AUC_Borji.m

% created: Zoya Bylinskii, Aug 2014
% Based on code by Ali Borji

% This measures how well the saliencyMap of an image predicts the ground
% truth human fixations on the image. 

% ROC curve created by sweeping through threshold values at fixed step size 
% until the maximum saliency map value;
% true positive (tp) rate correspond to the ratio of saliency map values above 
% threshold at fixation locations to the total number of fixation locations
% false positive (fp) rate correspond to the ratio of saliency map values above 
% threshold at random locations to the total number of random locations 
% (as many random locations as fixations, sampled uniformly from 
% ALL IMAGE PIXELS), averaging over Nsplits number of selections of
% random locations.

function [score,res] = AUC_Borji(saliencyMap, fixationMap, Nsplits, stepSize, toPlot)
% saliencyMap is the saliency map
% fixationMap is the human fixation map (binary matrix)
% Nsplits is number of random splits
% stepSize is for sweeping through saliency map
% if toPlot=1, displays ROC curve

if nargin < 5, toPlot = 0; end
if nargin < 4, stepSize = .1; end
if nargin < 3, Nsplits = 100; end

% If there are no fixations to predict, return NaN
if ~any(fixationMap)
    score=NaN;
    disp('no fixationMap');
    return
end 

% make the saliencyMap the size of the image of fixationMap
if size(saliencyMap, 1)~=size(fixationMap, 1) || size(saliencyMap, 2)~=size(fixationMap, 2)
    saliencyMap = imresize(saliencyMap, size(fixationMap));
end

% normalize saliency map
saliencyMap = (saliencyMap-min(saliencyMap(:)))/(max(saliencyMap(:))-min(saliencyMap(:)));

S = saliencyMap(:);
F = fixationMap(:);

Sth = S(F>0); % sal map values at fixation locations
Nfixations = length(Sth);
Npixels = length(S);

% for each fixation, sample Nsplits values from anywhere on the sal map
r = randi([1 Npixels],[Nfixations,Nsplits]);
randfix = S(r); % sal map values at random locations

% calculate AUC per random split (set of random locations)
auc = nan(1,Nsplits);
for s = 1:Nsplits
    
    curfix = randfix(:,s);
    
    allthreshes = fliplr([0:stepSize:max([Sth;curfix])]);
    tp = zeros(length(allthreshes)+2,1);
    fp = zeros(length(allthreshes)+2,1);
    tp(1)=0; tp(end) = 1; 
    fp(1)=0; fp(end) = 1; 
    
    for i = 1:length(allthreshes)
        thresh = allthreshes(i);
        tp(i+1) = sum((Sth >= thresh))/Nfixations;
        fp(i+1) = sum((curfix >= thresh))/Nfixations;
    end

    auc(s) = trapz(fp,tp);
end

score = mean(auc); % mean across random splits
res{1} = tp;
res{2} = fp;
if toPlot
    subplot(121); imshow(saliencyMap, []); title('SaliencyMap with fixations to be predicted');
    hold on;
    [y, x] = find(fixationMap);
    plot(x, y, '.r');
    subplot(122); plot(fp, tp, '.b-');   title(['Area under ROC curve: ', num2str(score)])
end
end