% CS143, Intro to Computer Vision, Michael Black
% Matlab code for lecture 5 (pyramids and edges)

im=double(imread('barbara.tif'));
% plot a 1D signal that shows what edges look like
plot(im(250,:))

% build our Gaussian filter
G=fspecial('gaussian',3,1);

% smooth the image a few times
cim = imfilter(im,G,'symmetric','conv');
cim = imfilter(cim,G,'symmetric','conv');
cim = imfilter(cim,G,'symmetric','conv');

% plot the smoothed intensity profile
s=cim(250,:);
plot(s)

% look at the smoothed image
imagesc(cim)

% plot the first difference of the smoothed signal
% Note that I cut off the ends of the signal.
clf
ds=(s(3:length(s)-1)-s(2:length(s)-2));
plot(ds);
hold on
plot((s(2:length(ds))-mean(s))/5,'r');

% Simple example of an edge:
clf
im=zeros(100,100);
im(:,1:30)=100;
im(:,70:100)=100;
imagesc(im)

cim = imfilter(im,G,'symmetric','conv');
cim = imfilter(cim,G,'symmetric','conv');
cim = imfilter(cim,G,'symmetric','conv');
imagesc(cim)

% plot original image intensity along a line
clf
plot(cim(50,:));
% plot smoothed intensity
% cut off ends to remove boundary effects
sim=cim(5:95,5:95);
plot(sim(50,:))

% compute and plot the first derivative using finite differences
sderiv=(sim(50,2:size(sim,1))-sim(50,1:size(sim,1)-1));
plot(sderiv)

% compute and plot the second derivative
sderiv2=sderiv(2:length(sderiv))-sderiv(1:length(sderiv)-1);
plot(sderiv2)