RECO: Relative Polar Edge Coherence

reco.py

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+"""
+Video Quality Metrics
+Copyright (c) 2015 Alex Izvorski <[email protected]>
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation, either version 3 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program.  If not, see <http://www.gnu.org/licenses/>.
+"""
+
+"""
+RECO: Relative Polar Edge Coherence
+
+An excellent reduced-reference metric (need just one number from the source image to compare with).
+
+This implementation follows closely the notation and terminology in the original paper, except that some of the kernels are reflected 
+(probably due to y axis pointing down rather than up in images).
+
+Cite:
+Baroncini, V., Capodiferro, L., Di Claudio, E. D., & Jacovitti, G. (2009). The polar edge coherence: 
+a quasi blind metric for video quality assessment. EUSIPCO 2009, Glasgow, 564-568.
+"""
+
+import numpy
+from numpy import sqrt, pi
+import scipy.ndimage.filters
+
+def Laguerre_Gauss_Circular_Harmonic_3_0(size, sigma):
+    x = numpy.linspace(-size/2.0, size/2.0, size)
+    y = numpy.linspace(-size/2.0, size/2.0, size)
+    xx, yy = numpy.meshgrid(x, y)
+
+    r = numpy.sqrt(xx*xx + yy*yy)
+    gamma = numpy.arctan2(yy, xx)
+    l30 = - (1/6.0) * (1 / (sigma * sqrt(pi))) * numpy.exp( -r*r / (2*sigma*sigma)) * (sqrt(r*r/(sigma*sigma)) ** 3) * numpy.exp( -1j * 3 * gamma )
+    return l30
+
+def Laguerre_Gauss_Circular_Harmonic_1_0(size, sigma):
+    x = numpy.linspace(-size/2.0, size/2.0, size)
+    y = numpy.linspace(-size/2.0, size/2.0, size)
+    xx, yy = numpy.meshgrid(x, y)
+
+    r = numpy.sqrt(xx*xx + yy*yy)
+    gamma = numpy.arctan2(yy, xx)
+    l10 = - (1 / (sigma * sqrt(pi))) * numpy.exp( -r*r / (2*sigma*sigma)) * sqrt(r*r/(sigma*sigma)) * numpy.exp( -1j * gamma )
+    return l10
+
+"""
+Polar edge coherence map
+Same size as source image
+"""
+def pec(img):
+    # TODO scale parameter should depend on resolution
+    l10 = Laguerre_Gauss_Circular_Harmonic_1_0(17, 2)
+    l30 = Laguerre_Gauss_Circular_Harmonic_3_0(17, 2)
+    y10 = scipy.ndimage.filters.convolve(img, numpy.real(l10)) + 1j * scipy.ndimage.filters.convolve(img, numpy.imag(l10))
+    y30 = scipy.ndimage.filters.convolve(img, numpy.real(l30)) + 1j * scipy.ndimage.filters.convolve(img, numpy.imag(l30))
+    pec_map = - (numpy.absolute(y30) / numpy.absolute(y10)) * numpy.cos( numpy.angle(y30) - 3 * numpy.angle(y10) )
+    return pec_map
+
+"""
+Edge coherence metric
+Just one number summarizing typical edge coherence in this image.
+"""
+def eco(img):
+    l10 = Laguerre_Gauss_Circular_Harmonic_1_0(17, 2)
+    l30 = Laguerre_Gauss_Circular_Harmonic_3_0(17, 2)
+    y10 = scipy.ndimage.filters.convolve(img, numpy.real(l10)) + 1j * scipy.ndimage.filters.convolve(img, numpy.imag(l10))
+    y30 = scipy.ndimage.filters.convolve(img, numpy.real(l30)) + 1j * scipy.ndimage.filters.convolve(img, numpy.imag(l30))
+    eco = numpy.sum( - (numpy.absolute(y30) * numpy.absolute(y10)) * numpy.cos( numpy.angle(y30) - 3 * numpy.angle(y10) ) )
+    return eco
+
+"""
+Relative edge coherence
+Ratio of ECO
+"""
+def reco(img1, img2):
+    C = 1 # TODO what is a good value?
+    return (eco(img2) + C) / (eco(img1) + C)
+