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‎HaarPSI.m

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function [similarity,similarityMaps,weightMaps] = HaarPSI(imgRef,imgDist,preprocessWithSubsampling)
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%HaarPSI Computes the Haar wavelet-based perceptual similarity index of two
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%images.
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%
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%Please make sure that grayscale and color values are given in the [0,255]
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%interval! If this is not the case, the HaarPSI cannot be computed
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%correctly.
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%
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%Usage (optional parameters in <>-brackets):
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%
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% [similarity,<similarityMaps>,<weightMaps>] = HaarPSI(imgRef, imgDist, <preprocessWithSubsampling>);
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%
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%
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%
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%Input:
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%
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% imgRef: RGB or grayscale image with values ranging from 0
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% to 255.
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% imgDist: RGB or grayscale image with values ranging from 0
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% to 255.
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% preprocessWithSubsampling: <optional> If 0, the preprocssing step to acommodate for the
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% viewing distance in psychophysical experimentes is omitted.
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%
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%
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%Output:
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%
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% similarity: The Haar wavelet-based perceptual similarity index, measured
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% in the interval [0,1].
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% similarityMaps: <optional> Maps of horizontal and vertical local similarities.
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% For RGB images, this variable also includes
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% a similarity map with respect to the two
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% color channesl in the YIQ space.
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% weightMaps: <optional> Weight maps measuring the importance of
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% the local similarities in similarityMaps.
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%
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%
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%Example:
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%
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% imgRef = double(imread('peppers.png'));
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% imgDist = imgRef + randi([-20,20],size(imgRef));
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% imgDist = min(max(imgDist,0),255);
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% similarity = HaarPSI(imgRef,imgDist);
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%
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%Reference:
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%
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% R. Reisenhofer, S. Bosse, G. Kutyniok & T. Wiegand: 'A Haar Wavelet-Based Perceptual Similarity Index for Image Quality Assessment', 2017.
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if nargin < 3
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preprocessWithSubsampling = 1;
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end
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colorImage = size(imgRef,3) == 3;
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imgRef = double(imgRef);
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imgDist = double(imgDist);
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%% initialization and preprocessing
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%constants
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C = 30;
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alpha = 4.2;
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%transform to YIQ colorspace
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if colorImage
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imgRefY = 0.299 * (imgRef(:,:,1)) + 0.587 * (imgRef(:,:,2)) + 0.114 * (imgRef(:,:,3));
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imgDistY = 0.299 * (imgDist(:,:,1)) + 0.587 * (imgDist(:,:,2)) + 0.114 * (imgDist(:,:,3));
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imgRefI = 0.596 * (imgRef(:,:,1)) - 0.274 * (imgRef(:,:,2)) - 0.322 * (imgRef(:,:,3));
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imgDistI = 0.596 * (imgDist(:,:,1)) - 0.274 * (imgDist(:,:,2)) - 0.322 * (imgDist(:,:,3));
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imgRefQ = 0.211 * (imgRef(:,:,1)) - 0.523 * (imgRef(:,:,2)) + 0.312 * (imgRef(:,:,3));
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imgDistQ = 0.211 * (imgDist(:,:,1)) - 0.523 * (imgDist(:,:,2)) + 0.312 * (imgDist(:,:,3));
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else
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imgRefY = double(imgRef);
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imgDistY = double(imgDist);
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end
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%% subsampling
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if preprocessWithSubsampling
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imgRefY = HaarPSISubsample(imgRefY);
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imgDistY = HaarPSISubsample(imgDistY);
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if colorImage
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imgRefQ = HaarPSISubsample(imgRefQ);
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imgDistQ = HaarPSISubsample(imgDistQ);
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imgRefI = HaarPSISubsample(imgRefI);
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imgDistI = HaarPSISubsample(imgDistI);
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end
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end
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%% pre-allocate variables
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if colorImage
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localSimilarities = zeros([size(imgRefY),3]);
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weights = zeros([size(imgRefY),3]);
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else
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localSimilarities = zeros([size(imgRefY),2]);
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weights = zeros([size(imgRefY),2]);
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end
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%% Haar wavelet decomposition
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nScales = 3;
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coeffsRefY = HaarPSIDec(imgRefY,nScales);
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coeffsDistY = HaarPSIDec(imgDistY,nScales);
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if colorImage
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coeffsRefQ = abs(conv2(imgRefQ,ones(2,2)/4,'same'));
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coeffsDistQ = abs(conv2(imgDistQ,ones(2,2)/4,'same'));
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coeffsRefI = abs(conv2(imgRefI,ones(2,2)/4,'same'));
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coeffsDistI = abs(conv2(imgDistI,ones(2,2)/4,'same'));
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end
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%% compute weights and similarity for each orientation
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for ori = 1:2
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weights(:,:,ori) = max(abs(coeffsRefY(:,:,3 + (ori-1)*nScales)), abs(coeffsDistY(:,:,3 + (ori-1)*nScales)));
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coeffsRefYMag = abs(coeffsRefY(:,:,(1:2) + (ori-1)*nScales));
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coeffsDistYMag = abs(coeffsDistY(:,:,(1:2) + (ori-1)*nScales));
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localSimilarities(:,:,ori) = sum(((2*coeffsRefYMag.*coeffsDistYMag + C)./(coeffsRefYMag.^2 + coeffsDistYMag.^2 + C)),3)/2;
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end
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%% compute similarities for color channels
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if colorImage
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similarityI = ((2*coeffsRefI.*coeffsDistI + C) ./(coeffsRefI.^2 + coeffsDistI.^2 + C));
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similarityQ = ((2*coeffsRefQ.*coeffsDistQ + C) ./(coeffsRefQ.^2 + coeffsDistQ.^2 + C));
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localSimilarities(:,:,3) = ((similarityI)+(similarityQ))/2;
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weights(:,:,3) = (weights(:,:,1) + weights(:,:,2))/2;
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end
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%% compute final score
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similarity = HaarPSILogInv(sum((HaarPSILog(localSimilarities(:),alpha)).*weights(:))/sum(weights(:)),alpha)^2;
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%% output maps
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if nargout > 1
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similarityMaps = localSimilarities;
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end
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if nargout > 2
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weightMaps = weights;
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end
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end
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function coeffs = HaarPSIDec(X,nScales)
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coeffs = zeros([size(X),2*nScales]);
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for k = 1:nScales
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haarFilter = 2^(-k)*ones(2^k,2^k);
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haarFilter(1:(end/2),:) = -haarFilter(1:(end/2),:);
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coeffs(:,:,k) = conv2(X,haarFilter,'same');
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coeffs(:,:,k + nScales) = conv2(X,haarFilter','same');
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end
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end
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function imgSubsampled = HaarPSISubsample(img)
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imgSubsampled = conv2(img, ones(2,2)/4,'same');
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imgSubsampled = imgSubsampled(1:2:end,1:2:end);
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end
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function val = HaarPSILog(x,alpha)
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val = 1./(1 + exp(-alpha.*(x)));
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end
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function val = HaarPSILogInv(x,alpha)
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val = log(x./(1-x))./alpha;
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end
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% Written by Rafael Reisenhofer
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% Built on 08/05/2017
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‎HaarPSIExt.m

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function [similarity,similarityMaps,weightMaps] = HaarPSIExt(imgRef,imgDist,preprocessWithSubsampling,wavelet,boundaryTreatment)
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%HaarPSIExt Computes the Haar wavelet-based perceptual similarity index of two
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%images.
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%
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%Please make sure that grayscale and color values are given in the [0,255]
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%interval! If this is not the case, the HaarPSI cannot be computed
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%correctly.
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%
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%Usage (optional parameters in <>-brackets):
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%
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% [similarity,<similarityMaps>,<weightMaps>] = HaarPSI(imgRef, imgDist, <preprocessWithSubsampling>, <wavelet>, <boundaryTreatment>);
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%
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%
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%
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%Input:
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%
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% imgRef: RGB or grayscale image with values ranging from 0
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% to 255.
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% imgDist: RGB or grayscale image with values ranging from 0
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% to 255.
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% preprocessWithSubsampling: <optional> If 0, the preprocssing step to acommodate for the
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% viewing distance in psychophysical experimentes is omitted.
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% wavelet: <optional> A string specifying the wavelet
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% used in the definition of the perceptual
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% simlarity measure. For a list of possible
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% choices, see the documentation of wfilters.
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% boundaryTreatment: <optional> A string or number specifying
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% boundary treatment. For possible choices,
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% see the documentation of imfilter.
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%
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%
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%
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%Output:
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%
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% similarity: The Haar wavelet-based perceptual similarity index, measured
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% in the interval [0,1].
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% similarityMaps: <optional> Maps of horizontal and vertical local similarities.
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% For RGB images, this variable also includes
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% a similarity map with respect to the two
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% color channesl in the YIQ space.
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% weightMaps: <optional> Weight maps measuring the importance of
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% the local similarities in similarityMaps.
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%
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%
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%Example:
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%
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% imgRef = double(imread('peppers.png'));
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% imgDist = imgRef + randi([-20,20],size(imgRef));
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% imgDist = min(max(imgDist,0),255);
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% similarity = HaarPSI(imgRef,imgDist);
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%
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%Reference:
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%
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% R. Reisenhofer, S. Bosse, G. Kutyniok & T. Wiegand: 'A Haar Wavelet-Based Perceptual Similarity Index for Image Quality Assessment', 2017.
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if nargin < 3
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preprocessWithSubsampling = 1;
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end
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if nargin < 4
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wavelet = 'haar';
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end
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if nargin < 5
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boundaryTreatment = 0;
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end
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colorImage = size(imgRef,3) == 3;
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imgRef = double(imgRef);
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imgDist = double(imgDist);
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%% initialization and preprocessing
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%constants
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C = 30;
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alpha = 4.2;
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%transform to YIQ colorspace
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if colorImage
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imgRefY = 0.299 * (imgRef(:,:,1)) + 0.587 * (imgRef(:,:,2)) + 0.114 * (imgRef(:,:,3));
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imgDistY = 0.299 * (imgDist(:,:,1)) + 0.587 * (imgDist(:,:,2)) + 0.114 * (imgDist(:,:,3));
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imgRefI = 0.596 * (imgRef(:,:,1)) - 0.274 * (imgRef(:,:,2)) - 0.322 * (imgRef(:,:,3));
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imgDistI = 0.596 * (imgDist(:,:,1)) - 0.274 * (imgDist(:,:,2)) - 0.322 * (imgDist(:,:,3));
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imgRefQ = 0.211 * (imgRef(:,:,1)) - 0.523 * (imgRef(:,:,2)) + 0.312 * (imgRef(:,:,3));
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imgDistQ = 0.211 * (imgDist(:,:,1)) - 0.523 * (imgDist(:,:,2)) + 0.312 * (imgDist(:,:,3));
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else
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imgRefY = double(imgRef);
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imgDistY = double(imgDist);
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end
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%% subsampling
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if preprocessWithSubsampling
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imgRefY = HaarPSISubsample(imgRefY,boundaryTreatment);
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imgDistY = HaarPSISubsample(imgDistY,boundaryTreatment);
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if colorImage
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imgRefQ = HaarPSISubsample(imgRefQ,boundaryTreatment);
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imgDistQ = HaarPSISubsample(imgDistQ,boundaryTreatment);
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imgRefI = HaarPSISubsample(imgRefI,boundaryTreatment);
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imgDistI = HaarPSISubsample(imgDistI,boundaryTreatment);
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end
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end
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%% pre-allocate variables
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if colorImage
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localSimilarities = zeros([size(imgRefY),3]);
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weights = zeros([size(imgRefY),3]);
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else
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localSimilarities = zeros([size(imgRefY),2]);
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weights = zeros([size(imgRefY),2]);
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end
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%% Haar wavelet decomposition
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nScales = 3;
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coeffsRefY = HaarPSIDec(imgRefY,wavelet,boundaryTreatment,nScales);
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coeffsDistY = HaarPSIDec(imgDistY,wavelet,boundaryTreatment,nScales);
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if colorImage
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coeffsRefQ = abs(imfilter(imgRefQ,ones(2,2)/4,'same','conv',boundaryTreatment));
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coeffsDistQ = abs(imfilter(imgDistQ,ones(2,2)/4,'same','conv',boundaryTreatment));
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coeffsRefI = abs(imfilter(imgRefI,ones(2,2)/4,'same','conv',boundaryTreatment));
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coeffsDistI = abs(imfilter(imgDistI,ones(2,2)/4,'same','conv',boundaryTreatment));
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end
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%% compute weights and similarity for each orientation
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for ori = 1:2
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weights(:,:,ori) = max(abs(coeffsRefY(:,:,3 + (ori-1)*nScales)), abs(coeffsDistY(:,:,3 + (ori-1)*nScales)));
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coeffsRefYMag = abs(coeffsRefY(:,:,(1:2) + (ori-1)*nScales));
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coeffsDistYMag = abs(coeffsDistY(:,:,(1:2) + (ori-1)*nScales));
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localSimilarities(:,:,ori) = sum(((2*coeffsRefYMag.*coeffsDistYMag + C)./(coeffsRefYMag.^2 + coeffsDistYMag.^2 + C)),3)/2;
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end
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%% compute similarities for color channels
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if colorImage
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similarityI = ((2*coeffsRefI.*coeffsDistI + C) ./(coeffsRefI.^2 + coeffsDistI.^2 + C));
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similarityQ = ((2*coeffsRefQ.*coeffsDistQ + C) ./(coeffsRefQ.^2 + coeffsDistQ.^2 + C));
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localSimilarities(:,:,3) = ((similarityI)+(similarityQ))/2;
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weights(:,:,3) = (weights(:,:,1) + weights(:,:,2))/2;
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end
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%% compute final score
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similarity = HaarPSILogInv(sum((HaarPSILog(localSimilarities(:),alpha)).*weights(:))/sum(weights(:)),alpha)^2;
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%% output maps
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if nargout > 1
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similarityMaps = localSimilarities;
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end
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if nargout > 2
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weightMaps = weights;
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end
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end
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function coeffs = HaarPSIDec(X,wavelet,boundaryTreatment,nScales)
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[h,g] = wfilters(wavelet);
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coeffs = zeros([size(X),2*nScales]);
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hnew = h;
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hnew2 = hnew;
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g2 = g;
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for k = 1:nScales
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waveletFilter = hnew2'*g2;
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coeffs(:,:,k) = imfilter(X,waveletFilter,'same','conv',boundaryTreatment);
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coeffs(:,:,k + nScales) = imfilter(X,waveletFilter','same','conv',boundaryTreatment);
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g = conv(h,dyadup(g));
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hnew = conv(h,dyadup(hnew));
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g2 = g((find(abs(g)>0,1,'first')):(find(abs(g)>0,1,'last')));
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hnew2 = hnew((find(abs(hnew)>0,1,'first')):(find(abs(hnew)>0,1,'last')));
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end
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end
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function imgSubsampled = HaarPSISubsample(img,boundaryTreatment)
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imgSubsampled = imfilter(img, ones(2,2)/4,'same','conv',boundaryTreatment);
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imgSubsampled = imgSubsampled(1:2:end,1:2:end);
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end
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function val = HaarPSILog(x,alpha)
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val = 1./(1 + exp(-alpha.*(x)));
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end
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function val = HaarPSILogInv(x,alpha)
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val = log(x./(1-x))./alpha;
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end
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% Written by Rafael Reisenhofer
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% Built on 08/05/2017

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