int) -> return ifftshift(1. / (1.0 + (radius / cutoff) ** (2 * n))) -def ifftshift(x, dim=None): - """ - Similar to np.fft.ifftshift but applies to PyTorch Tensors - """ - dim = tuple(range(x.dim())) - shift = [(dim + 1) // 2 for dim in x.shape] +class FSIMLoss(_Loss): + r"""Creates a criterion that measures the FSIM or FSIMc for input :math:`x` and target :math:`y`. - return roll(x, shift, dim) + In order to be considered as a loss, value `1 - clip(FSIM, min=0, max=1)` is returned. If you need FSIM value, + use function `fsim` instead. + Args: + chromatic: Flag to compute FSIMc, which also takes into account chromatic components + reduction: Specifies the reduction to apply to the output: + ``'none'`` | ``'mean'`` | ``'sum'``. ``'none'``: no reduction will be applied, + ``'mean'``: the sum of the output will be divided by the number of + elements in the output, ``'sum'``: the output will be summed. Note: :attr:`size_average` + and :attr:`reduce` are in the process of being deprecated, and in the meantime, + specifying either of those two args will override :attr:`reduction`. Default: ``'mean'`` + data_range: The difference between the maximum and minimum of the pixel value, + i.e., if for image x it holds min(x) = 0 and max(x) = 1, then data_range = 1. + The pixel value interval of both input and output should remain the same. + scales: Number of wavelets used for computation of phase congruensy maps + orientations: Number of filter orientations used for computation of phase congruensy maps + min_length: Wavelength of smallest scale filter + mult: Scaling factor between successive filters + sigma_f: Ratio of the standard deviation of the Gaussian describing the log Gabor filter's + transfer function in the frequency domain to the filter center frequency. + delta_theta: Ratio of angular interval between filter orientations and the standard deviation + of the angular Gaussian function used to construct filters in the frequency plane. + k: No of standard deviations of the noise energy beyond the mean at which we set the noise + threshold point, below which phase congruency values get penalized. + + Shape: + - Input: Required to be 2D (H, W), 3D (C,H,W), 4D (N,C,H,W) or 5D (N,C,H,W,2), channels first. + - Target: Required to be 2D (H, W), 3D (C,H,W), 4D (N,C,H,W) or 5D (N,C,H,W,2), channels first. + + Examples:: + + >>> loss = FSIMLoss() + >>> prediction = torch.rand(3, 3, 256, 256, requires_grad=True) + >>> target = torch.rand(3, 3, 256, 256) + >>> output = loss(prediction, target) + >>> output.backward() + + References: + .. [1] Anish Mittal et al. "No-Reference Image Quality Assessment in the Spatial Domain", + https://live.ece.utexas.edu/publications/2012/TIP%20BRISQUE.pdf + """ + def __init__(self, data_range: Union[int, float] = 1., reduction: str = 'mean', scales: int = 4, + orientations: int = 4, min_length: int = 6, mult: int = 2, sigma_f: float = 0.55, + delta_theta: float = 1.2, k: float = 2.0) -> None: + + super().__init__() + self.data_range = data_range + self.reduction = reduction + + # Save function with predefined parameters, rather than parameters themself + self.fsim = functools.partial( + fsim, + data_range=data_range, + reduction=reduction, + scales=scales, + orientations=orientations, + min_length=min_length, + mult=mult, + sigma_f=sigma_f, + delta_theta=delta_theta, + k=k, + ) + + def forward(self, prediction: torch.Tensor, target: torch.Tensor) -> torch.Tensor: + r"""Computation of FSIM as a loss function. + Args: + prediction: Tensor of prediction of the network. + target: Reference tensor. + Returns: + Value of FSIM loss to be minimized. 0 <= FSIM <= 1. + """ + # All checks are done inside fsim function + score = self.fsim(prediction, target) -def roll(x, shift, dim): - """ - Similar to np.roll but applies to PyTorch Tensors - """ - if isinstance(shift, (tuple, list)): - assert len(shift) == len(dim) - for s, d in zip(shift, dim): - x = roll(x, s, d) - return x - shift = shift % x.size(dim) - if shift == 0: - return x - left = x.narrow(dim, 0, x.size(dim) - shift) - right = x.narrow(dim, x.size(dim) - shift, shift) - return torch.cat((right, left), dim=dim) + # Make sure value to be in [0, 1] range and convert to loss + return 1 - torch.clamp(score, 0, 1) diff --git a/piq/functional.py b/piq/functional.py new file mode 100644 index 00000000..3c7fcf9e --- /dev/null +++ b/piq/functional.py @@ -0,0 +1,72 @@ +from typing import Tuple + +import torch + + +def ifftshift(x: torch.Tensor): + """ Similar to np.fft.ifftshift but applies to PyTorch Tensors + """ + shift = [-(ax // 2) for ax in x.size()] + return torch.roll(x, shift, tuple(range(len(shift)))) + + +def get_meshgrid(size: Tuple[int, int]) -> torch.Tensor: + """ + Args: + size: Shape of meshgrid to create + """ + if size[0] % 2: + # Odd + x = torch.range(-(size[0] - 1) / 2, (size[0] - 1) / 2) / (size[0] - 1) + else: + # Even + x = torch.range(- size[0] / 2, size[0] / 2 - 1) / size[0] + + if size[1] % 2: + # Odd + y = torch.range(-(size[1] - 1) / 2, (size[1] - 1) / 2) / (size[1] - 1) + else: + # Even + y = torch.range(- size[1] / 2, size[1] / 2 - 1) / size[1] + return torch.meshgrid(x, y) + + +def similarity_map(map_x: torch.Tensor, map_y: torch.Tensor, C: float) -> torch.Tensor: + """ Compute similarity_map between two tensors using Dice-like equation. + + Args: + map_x: Tensor with map to be compared + map_y: Tensor with map to be compared + constant: Used for numerical stability + """ + return (2.0 * map_x * map_y + C) / (map_x ** 2 + map_y ** 2 + C) + + +def gradient_map(x: torch.Tensor, kernels: torch.Tensor) -> torch.Tensor: + """ Compute gradient map for a given tensor and stack of kernels. + + Args: + x: Tensor with shape B x C x H x W + kernels: Stack of tensors for gradient computation with shape N x k_W x k_H + Returns: + Gradients of x per-channel with shape B x C x H x W + """ + padding = kernels.size(-1) // 2 + grads = torch.nn.functional.conv2d(x, kernels.to(x), padding=padding) + + return torch.sqrt(torch.sum(grads ** 2, dim=-3, keepdim=True)) + + +# Gradinet operator kernels +def scharr_filter() -> torch.Tensor: + """Utility function that returns a normalized 3x3 Scharr kernel in X direction + Returns: + kernel: Tensor with shape 1x3x3""" + return torch.tensor([[[-3., 0., 3.], [-10., 0., 10.], [-3., 0., 3.]]]) / 16 + + +def prewitt_filter() -> torch.Tensor: + """Utility function that returns a normalized 3x3 Prewitt kernel in X direction + Returns: + kernel: Tensor with shape 1x3x3""" + return torch.tensor([[[-1., 0., 1.], [-1., 0., 1.], [-1., 0., 1.]]]) / 3 diff --git a/piq/gmsd.py b/piq/gmsd.py index f7aa8caf..32e3a6d4 100644 --- a/piq/gmsd.py +++ b/piq/gmsd.py @@ -15,13 +15,7 @@ from torch.nn.modules.loss import _Loss from piq.utils import _adjust_dimensions, _validate_input - - -def _prewitt_filter() -> torch.Tensor: - """Utility function that returns a normalized 3x3 prewitt kernel in X direction""" - # Normalize - kernel = torch.tensor([[-1., 0., 1.], [-1., 0., 1.], [-1., 0., 1.]]) / 3 - return kernel +from piq.functional import similarity_map, gradient_map, prewitt_filter def _gmsd(prediction: torch.Tensor, target: torch.Tensor, @@ -54,23 +48,14 @@ def _gmsd(prediction: torch.Tensor, target: torch.Tensor, # Add channel dimension prediction = prediction[:, None, :, :] target = target[:, None, :, :] - - kernel = _prewitt_filter() - kernel_x = kernel.view(1, 1, 3, 3).to(prediction) - kernel_y = kernel.t().view(1, 1, 3, 3).to(prediction) - - pred_grad_x = F.conv2d(prediction, kernel_x) - pred_grad_y = F.conv2d(prediction, kernel_y) - - trgt_grad_x = F.conv2d(target, kernel_x) - trgt_grad_y = F.conv2d(target, kernel_y) # Compute grad direction - pred_grad = torch.sqrt(pred_grad_x ** 2 + pred_grad_y ** 2) - trgt_grad = torch.sqrt(trgt_grad_x ** 2 + trgt_grad_y ** 2) - + kernels = torch.stack([prewitt_filter(), prewitt_filter().transpose(-1, -2)]) + pred_grad = gradient_map(prediction, kernels) + trgt_grad = gradient_map(target, kernels) + # Compute GMS - gms = (2.0 * pred_grad * trgt_grad + EPS) / (pred_grad ** 2 + trgt_grad ** 2 + EPS) + gms = similarity_map(pred_grad, trgt_grad, EPS) mean_gms = torch.mean(gms, dim=[1, 2, 3], keepdims=True) # Compute GMSD along spatial dimensions. Shape (batch_size ) From 310352dd5854f00d21db4a5d1a8943235beef8d2 Mon Sep 17 00:00:00 2001 From: Emil Zakirov Date: Thu, 2 Jul 2020 01:53:15 +0300 Subject: [PATCH 7/8] feature/fsim: Sonar code smell fixes --- piq/fsim.py | 4 ++-- piq/functional.py | 4 ++-- 2 files changed, 4 insertions(+), 4 deletions(-) diff --git a/piq/fsim.py b/piq/fsim.py index d4043158..623d1061 100644 --- a/piq/fsim.py +++ b/piq/fsim.py @@ -299,7 +299,7 @@ def _phase_congruency(x: torch.Tensor, scales: int = 4, orientations: int = 4, mean_e2n = - median_e2n / math.log(0.5) # Estimate of noise power. - noisePower = mean_e2n / em_n + noise_power = mean_e2n / em_n # Now estimate the total energy^2 due to noise # Estimate for sum(An^2) + sum(Ai.*Aj.*(cphi.*cphj + sphi.*sphj)) @@ -314,7 +314,7 @@ def _phase_congruency(x: torch.Tensor, scales: int = 4, orientations: int = 4, sum_an2 = torch.sum(sum_an2, dim=[-1, -2], keepdim=True) sum_ai_aj = torch.sum(sum_ai_aj, dim=[-1, -2], keepdim=True) - noise_energy2 = 2 * noisePower * sum_an2 + 4 * noisePower * sum_ai_aj + noise_energy2 = 2 * noise_power * sum_an2 + 4 * noise_power * sum_ai_aj # Rayleigh parameter tau = torch.sqrt(noise_energy2 / 2) diff --git a/piq/functional.py b/piq/functional.py index 3c7fcf9e..b577e483 100644 --- a/piq/functional.py +++ b/piq/functional.py @@ -31,7 +31,7 @@ def get_meshgrid(size: Tuple[int, int]) -> torch.Tensor: return torch.meshgrid(x, y) -def similarity_map(map_x: torch.Tensor, map_y: torch.Tensor, C: float) -> torch.Tensor: +def similarity_map(map_x: torch.Tensor, map_y: torch.Tensor, constant: float) -> torch.Tensor: """ Compute similarity_map between two tensors using Dice-like equation. Args: @@ -39,7 +39,7 @@ def similarity_map(map_x: torch.Tensor, map_y: torch.Tensor, C: float) -> torch. map_y: Tensor with map to be compared constant: Used for numerical stability """ - return (2.0 * map_x * map_y + C) / (map_x ** 2 + map_y ** 2 + C) + return (2.0 * map_x * map_y + constant) / (map_x ** 2 + map_y ** 2 + constant) def gradient_map(x: torch.Tensor, kernels: torch.Tensor) -> torch.Tensor: From e96067509484bb2494a75993abab2f93e07aa8c2 Mon Sep 17 00:00:00 2001 From: Emil Zakirov Date: Mon, 6 Jul 2020 11:08:44 +0300 Subject: [PATCH 8/8] feature/fsim: Apply suggestions from code review. --- README.md | 2 +- piq/fsim.py | 65 +++++++++++++++++++++------------------------- tests/test_fsim.py | 6 ++--- 3 files changed, 34 insertions(+), 39 deletions(-) diff --git a/README.md b/README.md index 9e4bd219..e0db123d 100644 --- a/README.md +++ b/README.md @@ -222,7 +222,7 @@ output.backward()

Feature Similarity Index Measure (FSIM)

- To compute [FSIM ](https://www4.comp.polyu.edu.hk/~cslzhang/IQA/TIP_IQA_FSIM.pdf) as a measure, use lower case function from the library: + To compute [FSIM](https://www4.comp.polyu.edu.hk/~cslzhang/IQA/TIP_IQA_FSIM.pdf) as a measure, use lower case function from the library: ```python import torch from piq import fsim diff --git a/piq/fsim.py b/piq/fsim.py index 623d1061..78f16fd5 100644 --- a/piq/fsim.py +++ b/piq/fsim.py @@ -12,7 +12,7 @@ from torch.nn.modules.loss import _Loss from piq.utils import _adjust_dimensions, _validate_input -from piq.functional import ifftshift, get_meshgrid, similarity_map, gradient_map, scharr_filter +from piq.functional import ifftshift, get_meshgrid, similarity_map, gradient_map, scharr_filter, rgb2yiq def fsim(x: torch.Tensor, y: torch.Tensor, reduction: str = 'mean', @@ -41,9 +41,9 @@ def fsim(x: torch.Tensor, y: torch.Tensor, reduction: str = 'mean', Returns: FSIM: Index of similarity betwen two images. Usually in [0, 1] interval. - Can be bigger than 1 for predicted images with higher contrast than original one. + Can be bigger than 1 for predicted images with higher contrast than the original ones. Note: - This implementation is based on original authors MATLAB code. + This implementation is based on the original MATLAB code. https://www4.comp.polyu.edu.hk/~cslzhang/IQA/FSIM/FSIM.htm """ @@ -61,27 +61,23 @@ def fsim(x: torch.Tensor, y: torch.Tensor, reduction: str = 'mean', # Apply average pooling kernel_size = max(1, round(min(x.shape[-2:]) / 256)) - x = torch.nn.functional.avg_pool2d(x, kernel_size, stride=2) - y = torch.nn.functional.avg_pool2d(y, kernel_size, stride=2) + x = torch.nn.functional.avg_pool2d(x, kernel_size) + y = torch.nn.functional.avg_pool2d(y, kernel_size) num_channels = x.size(1) # Convert RGB to YIQ color space https://en.wikipedia.org/wiki/YIQ if num_channels == 3: - yiq_weights = torch.tensor([ - [0.299, 0.587, 0.114], - [0.5959, -0.2746, -0.3213], - [0.2115, -0.5227, 0.3112]]).t().to(x) - x = torch.matmul(x.permute(0, 2, 3, 1), yiq_weights).permute(0, 3, 1, 2) - y = torch.matmul(y.permute(0, 2, 3, 1), yiq_weights).permute(0, 3, 1, 2) - - x_lum = x[:, : 1, :, :] - y_lum = y[:, : 1, :, :] + x_yiq = rgb2yiq(x) + y_yiq = rgb2yiq(y) + + x_lum = x_yiq[:, : 1] + y_lum = y_yiq[:, : 1] - x_i = x[:, 1:2, :, :] - y_i = y[:, 1:2, :, :] - x_q = x[:, 2:, :, :] - y_q = y[:, 2:, :, :] + x_i = x_yiq[:, 1:2] + y_i = y_yiq[:, 1:2] + x_q = x_yiq[:, 2:] + y_q = y_yiq[:, 2:] else: x_lum = x @@ -104,7 +100,7 @@ def fsim(x: torch.Tensor, y: torch.Tensor, reduction: str = 'mean', grad_map_x = gradient_map(x_lum, kernels) grad_map_y = gradient_map(y_lum, kernels) - # Constants from paper + # Constants from the paper T1, T2, T3, T4, lmbda = 0.85, 160, 200, 200, 0.03 # Compute FSIM @@ -133,7 +129,7 @@ def fsim(x: torch.Tensor, y: torch.Tensor, reduction: str = 'mean', def _construct_filters(x: torch.Tensor, scales: int = 4, orientations: int = 4, min_length: int = 6, mult: int = 2, sigma_f: float = 0.55, delta_theta: float = 1.2, k: float = 2.0): - """Creates stack of filters used for computation of phase congruensy maps + """Creates a stack of filters used for computation of phase congruensy maps Args: x: Tensor with shape Bx1xHxW @@ -187,8 +183,8 @@ def _construct_filters(x: torch.Tensor, scales: int = 4, orientations: int = 4, log_gabor = [] for s in range(scales): wavelength = min_length * mult ** s - fo = 1.0 / wavelength # Centre frequency of filter. - gabor_filter = torch.exp((- torch.log(radius / fo) ** 2) / (2 * math.log(sigma_f) ** 2)) + omega_0 = 1.0 / wavelength + gabor_filter = torch.exp((- torch.log(radius / omega_0) ** 2) / (2 * math.log(sigma_f) ** 2)) gabor_filter = gabor_filter * lp gabor_filter[0, 0] = 0 log_gabor.append(gabor_filter) @@ -239,7 +235,7 @@ def _phase_congruency(x: torch.Tensor, scales: int = 4, orientations: int = 4, PCmap: Tensor with shape BxHxW """ - EPS = 1e-4 + EPS = torch.finfo(x.dtype).eps B, _, H, W = x.shape @@ -252,10 +248,10 @@ def _phase_congruency(x: torch.Tensor, scales: int = 4, orientations: int = 4, filters_ifft = torch.ifft(torch.stack([filters, torch.zeros_like(filters)], dim=-1), 2)[..., 0] * math.sqrt(H * W) # Convolve image with even and odd filters - E0 = torch.ifft(imagefft * filters.unsqueeze(-1), 2).view(B, orientations, scales, H, W, 2) + even_odd = torch.ifft(imagefft * filters.unsqueeze(-1), 2).view(B, orientations, scales, H, W, 2) # Amplitude of even & odd filter response. An = sqrt(real^2 + imag^2) - an = torch.sqrt(torch.sum(E0 ** 2, dim=-1)) + an = torch.sqrt(torch.sum(even_odd ** 2, dim=-1)) # Take filter at scale 0 and sum spatially # Record mean squared filter value at smallest scale. @@ -263,10 +259,10 @@ def _phase_congruency(x: torch.Tensor, scales: int = 4, orientations: int = 4, em_n = (filters.view(1, orientations, scales, H, W)[:, :, :1, ...] ** 2).sum(dim=[-2, -1], keepdims=True) # Sum of even filter convolution results. - sum_e = E0[..., 0].sum(dim=2, keepdims=True) + sum_e = even_odd[..., 0].sum(dim=2, keepdims=True) # Sum of odd filter convolution results. - sum_o = E0[..., 1].sum(dim=2, keepdims=True) + sum_o = even_odd[..., 1].sum(dim=2, keepdims=True) # Get weighted mean filter response vector, this gives the weighted mean phase angle. x_energy = torch.sqrt(sum_e ** 2 + sum_o ** 2) + EPS @@ -280,10 +276,10 @@ def _phase_congruency(x: torch.Tensor, scales: int = 4, orientations: int = 4, # This quantity is phase congruency multiplied by An, which we call energy. # Extract even and odd convolution results. - E = E0[..., 0] - O = E0[..., 1] + even = even_odd[..., 0] + odd = even_odd[..., 1] - energy = (E * mean_e + O * mean_o - torch.abs(E * mean_o - O * mean_e)).sum(dim=2, keepdim=True) + energy = (even * mean_e + odd * mean_o - torch.abs(even * mean_o - odd * mean_e)).sum(dim=2, keepdim=True) # Compensate for noise # We estimate the noise power from the energy squared response at the @@ -293,8 +289,8 @@ def _phase_congruency(x: torch.Tensor, scales: int = 4, orientations: int = 4, # The estimate of noise power is obtained by dividing the mean squared # energy value by the mean squared filter value - abs_e0 = torch.sqrt(torch.sum(E0[:, :, :1, ...] ** 2, dim=-1)).reshape(B, orientations, 1, 1, H * W) - median_e2n = torch.median(abs_e0 ** 2, dim=-1, keepdims=True).values + abs_eo = torch.sqrt(torch.sum(even_odd[:, :, :1, ...] ** 2, dim=-1)).reshape(B, orientations, 1, 1, H * W) + median_e2n = torch.median(abs_eo ** 2, dim=-1, keepdims=True).values mean_e2n = - median_e2n / math.log(0.5) @@ -360,9 +356,8 @@ def _lowpassfilter(size: Union[int, Tuple[int, int]], cutoff: float, n: int) -> The frequency origin of the returned filter is at the corners. """ - - assert (cutoff >= 0) and (cutoff <= 0.5), "Cutoff frequency must be between 0 and 0.5" - assert n > 1, "n must be an integer >= 1" + assert 0 < cutoff <= 0.5, "Cutoff frequency must be between 0 and 0.5" + assert n > 1 and int(n) == n, "n must be an integer >= 1" grid_x, grid_y = get_meshgrid(size) diff --git a/tests/test_fsim.py b/tests/test_fsim.py index e686cd8e..806e1d77 100644 --- a/tests/test_fsim.py +++ b/tests/test_fsim.py @@ -65,7 +65,7 @@ def test_fsim_simmular_to_matlab_implementation(): goldhill = torch.tensor(imread('tests/assets/goldhill.gif')) goldhill_jpeg = torch.tensor(imread('tests/assets/goldhill_jpeg.gif')) - score = fsim(goldhill_jpeg, goldhill, data_range=255, chromatic=False) + score = fsim(goldhill_jpeg, goldhill, data_range=255, chromatic=False, reduction='none') score_baseline = torch.tensor(0.89691) assert torch.allclose(score, score_baseline), \ @@ -75,8 +75,8 @@ def test_fsim_simmular_to_matlab_implementation(): I01 = torch.tensor(imread('tests/assets/I01.BMP')).permute(2, 0, 1) i1_01_5 = torch.tensor(imread('tests/assets/i01_01_5.bmp')).permute(2, 0, 1) - score = fsim(i1_01_5, I01, data_range=255, chromatic=False) - score_chromatic = fsim(i1_01_5, I01, data_range=255, chromatic=True) + score = fsim(i1_01_5, I01, data_range=255, chromatic=False, reduction='none') + score_chromatic = fsim(i1_01_5, I01, data_range=255, chromatic=True, reduction='none') # Baseline values are from original MATLAB code score_baseline = torch.tensor(0.93674)

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