frcs-colour-transfer

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%
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%   simple implementation of N-Dimensional PDF Transfer 
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%
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%   [DR] = pdf_transferND(D0, D1, rotations);
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%
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%     D0, D1 = NxM matrix containing N-dimensional features
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%     rotations = { {R_1}, ... , {R_n} } with R_i PxN 
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%
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%     note that we can use more than N projection axes. In this case P > N
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%     and the inverse transformation is done by least mean square. 
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%     Using more than N axes leads to a more stable (but also slower) 
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%     convergence.
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%
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%  (c) F. Pitie 2007
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%
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%  see reference:
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%  Automated colour grading using colour distribution transfer. (2007) 
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%  Computer Vision and Image Understanding.
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%
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function [DR] = pdf_transfer(D0, D1, Rotations, varargin)
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nb_iterations = length(Rotations);
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numvarargs = length(varargin);
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if numvarargs > 1
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    error('pdf_transfer:TooManyInputs', ...
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        'requires at most 1 optional input');
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end
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optargs = {1};
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optargs(1:numvarargs) = varargin;
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[relaxation] = optargs{:};
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prompt = '';
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for it=1:nb_iterations
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    fprintf(repmat('\b',[1, length(prompt)]))
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    prompt = sprintf('IDT iteration %02d / %02d', it, nb_iterations);
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    fprintf(prompt);
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    R = Rotations{it};    
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    nb_projs = size(R,1);
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    % apply rotation
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    D0R = R * D0;
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    D1R = R * D1;
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    D0R_ = zeros(size(D0));
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    % get the marginals, match them, and apply transformation
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    for i=1:nb_projs
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        % get the data range
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        datamin = min([D0R(i,:) D1R(i,:)])-eps;
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        datamax = max([D0R(i,:) D1R(i,:)])+eps;
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        u = (0:(300-1))/(300-1)*(datamax - datamin) + datamin;
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        % get the projections
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        p0R = hist(D0R(i,:), u);
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        p1R = hist(D1R(i,:), u);
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        % get the transport map
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        f = pdf_transfer1D(p0R, p1R);
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        % apply the mapping
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        D0R_(i,:) = (interp1(u, f', D0R(i,:))-1)/(300-1)*(datamax-datamin) + datamin;
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    end
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    D0 = relaxation * (R \ (D0R_ - D0R)) + D0;
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end
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fprintf(repmat('\b',[1, length(prompt)]))
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DR = D0;
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end
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%
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% 1D - PDF Transfer
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%
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function f = pdf_transfer1D(pX,pY)
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    nbins = max(size(pX));
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    eps = 1e-6; % small damping term that faciliates the inversion
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    PX = cumsum(pX + eps);
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    PX = PX/PX(end);
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    PY = cumsum(pY + eps);
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    PY = PY/PY(end);
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    % inversion
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    f = interp1(PY, 0:nbins-1, PX, 'linear');
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    f(PX<=PY(1)) = 0;
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    f(PX>=PY(end)) = nbins-1;
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    if sum(isnan(f))>0
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        error('colour_transfer:pdf_transfer:NaN', ...
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              'pdf_transfer has generated NaN values');
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    end   
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end
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