ssim.py

# This code is referenced from https://github.com/VainF/pytorch-msssim/blob/master/pytorch_msssim/ssim.py


import torch
import torch.nn.functional as F


def _fspecial_gauss_1d(size, sigma):
    r"""Create 1-D gauss kernel
    Args:
        size (int): the size of gauss kernel
        sigma (float): sigma of normal distribution
    Returns:
        torch.Tensor: 1D kernel (1 x 1 x size)
    """
    coords = torch.arange(size).to(dtype=torch.float)
    coords -= size//2

    g = torch.exp(-(coords**2) / (2*sigma**2))
    g /= g.sum()

    return g.unsqueeze(0).unsqueeze(0)


def gaussian_filter(input, win):
    r""" Blur input with 1-D kernel
    Args:
        input (torch.Tensor): a batch of tensors to be blured
        window (torch.Tensor): 1-D gauss kernel
    Returns:
        torch.Tensor: blured tensors
    """
    N, C, H, W = input.shape
    out = F.conv2d(input, win, stride=1, padding=0, groups=C)
    out = F.conv2d(out, win.transpose(2, 3), stride=1, padding=0, groups=C)
    return out


def _ssim(X, Y, 
          data_range, 
          win, 
          size_average=True, 
          K=(0.01,0.03)):
          
    r""" Calculate ssim index for X and Y
    Args:
        X (torch.Tensor): images
        Y (torch.Tensor): images
        win (torch.Tensor): 1-D gauss kernel
        data_range (float or int, optional): value range of input images. (usually 1.0 or 255)
        size_average (bool, optional): if size_average=True, ssim of all images will be averaged as a scalar
    Returns:
        torch.Tensor: ssim results.
    """
    K1, K2 = K
    batch, channel, height, width = X.shape
    compensation = 1.0

    C1 = (K1 * data_range)**2
    C2 = (K2 * data_range)**2

    win = win.to(X.device, dtype=X.dtype)

    mu1 = gaussian_filter(X, win)
    mu2 = gaussian_filter(Y, win)

    mu1_sq = mu1.pow(2)
    mu2_sq = mu2.pow(2)
    mu1_mu2 = mu1 * mu2

    sigma1_sq = compensation * ( gaussian_filter(X * X, win) - mu1_sq )
    sigma2_sq = compensation * ( gaussian_filter(Y * Y, win) - mu2_sq )
    sigma12   = compensation * ( gaussian_filter(X * Y, win) - mu1_mu2 )

    cs_map = (2 * sigma12 + C2) / (sigma1_sq + sigma2_sq + C2) # set alpha=beta=gamma=1
    ssim_map = ((2 * mu1_mu2 + C1) / (mu1_sq + mu2_sq + C1)) * cs_map
    
    ssim_per_channel = torch.flatten(ssim_map, 2).mean(-1)
    cs = torch.flatten( cs_map, 2 ).mean(-1)
    return ssim_per_channel, cs


def ssim(X, Y, 
         data_range=255, 
         size_average=True, 
         win_size=11, 
         win_sigma=1.5, 
         win=None, 
         K=(0.01, 0.03), 
         nonnegative_ssim=False):
    r""" interface of ssim
    Args:
        X (torch.Tensor): a batch of images, (N,C,H,W)
        Y (torch.Tensor): a batch of images, (N,C,H,W)
        data_range (float or int, optional): value range of input images. (usually 1.0 or 255)
        size_average (bool, optional): if size_average=True, ssim of all images will be averaged as a scalar
        win_size: (int, optional): the size of gauss kernel
        win_sigma: (float, optional): sigma of normal distribution
        win (torch.Tensor, optional): 1-D gauss kernel. if None, a new kernel will be created according to win_size and win_sigma
        K (list or tuple, optional): scalar constants (K1, K2). Try a larger K2 constant (e.g. 0.4) if you get a negative or NaN results.
        nonnegative_ssim (bool, optional): force the ssim response to be nonnegative with relu
    Returns:
        torch.Tensor: ssim results
    """

    if len(X.shape) != 4:
        raise ValueError('Input images should be 4-d tensors.')

    if not X.type() == Y.type():
        raise ValueError('Input images should have the same dtype.')

    if not X.shape == Y.shape:
        raise ValueError('Input images should have the same shape.')
    
    if win is not None: # set win_size
        win_size = win.shape[-1]

    if not (win_size % 2 == 1):
        raise ValueError('Window size should be odd.')
    
    if win is None:
        win = _fspecial_gauss_1d(win_size, win_sigma)
        win = win.repeat(X.shape[1], 1, 1, 1)
    
    ssim_per_channel, cs = _ssim(X, Y,
                                data_range=data_range,
                                win=win,
                                size_average=False,
                                K=K)
    if nonnegative_ssim:
        ssim_per_channel = torch.relu(ssim_per_channel)
    
    if size_average:
        return ssim_per_channel.mean()
    else:
        return ssim_per_channel.mean(1)
  

def ms_ssim(X, Y, 
            data_range=255, 
            size_average=True, 
            win_size=11, 
            win_sigma=1.5, 
            win=None, 
            weights=None, 
            K=(0.01, 0.03)):

    r""" interface of ms-ssim
    Args:
        X (torch.Tensor): a batch of images, (N,C,H,W)
        Y (torch.Tensor): a batch of images, (N,C,H,W)
        data_range (float or int, optional): value range of input images. (usually 1.0 or 255)
        size_average (bool, optional): if size_average=True, ssim of all images will be averaged as a scalar
        win_size: (int, optional): the size of gauss kernel
        win_sigma: (float, optional): sigma of normal distribution
        win (torch.Tensor, optional): 1-D gauss kernel. if None, a new kernel will be created according to win_size and win_sigma
        weights (list, optional): weights for different levels
        K (list or tuple, optional): scalar constants (K1, K2). Try a larger K2 constant (e.g. 0.4) if you get a negative or NaN results.
    Returns:
        torch.Tensor: ms-ssim results
    """
    if len(X.shape) != 4:
        raise ValueError('Input images should be 4-d tensors.')

    if not X.type() == Y.type():
        raise ValueError('Input images should have the same dtype.')

    if not X.shape == Y.shape:
        raise ValueError('Input images should have the same dimensions.')
    
    if win is not None: # set win_size
        win_size = win.shape[-1]

    if not (win_size % 2 == 1):
        raise ValueError('Window size should be odd.')

    smaller_side = min( X.shape[-2:] )
    assert smaller_side > (win_size-1) * (2**4), \
         "Image size should be larger than %d due to the 4 downsamplings in ms-ssim"% ((win_size-1) * (2**4))

    if weights is None:
        weights = [0.0448, 0.2856, 0.3001, 0.2363, 0.1333]
    weights = torch.FloatTensor(weights).to(X.device, dtype=X.dtype)

    if win is None:
        win = _fspecial_gauss_1d(win_size, win_sigma)
        win = win.repeat(X.shape[1], 1, 1, 1)

    levels = weights.shape[0]
    mcs = []
    for i in range(levels):
        ssim_per_channel, cs = _ssim(X, Y,
                             win=win,
                             data_range=data_range,
                             size_average=False,
                             K=K)

        if i<levels-1: 
            mcs.append(torch.relu(cs))
            padding = (X.shape[2] % 2, X.shape[3] % 2)
            X = F.avg_pool2d(X, kernel_size=2, padding=padding)
            Y = F.avg_pool2d(Y, kernel_size=2, padding=padding)
    
    ssim_per_channel = torch.relu( ssim_per_channel ) # (batch, channel)
    mcs_and_ssim = torch.stack( mcs+[ssim_per_channel], dim=0 ) # (level, batch, channel)
    ms_ssim_val = torch.prod( mcs_and_ssim ** weights.view(-1, 1, 1), dim=0 )

    if size_average:
        return ms_ssim_val.mean()
    else:
        return ms_ssim_val.mean(1)


class SSIM(torch.nn.Module):
    def __init__(self, 
                 data_range=255, 
                 size_average=True, 
                 win_size=11, 
                 win_sigma=1.5, 
                 channel=1, 
                 K=(0.01, 0.03), 
                 nonnegative_ssim=False):
        r""" class for ssim
        Args:
            data_range (float or int, optional): value range of input images. (usually 1.0 or 255)
            size_average (bool, optional): if size_average=True, ssim of all images will be averaged as a scalar
            win_size: (int, optional): the size of gauss kernel
            win_sigma: (float, optional): sigma of normal distribution
            channel (int, optional): input channels (default: 3)
            K (list or tuple, optional): scalar constants (K1, K2). Try a larger K2 constant (e.g. 0.4) if you get a negative or NaN results.
            nonnegative_ssim (bool, optional): force the ssim response to be nonnegative with relu.
        """

        super(SSIM, self).__init__()
        self.win_size = win_size
        self.win = _fspecial_gauss_1d(win_size, win_sigma).repeat(channel, 1, 1, 1)
        self.size_average = size_average
        self.data_range = data_range
        self.K = K
        self.nonnegative_ssim = nonnegative_ssim

    def forward(self, X, Y):
        return ssim(X, Y, 
                    data_range=self.data_range, 
                    size_average=self.size_average, 
                    win=self.win, 
                    K=self.K, 
                    nonnegative_ssim=self.nonnegative_ssim)


class MS_SSIM(torch.nn.Module):
    def __init__(self, 
                 data_range=255, 
                 size_average=True, 
                 win_size=11, 
                 win_sigma=1.5, 
                 channel=1, 
                 weights=None, 
                 K=(0.01, 0.03)):
        r""" class for ms-ssim
        Args:
            data_range (float or int, optional): value range of input images. (usually 1.0 or 255)
            size_average (bool, optional): if size_average=True, ssim of all images will be averaged as a scalar
            win_size: (int, optional): the size of gauss kernel
            win_sigma: (float, optional): sigma of normal distribution
            channel (int, optional): input channels (default: 3)
            weights (list, optional): weights for different levels
            K (list or tuple, optional): scalar constants (K1, K2). Try a larger K2 constant (e.g. 0.4) if you get a negative or NaN results.
        """

        super(MS_SSIM, self).__init__()
        self.win_size = win_size
        self.win = _fspecial_gauss_1d(win_size, win_sigma).repeat(channel, 1, 1, 1)
        self.size_average = size_average
        self.data_range = data_range
        self.weights = weights
        self.K = K

    def forward(self, X, Y):
        return ms_ssim(X, Y, 
                       data_range=self.data_range, 
                       size_average=self.size_average, 
                       win=self.win, 
                       weights=self.weights, 
                       K=self.K)


class SSIM_Loss(SSIM):
    def forward(self, img1, img2):
        return 1 - super(SSIM_Loss, self).forward(img1, img2)


class MSSSIM_Loss(MS_SSIM):
    def forward(self, img1, img2):
        return 1 - super(MSSSIM_Loss, self).forward(img1, img2)