function ID=create_scene(templates)
%lets the user choose object types (generator index for templates),
%deformation strength, and noise level.Computes the deformed image ID.
%templates are stored in the 3D array templates
%1.ENTER.
answer='y';objects=[];[l1,l2]=size(templates(:,:,1));I=zeros(l1,l2);
'To select a template type press ENTER'
pause 

while answer =='y'
val1=0;val2=0;val3=0;val4=0;val5=0;
select_t
pause
close
load types
objects=[objects,val1+2*val2+3*val3+4*val4+5*val5];
answer=input('Do you want more objects in the scene ? Answer y/n','s')
end
nobjects=length(objects)

%2. EUCLID. Apply Euclidean group SE(2) to templates
for i=1:nobjects
    DX=0;DY=0;ROT=0;
   'To apply Eucldean group to (next) template press ENTER'
    select_Euclid
    pause
    close
    load Euclid
    dx=DX;dy=DY;rot=ROT;
   
	 Inew=Euclid([dx dy], rot, templates(:,:,objects(i)));  
    I=max(I,Inew);
   
end 
%3.CLUTTER,
%compute cluttered background
level=0;
noise_create
pause
close
load Noise
'clutter level='
level
w=7;l=5;N=30;background=zeros(l1,l2);
ws=[-round(w/2):round(w/2)];
ls=[-round(l/2):round(l/2)];
%start simulating clutter
for i=1:ceil(rand(1)*N)
   x1=ceil(l1*rand(1));
   x2=ceil(l2*rand(1));
   v1=round(x1+ls);v2=round(x2+ws);
   v1=max(1,min(v1,l1));v2=max(1,min(v2,l2));
   new=zeros(l1,l2);new(v1,v2)=level/200.*rand(1).*ones(length(v1),length(v2));
   background=max(background, new);
end
	background=diffeo(background,level/100);
	deflevel=0;
   def_create
   pause
   close
   load Noise
   'deformation level='
   deflevel
   
%4.DIFFEO.
   I=diffeo(I,1.5*deflevel);
%form cluttered and deformed image
ID=max(I,background);
ID=ID>.5;

%5. NOISE.
%add binary noise to BW image
errorb=0;
bin_noise_create
pause
close
load Noise
'binary noise level='
errorb
ID=addbin(ID,errorb/100);


%6. DISPLAY.
%display I and ID
subplot(1,2,1), see(I)
title('image I')
axis('image')
subplot(1,2,2),see(ID)
title('observed image ID');
axis('image')
	





%auxiliary functions:

function fig = select_t()

load select_t

h0 = figure('Color',[0.8 0.8 0.8], ...
	'Colormap',mat0, ...
	'PointerShapeCData',mat1, ...
	'Position',[364 111 560 420], ...
	'Tag','Fig1');
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'BackgroundColor',[0.752941176470588 0.752941176470588 0.752941176470588], ...
	'FontSize',22, ...
	'ListboxTop',0, ...
	'Position',[70.5 189.75 295.5 99], ...
	'String','Select one object type (template generator) by pushing the relevant button', ...
	'Style','text', ...
	'Tag','StaticText1');
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'Callback','val1=get(gco,''Value'');save types val1', ...
	'FontSize',22, ...
	'ListboxTop',0, ...
	'Position',[16.5 62.25 33.75 24], ...
	'String','1', ...
	'Tag','Pushbutton1', ...
	'Value',1);
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'Callback','val2=get(gco,''Value'');save types val2', ...
	'FontSize',22, ...
	'ListboxTop',0, ...
	'Position',[88.875 61.875 31.5 25.5], ...
	'String','2', ...
	'Tag','Pushbutton2', ...
	'Value',1);
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'Callback','val5=get(gco,''Value'');save types val5', ...
	'FontSize',22, ...
	'ListboxTop',0, ...
	'Position',[310.5 61.5 33 24.75], ...
	'String','5', ...
	'Tag','Pushbutton3');
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'ButtonDownFcn','4', ...
	'Callback','val4=get(gco,''Value'');save types val4', ...
	'FontSize',22, ...
	'ListboxTop',0, ...
	'Position',[231.75 62.25 39.75 23.25], ...
	'String','4', ...
	'Tag','Pushbutton4');
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'Callback','val3=get(gco,''Value'');save types val3', ...
	'FontSize',22, ...
	'ListboxTop',0, ...
	'Position',[159 62.25 34.5 24], ...
	'String','3', ...
	'Tag','Pushbutton5');
if nargout > 0, fig = h0; end


function result=fastint(I,s1,s2)
%interpolates (bilinearly) matrix I given at equally spaced grid points
%to points displaced by vector field s with components s1 and s2
[l1,l2]=size(I);
[Y,X]=meshgrid(1:l2,(1:l1)');
XI=X+s1;M=XI>l1.*ones(l1,l2);XI=(1-M).*XI+M.*l1.*ones(l1,l2);
M=XI<ones(l1,l2);XI=(1-M).*XI+M.*ones(l1,l2);
YI=Y+s2;M=YI>l2.*ones(l1,l2);YI=(1-M).*YI+M.*l2.*ones(l1,l2);
M=YI<ones(l1,l2);YI=(1-M).*YI+M.*ones(l1,l2);
result=interp2(Y,X,I,YI,XI);


function [Inew]=Euclid(trans,rot,I)
%implement the uclidean group
%trans =2-vector in percentages of l1 and l2
%rot =scalar in degrees
rot=rot*pi/180;
[l1,l2]=size(I);
[X2,X1]=meshgrid(1:l2,1:l1);
X1t=X1-trans(1)*l1/100;X2t=X2-trans(2)*l2/100;
mid1=l1/2;mid2=l2/2;
X1t=X1t-mid1;X2t=X2t-mid2;
Y1=mid1+cos(rot).*X1t+sin(rot).*X2t;
Y2=mid2-sin(rot).*X1t+cos(rot).*X2t;
Inew=fastint(I,Y1-X1,Y2-X2);

function Idef=diffeo(Ibin,strength)
%transforms binary image Ibin by random diffeomorphism;strength is real parameter
%measuring the amount of deformation
[l1,l2]=size(Ibin);
%use 2*r^2 Fourier coefficients
r=5;
% for use in local group deformation compute basis function
v1=[1:l1];v2=[1:l2];w=[1:r];
M1=sin(pi/l1.*kron(v1,w'));M2=sin(pi/l2.*kron(v2,w'));
%and the two matrices
w=w.^2;
N1=kron(ones(1,r),w');N2=kron(w,ones(1,r)');
t1=strength.*randn(r);t2=strength.*randn(r);
s1=M1'*t1*M2;s2=M1'*t2*M2;
Idef=fastint(Ibin,s1,s2);

function fig = noise_create()

load noise_create

h0 = figure('Color',[0.8 0.8 0.8], ...
	'Colormap',mat0, ...
	'PointerShapeCData',mat1, ...
	'Position',[415 109 560 420], ...
	'Tag','Fig1');
h1 = uicontrol('Parent',h0, ...
	'BackgroundColor',[0.752941 0.752941 0.752941], ...
	'Callback','level=get(gco,''Value'');save Noise level', ...
	'ListboxTop',0, ...
	'Max',300, ...
	'Position',[21 20 20 320], ...
	'Style','slider', ...
	'Tag','Slider1');
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'BackgroundColor',[0.752941 0.752941 0.752941], ...
	'FontSize',22, ...
	'ListboxTop',0, ...
	'Position',[202.5 128.25 133.5 93], ...
	'String','Enter desired level of clutter', ...
	'Style','text', ...
	'Tag','StaticText1');
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'BackgroundColor',[0.752941 0.752941 0.752941], ...
	'ListboxTop',0, ...
	'Position',[42.75 225 46.5 20.25], ...
	'String','300', ...
	'Style','text', ...
	'Tag','StaticText2');
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'BackgroundColor',[0.752941 0.752941 0.752941], ...
	'ListboxTop',0, ...
	'Position',[42 6.75 45 25.5], ...
	'String','0', ...
	'Style','text', ...
	'Tag','StaticText3');
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'BackgroundColor',[0.752941 0.752941 0.752941], ...
	'ListboxTop',0, ...
	'Position',[43.5 75 47.25 25.5], ...
	'String','100', ...
	'Style','text', ...
	'Tag','StaticText5');
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'BackgroundColor',[0.752941 0.752941 0.752941], ...
	'ListboxTop',0, ...
	'Position',[43.5 152.25 48 32.25], ...
	'String','200', ...
	'Style','text', ...
	'Tag','StaticText6');
if nargout > 0, fig = h0; end

function JD=addbin(J,errorprob)
%computes deformed image JD by adding binary noise to 
%BW image J; addition modulo 2
[l1,l2]=size(J);
errors=rand(l1,l2)<errorprob;
JD=rem(J+errors,2);

function fig = bin_noise_create()

load bin_noise_create

h0 = figure('Color',[0.8 0.8 0.8], ...
	'Colormap',mat0, ...
	'PointerShapeCData',mat1, ...
	'Position',[225 120 560 420], ...
	'Tag','Fig1');
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'BackgroundColor',[0.752941176470588 0.752941176470588 0.752941176470588], ...
	'FontSize',22, ...
	'ListboxTop',0, ...
	'Position',[60 210.75 327.75 69.75], ...
	'String','SELECT BINARY NOISE LEVEL IN PERCENT', ...
	'Style','text', ...
	'Tag','StaticText1');
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'BackgroundColor',[0.752941176470588 0.752941176470588 0.752941176470588], ...
	'Callback','errorb =get(gco,''Value'');save Noise errorb', ...
	'ListboxTop',0, ...
	'Max',10, ...
	'Position',[58.5 107.25 347.25 25.5], ...
	'Style','slider', ...
	'Tag','Slider1');
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'BackgroundColor',[0.752941176470588 0.752941176470588 0.752941176470588], ...
	'FontSize',22, ...
	'ListboxTop',0, ...
	'Position',[65.25 137.25 22.5 24], ...
	'String','O', ...
	'Style','text', ...
	'Tag','StaticText2');
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'BackgroundColor',[0.752941176470588 0.752941176470588 0.752941176470588], ...
	'FontSize',22, ...
	'ListboxTop',0, ...
	'Position',[372 135 42.75 25.5], ...
	'String','10', ...
	'Style','text', ...
	'Tag','StaticText3');
if nargout > 0, fig = h0; end

function fig = def_create()

load def_create

h0 = figure('Color',[0.8 0.8 0.8], ...
	'Colormap',mat0, ...
	'PointerShapeCData',mat1, ...
	'Position',[120 120 560 420], ...
	'Tag','Fig1');
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'BackgroundColor',[0.752941176470588 0.752941176470588 0.752941176470588], ...
	'Callback','Select deformation level applied to template', ...
	'FontSize',22, ...
	'ListboxTop',0, ...
	'Position',[54 250.5 325.5 43.5], ...
	'String','Select deformation level applied to template', ...
	'Style','text', ...
	'Tag','StaticText1');
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'BackgroundColor',[0.752941176470588 0.752941176470588 0.752941176470588], ...
	'Callback','deflevel=get(gco,''Value'');save Noise deflevel', ...
	'ListboxTop',0, ...
	'Position',[55.5 138 312 27], ...
	'Style','slider', ...
	'Tag','Slider1');
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'BackgroundColor',[0.752941176470588 0.752941176470588 0.752941176470588], ...
	'ButtonDownFcn','0', ...
	'FontSize',12, ...
	'ListboxTop',0, ...
	'Position',[59.25 166.5 19.5 14.25], ...
	'String','0', ...
	'Style','text', ...
	'Tag','StaticText2');
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'BackgroundColor',[0.752941176470588 0.752941176470588 0.752941176470588], ...
	'FontSize',12, ...
	'ListboxTop',0, ...
	'Position',[354.75 167.25 14.25 15.75], ...
	'String','1', ...
	'Style','text', ...
	'Tag','StaticText3');
if nargout > 0, fig = h0; end

function fig = select_Euclid()

load select_Euclid

h0 = figure('Color',[0.8 0.8 0.8], ...
	'Colormap',mat0, ...
	'PointerShapeCData',mat1, ...
	'Position',[221 135 560 420], ...
	'Tag','Fig1');
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'BackgroundColor',[0.752941176470588 0.752941176470588 0.752941176470588], ...
	'Callback',mat2, ...
	'FontSize',22, ...
	'ListboxTop',0, ...
	'Position',[24 231.75 367.5 69], ...
	'String',mat3, ...
	'Style','text', ...
	'Tag','StaticText1');
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'BackgroundColor',[0.752941176470588 0.752941176470588 0.752941176470588], ...
	'Callback','DY=get(gco,''Value'');save Euclid DY', ...
	'ListboxTop',0, ...
	'Max',20, ...
	'Min',-20, ...
	'Position',[262.5 54.75 18.75 161.25], ...
	'Style','slider', ...
	'Tag','Slider1', ...
	'Value',3);
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'BackgroundColor',[0.752941176470588 0.752941176470588 0.752941176470588], ...
	'Callback','DX=get(gco,''Value''); save Euclid  DX', ...
	'ListboxTop',0, ...
	'Max',20, ...
	'Min',-20, ...
	'Position',[81.75 57.75 17.25 158.25], ...
	'Style','slider', ...
	'Tag','Slider2');
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'BackgroundColor',[0.752941176470588 0.752941176470588 0.752941176470588], ...
	'Callback','ROT=get(gco,''Value'');save Euclid  ROT', ...
	'ListboxTop',0, ...
	'Max',90, ...
	'Min',-90, ...
	'Position',[87.75 10.5 195.75 15], ...
	'String','6.3', ...
	'Style','slider', ...
	'Tag','Slider3', ...
	'Value',-29.16);
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'BackgroundColor',[0.752941176470588 0.752941176470588 0.752941176470588], ...
	'FontSize',11, ...
	'ListboxTop',0, ...
	'Position',[117.75 134.25 18 12.75], ...
	'String','DX', ...
	'Style','text', ...
	'Tag','StaticText2');
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'BackgroundColor',[0.752941176470588 0.752941176470588 0.752941176470588], ...
	'FontSize',11, ...
	'ListboxTop',0, ...
	'Position',[309 132 18.75 15], ...
	'String','DY', ...
	'Style','text', ...
	'Tag','StaticText3');
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'BackgroundColor',[0.752941176470588 0.752941176470588 0.752941176470588], ...
	'FontSize',11, ...
	'ListboxTop',0, ...
	'Position',[170.25 38.25 30 12.75], ...
	'String','ROT', ...
	'Style','text', ...
	'Tag','StaticText4');
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'BackgroundColor',[0.752941176470588 0.752941176470588 0.752941176470588], ...
	'ListboxTop',0, ...
	'Max',30, ...
	'Min',-30, ...
	'Position',[289.5 77.25 20.25 19.5], ...
	'String','20', ...
	'Style','text', ...
	'Tag','StaticText5');
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'BackgroundColor',[0.752941176470588 0.752941176470588 0.752941176470588], ...
	'Callback','30', ...
	'FontSize',11, ...
	'ListboxTop',0, ...
	'Position',[287.25 191.25 21 15], ...
	'String','20', ...
	'Style','text', ...
	'Tag','StaticText6');
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'BackgroundColor',[0.752941176470588 0.752941176470588 0.752941176470588], ...
	'FontSize',11, ...
	'ListboxTop',0, ...
	'Max',30, ...
	'Min',-30, ...
	'Position',[58.5 81.75 17.25 14.25], ...
	'String','-20', ...
	'Style','text', ...
	'Tag','StaticText7');
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'BackgroundColor',[0.752941176470588 0.752941176470588 0.752941176470588], ...
	'FontSize',11, ...
	'ListboxTop',0, ...
	'Position',[54.75 187.5 21 13.5], ...
	'String','20', ...
	'Style','text', ...
	'Tag','StaticText8');
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'BackgroundColor',[0.752941176470588 0.752941176470588 0.752941176470588], ...
	'ListboxTop',0, ...
	'Position',[59.25 11.25 21.75 13.5], ...
	'String','-90', ...
	'Style','text', ...
	'Tag','StaticText9');
h1 = uicontrol('Parent',h0, ...
	'Units','points', ...
	'BackgroundColor',[0.752941176470588 0.752941176470588 0.752941176470588], ...
	'ListboxTop',0, ...
	'Position',[290.25 9 24.75 15], ...
	'String','90', ...
	'Style','text', ...
	'Tag','StaticText10');
if nargout > 0, fig = h0;
end

function see(I)
%displays normalized image
z=I-min(min(I));z=z./max(max(z));
image(30.*z)