% Problem 2

clear all

% Use meshgrid as previously to get a grid of points in x-y space
x = linspace(-1,1,101)';
y = x;
[X Y] = meshgrid(x,y);

% Each row of this matrix hold the different combinations of sigma1 sigma2
% andrho we want to evaluate
sigrho = [0.5 0.5 0 ; .5 .25 0 ; .5 .5 -0.5 ; .5 .5 0.5 ; .5 .25 0.5];

figure(1);clf
% Loop over all values of s1, s2, and rho
for idx = 1:size(sigrho,1)
  % The sig1, sig2, and rho paramaters for this iteration
  s1 = sigrho(idx,1);
  s2 = sigrho(idx,2);
  rho = sigrho(idx,3);
  
  % Build the Gaussian
  h_tmp = exp(-(0.5/(1-rho*rho))*( ...
    (X/s1).^2 + (Y/s2).^2 - (2.*X.*Y*rho/(s1*s2)) ));
  % Normalize it so the area = 1
  h_tmp = h_tmp/sum(sum(h_tmp));
  g(:,:,idx) = h_tmp;
  
  % Plot
  subplot(3,2,idx);imagesc(x,y,g(:,:,idx));axis square
  title(['\sigma_1 = ',num2str(s1),' \sigma_2 = ',num2str(s2),' \rho = ',num2str(rho)]);
end

% McAndrew Problem 5.6
clear;
figure(1);clf;colormap(gray)
% Get the image as requested in the text
load('mandrill.mat');
m = im2uint8(ind2gray(X,map));5
% The four sizes of averagers we are going to use
a_size = [3 7 11 17];
% Loop over all sizes
for idx = 1:length(a_size)
  % Use fspecial to get the filters
  h = fspecial('average',[a_size(idx) a_size(idx)]);
  % Do the filtering
  m_filt = filter2(h,m,'same');
  % Plot
  subplot(2,2,idx);imshow(uint8(fix(m_filt)));
  title(['Filter size = ',num2str(a_size(idx))]);
end
print -djpeg ps02p5p6.jpg


% McAndrew Problem 5.7
% Same sequence of steps as in part 5.6
clear;
figure(1);clf;colormap(gray)
load('mandrill.mat');
m = im2uint8(ind2gray(X,map));

g_params = [...
  3 .5 ; 3 1 ; 3 2; ...
  7 1 ; 7 3 ; 7 6; ...
  11 1 ; 11 4 ; 11 8; ...
  21 1 ; 21 5 ; 21 10];

for idx = 1:size(g_params,1)
  h = fspecial('gaussian',g_params(idx,1),g_params(idx,2));
  m_filt = filter2(h,m,'same');
  subplot(4,3,idx);imshow(uint8(fix(m_filt)));
  title(['Size = ',num2str(g_params(idx,1)),' Std. dev. = ', num2str(idx,2)]);
end
print -djpeg ps02p5p7.jpg