%2a
syms x y sigma
h = exp(-(x.^2 + y.^2)/(2*sigma^2))/(2*pi*sigma^2);
h_y = diff(h,y,1)% first diffentiate of h with respect to y
%2b
sigma= 1.5;
delta = 1;
sigma = sigma.*delta;
L = 2*ceil(sigma*4)+1; % fill in a constant to define the matrix size
xymax = (L-1)/2; % the maximum of the x and the y coordinate
xrange = -xymax:xymax; % the range of x values
yrange = xrange; % the range of y values
figure(3)
N = (L-1)/2; % get the size of half of the full range
[x,y]=meshgrid(-N:N,-N:N); % create the coordinates of a 2D orthogonal grid
hy = -(y.*exp(-(x.^2 + y.^2)/(2*sigma^2)))/(2*sigma^4*pi)
C = cat(3, ones(size(hy)),ones(size(hy)),zeros(size(hy)));
% create a RGB matrix to define the colour of the surface plot
hd =surf(xrange,yrange,hy,C,'FaceColor','interp','Facelight','phong');
% % create the surface plot of the gaussian
camlight right % add a light at the right side of the scene
xlim([-xymax xymax]); % set appropriate axis limits
ylim([-xymax xymax]);
xlabel('x'); % add axis labels
ylabel('y');
zlabel('hy(x,y)');
print -r150 -dpng ex3_2b.png % print the result to file
imfiltered_hy = imfilter(im,hy) ; % apply the filter
imfiltered_hy = mat2gray(imfiltered_hy);
figure(4);imshow(imfiltered_hy,[]);
imwrite(imfiltered_hy, 'Imfiltered_hy_Ex3_Q2b.jpg')