%%% EE 148  - Some figures for lecture 2
%%% (c) March 29 2000 - P. Perona Caltech
%% Modified April 3, 2003

SIZE = 128; %% Width and height of image
SIZE2 = SIZE/2;
RADIUS = 3;
POS_JITTER = 10;

NOISE_LEVEL = [ 0 0.1 0.3 1 ];

noise = randn(SIZE,SIZE);
ima = zeros(SIZE,SIZE);
XX = round(POS_JITTER*randn(1))+[SIZE2-RADIUS:SIZE2+RADIUS]; %% X coordinates of signal
YY = round(POS_JITTER*randn(1))+[SIZE2-RADIUS:SIZE2+RADIUS]; %% Y coordinates of signal
ima(YY,XX) = 1;


%% Show image with different noise levels
for i=1:length(NOISE_LEVEL),
figure(i); clf; imagesc(ima+NOISE_LEVEL(i)*noise);
colormap gray; axis off
end;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% ROC
NOISE_LEVEL = [0.1 0.3 1 2];  %% St. dev. of noise
N_EXPER = 1000;
figure(10); clf

for i=1:length(NOISE_LEVEL),
    R_S = 1 + NOISE_LEVEL(i)*randn(1,N_EXPER);  %% Response to signal
    R_N = NOISE_LEVEL(i)*randn(1,N_EXPER);      %% Response to noise
    [NS,XS] = hist(R_S);
    [NN,XN] = hist(R_N);
    figure(10); 
    subplot(2,4,1+(i-1)*2); plot(XS,NS/N_EXPER,'g',XN,NN/N_EXPER,'r','LineWidth',2);
    xlabel('strength of response');
    ylabel('relative frequency');
    title(['Response to signal (green) and no-signal (red) for \sigma='  num2str(NOISE_LEVEL(i))]);
    
    %% Calculate and display ROC
    R_all = sort([R_S R_N]);
    for j=1:length(R_all),
        FA(j)=100*sum(R_N>=R_all(j))/N_EXPER; %% Percent false alarms
        PD(j)=100*sum(R_S>=R_all(j))/N_EXPER; %% Percent detected
    end;
    figure(10); subplot(2,4,2+(i-1)*2); plot(FA,PD,'LineWidth',2);
    xlabel('percent false alarms');
    ylabel('percent detected');
    title(['ROC curve for noise \sigma=' num2str(NOISE_LEVEL(i))]);
end;