Source code for sporco.metric

# -*- coding: utf-8 -*-
# Copyright (C) 2016-2017 by Brendt Wohlberg <brendt@ieee.org>
# All rights reserved. BSD 3-clause License.
# This file is part of the SPORCO package. Details of the copyright
# and user license can be found in the 'LICENSE.txt' file distributed
# with the package.

"""Image quality metrics and related functions

Note that the well-known SSIM metric is not implemented here as it is
available in a number of other Python packages, including:

  - `scikit-image <https://github.com/scikit-image/scikit-image>`_
  - `PyMetrikz <https://bitbucket.org/kuraiev/pymetrikz>`_
  - `Video Quality Metrics <https://github.com/aizvorski/video-quality>`_
  - `pyssim <https://github.com/jterrace/pyssim>`_

Some implementations are also available in unpackaged collections of
Python code:

  - `src <https://github.com/helderc/src>`_
  - `python <https://github.com/mubeta06/python>`_

|

"""

from __future__ import division

import numpy as np
from scipy import ndimage
from scipy import signal

__author__ = """Brendt Wohlberg <brendt@ieee.org>"""


[docs]def mae(vref, vcmp): """ Compute Mean Absolute Error (MAE) between two images. Parameters ---------- vref : array_like Reference image vcmp : array_like Comparison image Returns ------- x : float MAE between `vref` and `vcmp` """ r = np.asarray(vref, dtype=np.float64).ravel() c = np.asarray(vcmp, dtype=np.float64).ravel() return np.mean(np.abs(r - c))
[docs]def mse(vref, vcmp): """ Compute Mean Squared Error (MSE) between two images. Parameters ---------- vref : array_like Reference image vcmp : array_like Comparison image Returns ------- x : float MSE between `vref` and `vcmp` """ r = np.asarray(vref, dtype=np.float64).ravel() c = np.asarray(vcmp, dtype=np.float64).ravel() return np.mean(np.abs(r - c)**2)
[docs]def snr(vref, vcmp): """ Compute Signal to Noise Ratio (SNR) of two images. Parameters ---------- vref : array_like Reference image vcmp : array_like Comparison image Returns ------- x : float SNR of `vcmp` with respect to `vref` """ dv = np.var(vref) with np.errstate(divide='ignore'): rt = dv / mse(vref, vcmp) return 10.0 * np.log10(rt)
[docs]def psnr(vref, vcmp, rng=None): """ Compute Peak Signal to Noise Ratio (PSNR) of two images. The PSNR calculation defaults to using the less common definition in terms of the actual range (i.e. max minus min) of the reference signal instead of the maximum possible range for the data type (i.e. :math:`2^b-1` for a :math:`b` bit representation). Parameters ---------- vref : array_like Reference image vcmp : array_like Comparison image rng : None or int, optional (default None) Signal range, either the value to use (e.g. 255 for 8 bit samples) or None, in which case the actual range of the reference signal is used Returns ------- x : float PSNR of `vcmp` with respect to `vref` """ if rng is None: rng = vref.max() - vref.min() dv = (rng + 0.0)**2 with np.errstate(divide='ignore'): rt = dv / mse(vref, vcmp) return 10.0 * np.log10(rt)
[docs]def isnr(vref, vdeg, vrst): """ Compute Improvement Signal to Noise Ratio (ISNR) for reference, degraded, and restored images. Parameters ---------- vref : array_like Reference image vdeg : array_like Degraded image vrst : array_like Restored image Returns ------- x : float ISNR of `vrst` with respect to `vref` and `vdeg` """ msedeg = mse(vref, vdeg) mserst = mse(vref, vrst) with np.errstate(divide='ignore'): rt = msedeg / mserst return 10.0 * np.log10(rt)
[docs]def bsnr(vblr, vnsy): """ Compute Blurred Signal to Noise Ratio (BSNR) for a blurred and noisy image. Parameters ---------- vblr : array_like Blurred noise free image vnsy : array_like Blurred image with additive noise Returns ------- x : float BSNR of `vnsy` with respect to `vblr` and `vdeg` """ blrvar = np.var(vblr) nsevar = np.var(vnsy - vblr) with np.errstate(divide='ignore'): rt = blrvar / nsevar return 10.0 * np.log10(rt)
[docs]def pamse(vref, vcmp, rescale=True): """ Compute Perceptual-fidelity Aware Mean Squared Error (PAMSE) IQA metric :cite:`xue-2013-perceptual`. This implementation is a translation of the reference Matlab implementation provided by the authors of :cite:`xue-2013-perceptual`. Parameters ---------- vref : array_like Reference image vcmp : array_like Comparison image rescale : bool, optional (default True) Rescale inputs so that `vref` has a maximum value of 255, as assumed by reference implementation Returns ------- score : float PAMSE IQA metric """ # Calculate difference, promoting to float if vref and vcmp have integer # dtype emap = np.asarray(vref, dtype=np.float64) - \ np.asarray(vcmp, dtype=np.float64) # Input images in reference code on which this implementation is # based are assumed to be on range [0,...,255]. if rescale: emap *= (255.0 / vref.max()) sigma = 0.8 herr = ndimage.filters.gaussian_filter(emap, sigma) score = np.mean(herr**2) return score
[docs]def gmsd(vref, vcmp, rescale=True, returnMap=False): """ Compute Gradient Magnitude Similarity Deviation (GMSD) IQA metric :cite:`xue-2014-gradient`. This implementation is a translation of the reference Matlab implementation provided by the authors of :cite:`xue-2014-gradient`. Parameters ---------- vref : array_like Reference image vcmp : array_like Comparison image rescale : bool, optional (default True) Rescale inputs so that `vref` has a maximum value of 255, as assumed by reference implementation returnMap : bool, optional (default False) Flag indicating whether quality map should be returned in addition to scalar score Returns ------- score : float GMSD IQA metric quality_map : ndarray Quality map """ # Input images in reference code on which this implementation is # based are assumed to be on range [0,...,255]. if rescale: scl = (255.0 / vref.max()) else: scl = np.float32(1.0) T = 170.0 dwn = 2 dx = np.array([[1, 0, -1], [1, 0, -1], [1, 0, -1]]) / 3.0 dy = dx.T ukrn = np.ones((2, 2)) / 4.0 aveY1 = signal.convolve2d(scl * vref, ukrn, mode='same', boundary='symm') aveY2 = signal.convolve2d(scl * vcmp, ukrn, mode='same', boundary='symm') Y1 = aveY1[0::dwn, 0::dwn] Y2 = aveY2[0::dwn, 0::dwn] IxY1 = signal.convolve2d(Y1, dx, mode='same', boundary='symm') IyY1 = signal.convolve2d(Y1, dy, mode='same', boundary='symm') grdMap1 = np.sqrt(IxY1**2 + IyY1**2) IxY2 = signal.convolve2d(Y2, dx, mode='same', boundary='symm') IyY2 = signal.convolve2d(Y2, dy, mode='same', boundary='symm') grdMap2 = np.sqrt(IxY2**2 + IyY2**2) quality_map = (2*grdMap1*grdMap2 + T) / (grdMap1**2 + grdMap2**2 + T) score = np.std(quality_map) if returnMap: return (score, quality_map) else: return score