MAE

定义

Mean Absolute Error(平均绝对误差)， 观测值与真实值的误差绝对值的平均值。

计算方式

$MAE=\frac{1}{H\times W}{\sum }_{x=1}^H{\sum }_{y=1}^W|P(x,y)-G(x,y)|$

function mae = MAE(smap, gtImg)
% Code Author: Wangjiang Zhu
% Email: wangjiang88119@gmail.com
% Date: 3/24/2014
if size(smap, 1) ~= size(gtImg, 1) || size(smap, 2) ~= size(gtImg, 2)
    error('Saliency map and gt Image have different sizes!\n');
end

if ~islogical(gtImg)
    gtImg = gtImg(:,:,1) > 128;
end

fgPixels = smap(gtImg);
fgErrSum = length(fgPixels) - sum(fgPixels);
bgErrSum = sum(smap(~gtImg));
mae      = (fgErrSum + bgErrSum) / numel(gtImg);

Fmeasure

定义

用来平衡准确率和召回率的评估值

计算方式

$F_{\beta }=\frac{\left(1+{\beta }^2\right)\times \text{ Precision }\times \text{ Recall }}{{\beta }^2\times \text{ Precision }+\text{ Recall }}$
其中${\beta }^2$一般取0.3
$P=\frac{TP}{TP+FP}$
$R=\frac{TP}{TP+FN}$

这幅图形象地说明了精确率和召回率的计算关系。
这里贴出代码

function [PreFtem, RecallFtem, FmeasureF] = Fmeasure(sMap, gtMap, gtsize)

sumLabel = 2* mean(sMap(:));
if (sumLabel > 1)
    sumLabel = 1;
end

Label3 = zeros( gtsize );
Label3(sMap>=sumLabel ) = 1;

NumRec   = length( find( Label3==1 ) );
LabelAnd = Label3 & gtMap; %TP
NumAnd   = length( find ( LabelAnd==1 ) );
num_obj  = sum(sum(gtMap));

if NumAnd == 0
    PreFtem    = 0;
    RecallFtem = 0;
    FmeasureF  = 0;
else
    PreFtem    = NumAnd/NumRec;
    RecallFtem = NumAnd/num_obj;
    FmeasureF  = ((1.3*PreFtem*RecallFtem)/(0.3*PreFtem+RecallFtem));
end

Smeasure

定义

计算前景像素与真值的相似度

计算方式

$S_m=\alpha \ast S_o+(1-\alpha )\ast S_r$
$S_o=\frac{2\ast E(pre)}{E(pre{)}^2+1+\sigma +e}$
$S_r$表示按重心位置，然后切割成四个区域，对四个区域按像素占整张图的区域面积作为权重，计算四个区域SSIM的加权平均。其实就是对滑窗法做了改进

function Q = Smeasure(prediction,GT)
% Smeasure computes the similarity between the foreground map and
% ground truth(as proposed in "Structure-measure: A new way to evaluate
% foreground maps" [Deng-Ping Fan et. al - ICCV 2017])
% Usage:
%   Q = Smeasure(prediction,GT)
% Input:
%   prediction - Binary/Non binary foreground map with values in the range
%                [0 1]. Type: double.
%   GT - Binary ground truth. Type: logical. 
% Output:
%   Q - The computed similarity score
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Check input
if (~isa(prediction,'double'))
    error('The prediction should be double type...');
end
if ((max(prediction(:))>1) || min(prediction(:))<0)
    error('The prediction should be in the range of [0 1]...');
end
if (~islogical(GT))
    error('GT should be logical type...');
end

y = mean2(GT);

if (y==0)% if the GT is completely black
    x = mean2(prediction);
    Q = 1.0 - x; %only calculate the area of intersection
elseif(y==1)%if the GT is completely white
    x = mean2(prediction);
    Q = x; %only calcualte the area of intersection
else
    alpha = 0.5;
    Q = alpha*S_object(prediction,GT)+(1-alpha)*S_region(prediction,GT);
end

end

PR_Curve

定义

对精确率和召回率做直方图，然后对每个直方图做累加和，分别计算精确率和召回率，最终形成一组曲线。

计算方式

function [precision, recall] = CalPR(smapImg, gtImg)
% Code Author: Wangjiang Zhu
% Email: wangjiang88119@gmail.com
% Date: 3/24/2014

if ~islogical(gtImg)
    gtImg = gtImg(:,:,1) > 128;
end
if any(size(smapImg) ~= size(gtImg))
    error('saliency map and ground truth mask have different size');
end

gtPxlNum = sum(gtImg(:));
if 0 == gtPxlNum
    error('no foreground region is labeled');
end

targetHist = histc(smapImg(gtImg), 0:255);
nontargetHist = histc(smapImg(~gtImg), 0:255);

targetHist = flipud(targetHist);
nontargetHist = flipud(nontargetHist);

targetHist = cumsum( targetHist );
nontargetHist = cumsum( nontargetHist );

precision = targetHist ./ (targetHist + nontargetHist + eps);
if any(isnan(precision))
    warning('there exists NAN in precision, this is because your saliency map do not range from 0 to 255\n');
end
recall = targetHist / gtPxlNum;