ENH: Add some simple image comparison metrics: PSNR and NRMSE

skimage/measure/_simple_metrics.py

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+from __future__ import division
+
+import numpy as np
+from ..util.dtype import dtype_range
+
+__all__ = ['mse', 'nrmse', 'psnr']
+
+
+def mse(X, Y):
+    """ compute mean-squared error between two images.
+
+    Parameters
+    ----------
+    X, Y : ndarray
+        Image.  Any dimensionality.
+
+    Returns
+    -------
+    mse : float
+        The MSE metric.
+
+    """
+    if not X.shape == Y.shape:
+        raise ValueError('Input images must have the same dimensions.')
+    if not X.dtype == Y.dtype:
+        raise ValueError('Input images must have the same dtype.')
+    return np.square(X - Y).mean()
+
+
+def nrmse(im_true, im, norm_type='Euclidean'):
+    """ compute the normalized root mean-squared error between two images.
+
+    Parameters
+    ----------
+    im_true : ndarray
+        Ground-truth image.
+    im : ndarray
+        Test image.
+    norm_type : {'Euclidean', 'min-max', 'mean'}
+        Controls the normalization method to use in the denominator of the
+        NRMSE.
+
+    Returns
+    -------
+    nrmse : float
+        The NRMSE metric.
+
+    Notes
+    -----
+    There is no standard method of normalization across the literature [1]_.
+    The methods available here are as follows:
+
+    - 'Euclidean' : normalize by the Euclidean norm of ``im_true``.
+    - 'min-max'   : normalize by the intensity range of ``im_true``.
+    - 'mean'      : normalize by the mean of ``im_true``.
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Root-mean-square_deviation
+
+    """
+    if not im_true.dtype == im.dtype:
+        raise ValueError('Input images must have the same dtype.')
+
+    if not im_true.shape == im.shape:
+        raise ValueError('Input images must have the same dimensions.')
+
+    norm_type = norm_type.lower()
+    if norm_type == 'euclidean':
+        denom = np.sqrt((im_true*im_true).mean())
+    elif norm_type == 'min-max':
+        denom = im_true.max() - im_true.min()
+    elif norm_type == 'mean':
+        denom = im_true.mean()
+    return np.sqrt(mse(im_true, im)) / denom
+
+
+def psnr(im_true, im, dynamic_range=None):
+    """ Compute the peak signal to noise ratio (PSNR) for an image.
+
+    Parameters
+    ----------
+    im_true : ndarray
+        Ground-truth image.
+    im : ndarray
+        Test image.
+    dynamic_range : int
+        The dynamic range of the input image (distance between minimum and
+        maximum possible values).  By default, this is estimated from the image
+        data-type.
+
+    Returns
+    -------
+    psnr : float
+        The PSNR metric.
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Peak_signal-to-noise_ratio
+
+    """
+    if not im_true.dtype == im.dtype:
+        raise ValueError('Input images must have the same dtype.')
+
+    if not im_true.shape == im.shape:
+        raise ValueError('Input images must have the same dimensions.')
+
+    if dynamic_range is None:
+        dmin, dmax = dtype_range[im_true.dtype.type]
+        dynamic_range = dmax - dmin
+
+    im_true = im_true.astype(np.float64)
+    im = im.astype(np.float64)
+
+    err = mse(im_true, im)
+    psnr = 10 * np.log10((dynamic_range ** 2) / err)
+    return psnr