AUC預備知識：

1. 常用來評價一個二分類器的優劣。

2. 很多學習器是為測試樣本產生一個實值或概率預測，然後這個預測值與一個分類閾值進行比較，若大於閾值則為正類，否則為反類。

3. 實際上，根據這個實值或概率預測結果，可以將測試樣本進行排序，"最可能"（實值或概率預測最大）是正例的排在最前面，“最不可能”是正例的排在最後面。這個，分類過程就相當於在這個排序中以某個“截斷點”（即閾值）將樣本分為兩部分，前面為正，後面為反。

4. TP: 真正例，真實為正例，預測也為正例；

    FP: 假正例，真實為負例，預測為正例；

   TPR: 真正例率，真正例數 / 總真實的正例數；

   FPR: 假正例率，假正例數 / 總真實的負例數。

在顯著性檢測領域，生成的顯著圖的每個畫素即為一個樣本，顯著圖的畫素按從大到小排序，然後從第一個（畫素值最大）依次作為閾值，對所有畫素進行分類，然後求得一組TPR, FPR。再以第二大的畫素值為閾值，又可以得到一組。以FPR為橫軸，以TPR為縱軸，即可得到ROC曲線，如下，ROC曲線的面積值即為AUC (area under curve)

1，Matlab實現，算出auc = 0.8895，利用gongAUC_Judd.m，算出的auc = 0.8872

clear;
clc;

smap_full_path = strcat('D:\Code\Matlab\Map\smap.jpg');
gmap_full_path = strcat('D:\Code\Matlab\Map\gmap.jpg');
smap = imread(smap_full_path);
gmap = imread(gmap_full_path);

gmap = imresize(gmap,size(smap));
smap = imresize(smap,0.1);
gmap = imresize(gmap,0.1);

% 二值化ground truth map, 只要兩類
thresh_value = graythresh(gmap);
final_gmap = im2bw(gmap, thresh_value);

% smap歸一化到[0,1]
smap = mat2gray(smap);
% 
% [score,tp,fp,allthreshes] = AUC_Judd(smap, final_gmap, 1, 1);
% 陣列
smap_array = smap(:); 
gmap_array = final_gmap(:);

% 總真實為正例數
idex = find(gmap_array == 1);
P_num = length(idex);

% 總真實為負例數
N_num = length(gmap_array) - P_num;

% 從大到小排序,orig_location儲存了排序前畫素在smap_array的位置
[saliency_values, orig_location] = sort(smap_array, 'descend'); 

% TP(1) = 0; FP(1) = 0; 
% TP(end) = 1; FP(end) = 1;
% 當以salicy_values(i)為閾值時，前面陣列saliency_values前面i個都判為正例
for i=1:length(saliency_values)
    
    % 檢視前i個被判為正例的畫素，真實情況如何。
    TP(i) = 0; % 真正例，真實為正例，預測也為正例；
    FP(i) = 0; % 假正例，真實為負例，預測為正例；
    for m=1:i
        if gmap_array(orig_location(m)) == 1
            TP(i) = TP(i) + 1;
        else
            FP(i) = FP(i) + 1;
        end
    end
    
    FPR(i) = FP(i) / N_num;
    TPR(i) = TP(i) / P_num;
    
end

auc = trapz(FPR,TPR); % 以FPR為x軸，以TPR為y軸，算積分，即為ROC下的面積
plot(FPR, TPR, '.b-');   title(['Area under ROC curve: ', num2str(auc)])
 

2， AUC_Judd.m

% created: Tilke Judd, Oct 2009
% updated: Zoya Bylinskii, Aug 2014

% 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 
% determined by range of saliency map values at fixation locations;
% 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 all other locations to the total number of posible other
% locations (non-fixated image pixels)

function [score,tp,fp,allthreshes] = AUC_Judd(saliencyMap, fixationMap, jitter, toPlot)
% saliencyMap is the saliency map
% fixationMap is the human fixation map (binary matrix)
% jitter = 1 will add tiny non-zero random constant to all map locations
% to ensure ROC can be calculated robustly (to avoid uniform region)
% if toPlot=1, displays ROC curve

if nargin < 4, toPlot = 0; end
if nargin < 3, jitter = 1; end
score = nan;

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

if any(saliencyMap(:))
    saliencyMap = saliencyMap/sum(saliencyMap(:));
end

if any(fixationMap(:))
    fixationMap = fixationMap/sum(fixationMap(:));
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

% jitter saliency maps that come from saliency models that have a lot of
% zero values.  If the saliency map is made with a Gaussian then it does 
% not need to be jittered as the values are varied and there is not a large 
% patch of the same value. In fact jittering breaks the ordering 
% in the small values!
% if jitter
%     % jitter the saliency map slightly to distrupt ties of the same numbers
%     saliencyMap = saliencyMap+rand(size(saliencyMap))/10000000;
% end

% % normalize saliency map
% saliencyMap = (saliencyMap-min(saliencyMap(:)))/(max(saliencyMap(:))-min(saliencyMap(:)));
% 
% if sum(isnan(saliencyMap(:)))==length(saliencyMap(:))
%     disp('NaN saliencyMap');
%     return
% end

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

allthreshes = sort(Sth, 'descend'); % sort sal map values, to sweep through values
tp = zeros(Nfixations+2,1);
fp = zeros(Nfixations+2,1);
tp(1)=0; tp(end) = 1; 
fp(1)=0; fp(end) = 1;

for i = 1:Nfixations
    thresh = allthreshes(i);
    aboveth = sum(S >= thresh); % total number of sal map values above threshold
    tp(i+1) = i / Nfixations; % ratio sal map values at fixation locations above threshold
    fp(i+1) = (aboveth-i) / (Npixels - Nfixations); % ratio other sal map values above threshold
end 

score = trapz(fp,tp);
allthreshes = [1;allthreshes;0];

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