roc.m

％ This routine provides a convenient way to produce Pd/FAD information ％ from likelihood ratio info

 function [P_d,FAD] = roc(lr_tgt,lr_clutter,num_sq_km,P_d_lim,...
   FAD_lim, lintype)
 
%    This routine provides a convenient way to produce Pd/FAD information
% from likelihood ratio information.  To be more specific, consider the
% hypothesis test
%
%             target present           >=
%   Declare                   if  lr        T
%             target absent            <
%
% where lr is the test statistic (e.g., a likelihood ratio or log-likelihood
% ratio).  As the threshold T is varied from -infinity to +infinity,  
% corresponding probability of detection and false-alarm density (i.e., 
% the average number of false alarms per square kilometer) will sweep 
% over the whole ROC curve.  
%    This routine estimates this ROC curve from available samples of the
% test statistic lr, drawn from the conditional distributions of targets
% and clutter.  Alternatively, if no output arguments are specified, then
% the routine simply plots the estimated ROC curve in the current 
% figure window; in keeping with standard conventions for SAR ATR 
% ROC plots, a logarithmic scale is used for the x-axis and a linear
% scale for the y-axis.
%
% [P_d, FAD] = roc(lr_tgt, lr_clutter, num_sq_km, P_d_lim, ...
% FAD_lim, lintype)
%
% INPUTS
%   lr_tgt           Samples of test statistic, drawn from tgt distribution
%   lr_clutter       Samples of test statistic, drawn from clutter 
%                     distribution
%   num_sq_km        Number of square kilometers of terrain used to generate
%                     samples
%   P_d_lim          (OPTIONAL) 2-D vector, containing lower and upper
%                     limits of y-axis, for plot of ROC curve
%   FAD_lim          (OPTIONAL) 2-D vector, containing lower and upper
%                     limits of x-axis, for plot of ROC curve
%   lintype          (OPTIONAL) Type of line to use in plot, where the
%                     available types are the standard ones for MATLAB
%                     plots
% OUTPUTS
%   P_d              (OPTIONAL) Estimate of P_d, from available samples
%   FAD              (OPTIONAL) Estimate of FAD, from available samples

%  courtesy William Irving,  ALPHATECH,  9/96

 num_tgt = length(lr_tgt);
 num_clutter = length(lr_clutter);

 sorted_tgt = sort(lr_tgt);
 
 P_d = zeros(num_tgt, 1);
 FAD = zeros(num_tgt, 1);
 for i = 1:num_tgt
     P_d(i) = (num_tgt-i+1) / num_tgt;
     FAD(i) = sum(lr_clutter >= sorted_tgt(i)) / num_sq_km;
 end

 if (nargin >= 4)
     loc = find(P_d >= P_d_lim(1)  &  P_d <= P_d_lim(2));
     P_d = P_d(loc);
     FAD = FAD(loc);
 end
 if (nargin >= 5)
   loc = find(FAD >= FAD_lim(1)  &  FAD <= FAD_lim(2));
   P_d = P_d(loc);
   FAD = FAD(loc);
 end 

 if (nargout == 0)
     if (nargin < 6)
         semilogx(FAD, P_d)
     else
         semilogx(FAD, P_d, lintype)
     end
     xlabel('False Alarms per Square Kilometer');
     ylabel('Probability of Detection');
     grid on;
     FAD = [];
     P_d = [];
 end