Sir, I would like to calculate FAR & FRR dorsal hand images for that I have used EER_DET_Conf program but what type of input provided at Genuine score and Imposter score I dont understand please sort out my problem, I attached my program herewith.

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Balaji M. Sontakke
Balaji M. Sontakke 2016-12-6
回答： Gayathri Nayar 2020-10-27
function [EER confInterEER OP confInterOP]=EER_DET_conf(clients,imposteurs,OPvalue,pas0)
% function: EER_DET_conf
%
% DESCRIPTION:
% It plots traditional curves and gives also some interesting values in
% order to evaluate the performance of a biometric verification system.
% The curves are:
% - Receiver Operating Characteristic (ROC) curve
% - Detection Error Trade-off (DET) curve
% - FAR vs FRR
% The values are:
% - Equal Error Rate (EER) which is computed as the point where
% FAR=FRR
% - Operating Point (OP) which is defined in terms of FRR (%)
% achieved for a fixed FAR
% A 90% interval of confidence is provided for both values (parametric
% method).
%
% INPUTS:
% clients: vector of genuine/client scores
% imposteurs: vector of impostor scores
% OPvalue: value of FAR at which the OP value is estimated
% pas0: number of thresholds used the estimate the score distributions
% (10000 is advised for this parameter)
%
% OUTPUTS:
% EER: EER value
% confInterEER: error margin on EER value
% OP: OP value
% confInterOP: error margin on OP value
%
%
% CONTACT: aurelien.mayoue@int-edu.eu
% 19/11/2007
%%%%%estimation of thresholds used to calculate FAR et FRR
% maximum of client scores
m0 = max (clients);
% size of client vector
num_clients = length (clients);
% minimum impostor scores
m1 = min (imposteurs);
% size of impostor vector
num_imposteurs = length (imposteurs);
% calculation of the step
pas1 = (m0 - m1)/pas0;
x = [m1:pas1:m0]';
num = length (x);
%%%%%
%%%%%calculation of FAR and FRR
for i=1:num
fr=0;
fa=0;
for j=1:num_clients
if clients(j)<x(i)
fr=fr+1;
end
end
for k=1:num_imposteurs
if imposteurs(k)>=x(i)
fa=fa+1;
end
end
FRR(i)=100*fr/num_clients;
FAR(i)=100*fa/num_imposteurs;
end
%%%%%calculation of EER value
tmp1=find (FRR-FAR<=0);
tmps=length(tmp1);
if ((FAR(tmps)-FRR(tmps))<=(FRR(tmps+1)-FAR(tmps+1)))
EER=(FAR(tmps)+FRR(tmps))/2;tmpEER=tmps;
else
EER=(FRR(tmps+1)+FAR(tmps+1))/2;tmpEER=tmps+1;
end
%%%%%
%%%%%calculation of the OP value
tmp2=find (OPvalue-FAR<=0);
tmpOP=length(tmp2);
OP=FRR(tmpOP);
%%%%%
%%%%%calculation of the confidence intervals
[FARconfMIN FRRconfMIN FARconfMAX FRRconfMAX]=ParamConfInter(FAR/100,FRR/100,num_imposteurs,num_clients);
% EER
confInterEER=EER-100*(FARconfMIN(tmpEER)+FRRconfMIN(tmpEER))/2;
% Operating Point
confInterOP=OP-100*FRRconfMIN(tmpOP);
%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%plotting of curves
% FAR vs FRR
figure(1);
plot (x,FRR,'r');
hold on;plot (x,FAR,'b');
xlabel ('Threshold');
ylabel ('Error');
title ('FAR vs FRR graph');
legend('FRR','FAR');
%print('png/FFR-FAR.png','-dpng')
% interpolation for the plotting
equaX=x(tmps)*(FRR(tmps+1)-FAR(tmps+1))+x(tmps+1)*(FAR(tmps)-FRR(tmps));
equaY=FRR(tmps+1)-FAR(tmps+1)+FAR(tmps)-FRR(tmps);
threshold=equaX/equaY;
EERplot=threshold*(FAR(tmps)-FAR(tmps+1))/(x(tmps)-x(tmps+1))+(x(tmps)*FAR(tmps+1)-x(tmps+1)*FAR(tmps))/(x(tmps)-x(tmps+1));
% ROC curve
figure(2);
plot (FAR,100-FRR,'r');
xlabel ('Impostor Attempts Accepted = FAR (%)');
ylabel ('Genuine Attempts Accepted = 1-FRR (%)');
title ('ROC curve');
hold on;scatter (EERplot,100-EERplot,'ok');
hold on;scatter (FAR(tmpOP),100-FRR(tmpOP),'xk');
legend('ROC','EER','Op. Point');
axis([0 50 50 100]);
%print('png/ROC.png','-dpng')
% DET curve
figure(3);
h = Plot_DET(FRR/100,FAR/100,'r');
hold on; Plot_DET(EERplot/100,EERplot/100,'ok');
hold on; Plot_DET(FRR(tmpOP)/100,FAR(tmpOP)/100,'xk');
legend('DET','EER','Op. Point');
title ('DET curve');
%print('png/DET.png','-dpng')
end
function h = Plot_DET (Pmiss, Pfa, plot_code, opt_thickness)
%function h = Plot_DET (Pmiss, Pfa, plot_code, opt_thickness)
%
% Plot_DET plots detection performance tradeoff on a DET plot
% and returns the handle for plotting.
%
% Pmiss and Pfa are the vectors of miss and corresponding false
% alarm probabilities to be plotted.
%
% The usage of Plot_DET is analogous to the standard matlab
% p,ot function.
%
% See DET_usage for an example of how to use Plot_DET.
%
% opt_thickness : controls the line thickness. The default thickness
% is 0.5. A value between 2 and 5 will give a nice thick line.
%
Npts = max(size(Pmiss));
if Npts ~= max(size(Pfa))
error ('vector size of Pmiss and Pfa not equal in call to Plot_DET');
end
%------------------------------
% plot the DET
if ~exist('plot_code')
plot_code = 'y';
end
if ~exist('opt_thickness')
opt_thickness = 0.5;
end
Set_DET_limits;
h = thick(opt_thickness,plot(ppndf(Pfa), ppndf(Pmiss), plot_code));
Make_DET;
end
function Make_DET()
%function Make_DET()
%
% Make_DET creates a plot for displaying the Detection Error
% Trade-off for a detection system. The detection performance
% is characterized by the miss and false alarm probabilities,
% with the axes scaled and labeled so that a normal Gaussian
% distribution will plot as a straight line.
%
% The y axis represents the miss probability.
% The x axis represents the false alarm probability.
%
% See also Compute_DET, Plot_DET and Plot_DCF.
pticks = [0.00001 0.00002 0.00005 0.0001 0.0002 0.0005 ...
0.001 0.002 0.005 0.01 0.02 0.05 ...
0.1 0.2 0.4 0.6 0.8 0.9 ...
0.95 0.98 0.99 0.995 0.998 0.999 ...
0.9995 0.9998 0.9999 0.99995 0.99998 0.99999];
xlabels = [' 0.001' ; ' 0.002' ; ' 0.005' ; ' 0.01 ' ; ' 0.02 ' ; ' 0.05 ' ; ...
' 0.1 ' ; ' 0.2 ' ; ' 0.5 ' ; ' 1 ' ; ' 2 ' ; ' 5 ' ; ...
' 10 ' ; ' 20 ' ; ' 40 ' ; ' 60 ' ; ' 80 ' ; ' 90 ' ; ...
' 95 ' ; ' 98 ' ; ' 99 ' ; ' 99.5 ' ; ' 99.8 ' ; ' 99.9 ' ; ...
' 99.95' ; ' 99.98' ; ' 99.99' ; '99.995' ; '99.998' ; '99.999'];
ylabels = xlabels;
%---------------------------
% Get the min/max values of Pmiss and Pfa to plot
global DET_limits;
if isempty(DET_limits)
Set_DET_limits;
end
Pmiss_min = DET_limits(1);
Pmiss_max = DET_limits(2);
Pfa_min = DET_limits(3);
Pfa_max = DET_limits(4);
%----------------------------
% Find the subset of tick marks to plot
ntick = max(size(pticks));
for (n=ntick:-1:1)
if (Pmiss_min <= pticks(n))
tmin_miss = n;
end
if (Pfa_min <= pticks(n))
tmin_fa = n;
end
end
for (n=1:ntick)
if (pticks(n) <= Pmiss_max)
tmax_miss = n;
end
if (pticks(n) <= Pfa_max)
tmax_fa = n;
end
end
%-----------------------------
% Plot the DET grid
set (gca, 'xlim', ppndf([Pfa_min Pfa_max]));
set (gca, 'xtick', ppndf(pticks(tmin_fa:tmax_fa)));
set (gca, 'xticklabel', xlabels(tmin_fa:tmax_fa,:));
set (gca, 'xgrid', 'on');
xlabel ('False Acceptance Rate (in %)');
set (gca, 'ylim', ppndf([Pmiss_min Pmiss_max]));
set (gca, 'ytick', ppndf(pticks(tmin_miss:tmax_miss)));
set (gca, 'yticklabel', ylabels(tmin_miss:tmax_miss,:));
set (gca, 'ygrid', 'on')
ylabel ('False Reject Rate (in %)')
set (gca, 'box', 'on');
axis('square');
axis(axis);
end
function [FARconfMIN FRRconfMIN FARconfMAX FRRconfMAX]=ParamConfInter(FAR,FRR,num_imposteurs,num_clients)
% function: ParamConfInter
%
% DESCRIPTION:
% It calculates a 90% interval of confidence for each value of FAR and FRR
% using a parametric method
%
% INPUTS:
% FAR: FAR vector
% FAR: FRR vector
% num_imposteurs: number of impostor tests
% num_clients: number of client tests
%
% OUTPUTS:
% FARconfMIN: vector of minimum values of FAR
% FRRconfMIN: vector of minimum values of FRR
% FARconfMAX: vector of maximum values of FAR
% FRRconfMAX: vector of maximum values of FRR
%
%
% CONTACT: aurelien.mayoue@int-edu.eu
% 19/11/2007
% size of error vectors
numErr = length (FAR);
% calculation of the confidence interval
for i=1:numErr
varFRR=sqrt((FRR(i))*(1-FRR(i))/num_clients);
FRRconfMIN(i)=FRR(i)-1.645*varFRR;
FRRconfMAX(i)=FRR(i)+1.645*varFRR;
varFAR=sqrt((FAR(i))*(1-FAR(i))/num_imposteurs);
FARconfMIN(i)=FAR(i)-1.645*varFAR;
FARconfMAX(i)=FAR(i)+1.645*varFAR;
end
end
function norm_dev = ppndf (cum_prob)
%function ppndf (prob)
%The input endto this function is a cumulative probability.
%The output from this function is the Normal deviate
%that corresponds to that probability. For example:
% INPUT OUTPUT
% 0.001 -3.090
% 0.01 -2.326
% 0.1 -1.282
% 0.5 0.0
% 0.9 1.282
% 0.99 2.326
% 0.999 3.090
SPLIT = 0.42;
A0 = 2.5066282388;
A1 = -18.6150006252;
A2 = 41.3911977353;
A3 = -25.4410604963;
B1 = -8.4735109309;
B2 = 23.0833674374;
B3 = -21.0622410182;
B4 = 3.1308290983;
C0 = -2.7871893113;
C1 = -2.2979647913;
C2 = 4.8501412713;
C3 = 2.3212127685;
D1 = 3.5438892476;
D2 = 1.6370678189;
% the following code is matlab-tized for speed.
% on 200000 points, time went from 76 seconds to 5 seconds!
% original routine is included at end for reference
[Nrows Ncols] = size(cum_prob);
norm_dev = zeros(Nrows, Ncols); % preallocate norm_dev for speed
cum_prob(find(cum_prob>= 1.0)) = 1-eps;
cum_prob(find(cum_prob<= 0.0)) = eps;
R = zeros(Nrows, Ncols); % preallocate R for speed
% adjusted prob matrix
adj_prob=cum_prob-0.5;
centerindexes = find(abs(adj_prob) <= SPLIT);
tailindexes = find(abs(adj_prob) > SPLIT);
% do centerstuff first
R(centerindexes) = adj_prob(centerindexes) .* adj_prob(centerindexes);
norm_dev(centerindexes) = adj_prob(centerindexes) .* ...
(((A3 .* R(centerindexes) + A2) .* R(centerindexes) + A1) .* R(centerindexes) + A0);
norm_dev(centerindexes) = norm_dev(centerindexes) ./ ((((B4 .* R(centerindexes) + B3) .* R(centerindexes) + B2) .* ...
R(centerindexes) + B1) .* R(centerindexes) + 1.0);
% find left and right tails
right = find(cum_prob(tailindexes)> 0.5);
left = find(cum_prob(tailindexes)< 0.5);
% do tail stuff
R(tailindexes) = cum_prob(tailindexes);
% if prob > 0.5 then prob = 1-prob
R(tailindexes(right)) = 1 - cum_prob(tailindexes(right));
R(tailindexes) = sqrt ((-1.0) .* log (R(tailindexes)));
norm_dev(tailindexes) = (((C3 .* R(tailindexes) + C2) .* R(tailindexes) + C1) .* R(tailindexes) + C0);
norm_dev(tailindexes) = norm_dev(tailindexes) ./ ((D2 .* R(tailindexes) + D1) .* R(tailindexes) + 1.0);
% swap sign on left tail
norm_dev(tailindexes(left)) = norm_dev(tailindexes(left)) .* -1.0;
return
end
%--------------------
% here is the old routine, which is much slower
function norm_dev = oldppndf (cum_prob)
%function ppndf (prob)
%The input to this function is a cumulative probability.
%The output from this function is the Normal deviate
%that corresponds to that probability. For example:
% INPUT OUTPUT
% 0.001 -3.090
% 0.01 -2.326
% 0.1 -1.282
% 0.5 0.0
% 0.9 1.282
% 0.99 2.326
% 0.999 3.090
SPLIT = 0.42;
A0 = 2.5066282388;
A1 = -18.6150006252;
A2 = 41.3911977353;
A3 = -25.4410604963;
B1 = -8.4735109309;
B2 = 23.0833674374;
B3 = -21.0622410182;
B4 = 3.1308290983;
C0 = -2.7871893113;
C1 = -2.2979647913;
C2 = 4.8501412713;
C3 = 2.3212127685;
D1 = 3.5438892476;
D2 = 1.6370678189;
[Nrows Ncols] = size(cum_prob);
norm_dev = zeros(Nrows, Ncols); % preallocate norm_dev for speed
for irow=1:Nrows
for icol=1:Ncols
prob = cum_prob(irow, icol);
if (prob >= 1.0)
prob = 1-eps;
elseif (prob <= 0.0)
prob = eps;
end
q = prob - 0.5;
if (abs(prob-0.5) <= SPLIT)
r = q * q;
pf = q * (((A3 * r + A2) * r + A1) * r + A0);
pf = pf / ((((B4 * r + B3) * r + B2) * r + B1) * r + 1.0);
else
if (q>0.0)
r = 1.0-prob;
else
r = prob;
end
r = sqrt ((-1.0) * log (r));
pf = (((C3 * r + C2) * r + C1) * r + C0);
pf = pf / ((D2 * r + D1) * r + 1.0);
if (q < 0)
pf = pf * (-1.0);
end
end
norm_dev(irow, icol) = pf;
end
end
end
function Set_DET_limits(Pmiss_min, Pmiss_max, Pfa_min, Pfa_max)
% function Set_DET_limits(Pmiss_min, Pmiss_max, Pfa_min, Pfa_max)
%
% Set_DET_limits initializes the min.max plotting limits for P_min and P_fa.
%
% See DET_usage for an example of how to use Set_DET_limits.
Pmiss_min_default = 0.0005+eps;
Pmiss_max_default = 0.5-eps;
Pfa_min_default = 0.0005+eps;
Pfa_max_default = 0.5-eps;
global DET_limits;
%-------------------------
% If value not supplied as arguement, then use previous value
% or use default value if DET_limits hasn't been initialized.
if (~isempty(DET_limits))
Pmiss_min_default = DET_limits(1);
Pmiss_max_default = DET_limits(2);
Pfa_min_default = DET_limits(3);
Pfa_max_default = DET_limits(4);
end
if ~(exist('Pmiss_min')); Pmiss_min = Pmiss_min_default; end;
if ~(exist('Pmiss_max')); Pmiss_max = Pmiss_max_default; end;
if ~(exist('Pfa_min')); Pfa_min = Pfa_min_default; end;
if ~(exist('Pfa_max')); Pfa_max = Pfa_max_default; end;
%-------------------------
% Limit bounds to reasonable values
Pmiss_min = max(Pmiss_min,eps);
Pmiss_max = min(Pmiss_max,1-eps);
if Pmiss_max <= Pmiss_min
Pmiss_min = eps;
Pmiss_max = 1-eps;
end
Pfa_min = max(Pfa_min,eps);
Pfa_max = min(Pfa_max,1-eps);
if Pfa_max <= Pfa_min
Pfa_min = eps;
Pfa_max = 1-eps;
end
%--------------------------
% Load DET_limits with bounds to use
DET_limits = [Pmiss_min Pmiss_max Pfa_min Pfa_max];
end
function [lh] = thick(w,lh)
% THICK chages the width of the lines references by habdles
% lh, the line handles
% w, new width (default is 0.5)
% Example usage: thick(2,plot([1:5],[1,0,1,0,1],'b'))
for i=1:length(lh)
set (lh(i),'LineWidth',w);
end
end

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回答（3 个）

wisam kh
wisam kh 2019-2-1
Could you give us an example to apply this code?
sima
sima 2019-8-2
i need a main program plz
Gayathri Nayar
Gayathri Nayar 2020-10-27
The inputs for this function are the genuine and imposter scores that are generated after matching, operating point and the number of thresholds that you need for estimating the score distributions. After the testing phase, you will get a matrix having all the matching scores. The diagonal values of the matrix will give you the genune score and the remaining values are the imposter scores.

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