Matlab Commands Used in Class

Below is a summary of matlab commands used in class.

Class of Jan. 22nd, 2013

load mandrill
whos
image(X)
colormap(gray)
colormap(map)
load clown
whos
image(X)
colormap(map)
colormap(gray)
Y=X(1:2:end,1:2:end);
size(X)
size(Y)
image(Y)
Z=X(:,end:-1,1);
image(Z); colormap(gray)
figure(2); image(X); colormap(gray)
Z2=X(end:-1:1,:);
figure(3); image(Z2); colormap(gray)
A=imread('cameraman.tif');
whos
image(A)
colormap(gray)
B=imread('board.tif');
whos
image(B)
B1=B(:,:,1);
image(B1); colormap(gray)
Bgray=rgb2gray(B);
image(Bgray); colormap(gray)
help imread
help uint

 

Class of Jan. 29th, 2013

A=imread('autumn.tif');
A=imread('kids.tif');
[U,S,V]=svd(A,0);
A=double(A);
[U,S,V]=svd(A,0);
plot(diag(S))
ranK(A)
rank(A)
U40=U(:,1:40);
V40=V(:,1:40);
s=diag(S);
s40=s(1:40);
S40=diag(s40);
A40=U40*S40*V40';
figure(1); imagesc(A);colormap(gray)
figure(2); imagesc(A40);colormap(gray)
plot(s)
U4=U(:,1:4);
V4=V(:,1:4);
s4=s(1:4);
S4=diag(s4);
A4=U4*S4*V4';
figure(3); imagesc(A4);colormap(gray)

 

Class of Jan. 31st, 2013

A=imread('kids.tif);
whos
A=double(A);
image(A)


colormap(gray)
B=zeros(400,400);
B(:,1:318)=A;
image(B)
help meshgrid
[X,Y]=meshgrid(1:400,1:400);
Z=double(B);
help mesh
meshc(X,Y,Z)
whos A
C=A(:,1:200);
b=A(:,300);
whos
help regress
x=regress(b,C);
norm(Cx-b)
norm(C*x-b)
norm(C*x-b)/norm(x)
norm(C*x-b)/norm(b)

Class of Feb. 5th, 2013

For some reason the commands were not saved on my computer (unfortunately), but i used the following similar demo in a previous class (though somewhat different curves with different geometry of projection)

% projection of 10-dim data on top 3 principal components
clear; close all
N=1000;
A=zeros(N,10);
t = (1:1000)'/1000;
for i=1:10
A(:,i) = t.^i;
end
A(501:N,3)=t(501:N);
c=mean(A);
A=A-ones(N,1)*c;
[U,S,V]=svd(A);
An = A*V;
plot3(An(:,1),An(:,2),An(:,3),'.')
hold on; plot3(An(1:500,1),An(1:500,2),An(1:500,3),'r.')
figure; plot(An(:,1),An(:,2),'.')
hold on; plot(An(1:500,1),An(1:500,2),'r.')

Class of Feb. 7th, 2013

We use the files in the following zipped folder to convert image to patches and patches to images

mex im2colstep.c
mex col2imstep.c
help im2patch % example for bad documontation of code...
load mandrill
whos
imagesc(X); colormap(gray)
Y=im2patch(X,2,[3,3],[1,1]);
size(X)
size(Y)
478*498 % confirmation of size(Y)
Y=Y';
c=mean(Y,1);
size(c)
Y=Y-ones(238044,1)*c;
[U,S,V]=svd(Y,0);
plot(diag(S),'.')
(norm(Y,'fro')^2-S(1,1)^2)/(norm(Y,'fro')^2)
proj2V=V(:,1:2);
Yproj2=Y*proj2V;
scatter(Yproj2(:,1),Yproj2(:,2))
proj3V=V(:,1:3);
Yproj3=Y*proj3V;
scatter3(Yproj3(:,1),Yproj3(:,2),Yproj3(:,3))
close all
imagesc(X); colormap(gray)
Ynew=zeros(238044,9);
Ynew(:,1:3)=Yproj3;
imout = patch2im(X,Ynew',2,[3,3],[1,1]);
imagesc(imout); colormap(gray)
clear all
X=imread('cameraman.tif')
Y=im2patch(X,2,[3,3],[1,1]);
whos X
X=double(X);
Y=im2patch(X,2,[3,3],[1,1]);
Y=Y'
c=mean(Y,1);
sz=size(Y);
Y=Y-ones(sz(1),1)*c;
[U,S,V]=svd(Y,0);
proj2V=V(:,1:2);
Yproj2=Y*proj2V;
scatter(Yproj2(:,1),Yproj2(:,2))
imagesc(X); colormap(gray)
Ynew=zeros(sz(1),9);
Ynew(:,1:2)=Yproj2;
imout = patch2im(X,Ynew',2,[3,3],[1,1]);
imagesc(imout); colormap(gray)
imout=-imout;
imagesc(imout); colormap(gray)

Class of Feb. 12th, 2013

A=imread('tire.tif');
A=double(A);
imagesc(A); colormap(gray)
Alog=log(A);
figure(2)
imagesc(Alog); colormap(gray)
Ailog=exp(A);
figure(3)
imagesc(Ailog); colormap(gray)
min(min(A))
max(max(A))
% we used log, where there any zeros?
find(A==0)
find(Alog==-Inf)
% imagesc seems to know to scale -inf as the next integer lower value
% will compare the image with log(A+1)
Alog=log(A+1);
figure(4)
imagesc(Alog); colormap(gray)
% Histograms
A=imread('pout.tif');
imshow(A)
imhist(A)
a=reshape(A,size(A,1)*size(A,2),1);
% we could have use instead a=A(:);
hist(a)
a=double(a);
hist(a)
hist(a,256)
figure(2); imhist(A)
figure(2); imhist(A,256) % no difference as 256 is default value here
figure(2); ylim([0,4000])
% demonstration of a problem of imhist with double images and its correction
load clown
imhist(X)
X=X/max(max(X));
imhist(X)
imhist(X,12)
load clown
imhist(X,map)
colormap(gray)
A=imread('pout.tif');
A=imread('pout.tif');
B=histeq(A);
imagesc(B)
close all
imhist(B)

Class of Feb. 14th, 2013

help corr
help xcorr
%checking an example worked up on the board
f=[1,-1]
g=[2,3]
xcorr(f,g)
conv(f,g)
help conv2
help xcorr2

Class of Feb. 19th, 2013
(added few corrections)

A=rand(100);
B=ones(3)
B=B/9
C=xcorr2(A,B);
% mentioned filter2 command, but will not be used
C2=filter2(A,B);
size(C2)
C2=filter2(B,A);
size(C2)
% imfilter and hspecial will be commonly used
help imfilter
h=fspecial('average')
h=fspecial('average',[5,5])
B=imread('tire.tif');
whos B
C=imfilter(B,h);
imshow(B)
figure(2); imshow(C)
h=fspecial('average');
C=imfilter(B,h);
figure(2); imshow(C)
h=fspecial('disk');
h
imshow(h)
imagesc(h); colormap(gray)
h=fspecial('gaussian',10,1);
imagesc(h)
ih=fspecial('gaussian',10,4);
imagesc(h)
C=imfilter(B,h);
imshow(h)
imshow(C)
h=fspecial('gaussian',10,1);
C=imfilter(B,h);
imshow(C)
h=fspecial('prewitt');
% we work with negative filters, so it is better to change B to be double
B = double(B);
C=imfilter(B,h);
imshow(C) % should not use imshow
figure(2); imagesc(B); colormap(gray)
figure(1); imagesc(C); colormap(gray)
h=h';
C=imfilter(B,h);
figure(1); imagesc(C)
% looking for a better image to distinguish horizonal vs. vertical changes
B=imread('cameraman.tif');
B = double(B);
hy=fspecial('prewitt')
hx=hy'
Cx=imfilter(B,hx);
Cy=imfilter(B,hy);
figure(1); imagesc(B); colormap(gray)
figure(2); imagesc(Cx); colormap(gray)
figure(3); imagesc(Cy); colormap(gray)
figure(4); imagesc(abs(Cx)); colormap(gray)
figure(5); imagesc(abs(Cy)); colormap(gray)
C=abs(Cx)+abs(Cy)
figure(6); imagesc(C); colormap(gray)
C=sqrt(Cx.^2+Cy.^2);
figure(7); imagesc(C); colormap(gray)
hxx=ones(3,3);
hxx(2,:)=-2*ones(1,3);
hxx
hyy=hxx';
Cxx=imfilter(B,hxx);
Cyy=imfilter(B,hyy);
figure(8); imagesc(Cxx); colormap(gray)
figure(9); imagesc(Cyy); colormap(gray)
figure(10); imagesc(abs(Cxx)); colormap(gray)
figure(11); imagesc(abs(Cyy)); colormap(gray)

Class of Feb. 21st, 2013

h=fspecial('prewitt')
h=fspecial('sobel')
h=fspecial('laplacian', .7);
B=imread('cameraman.tif');
C7=imfilter(B,h);
imagesc(C7); colormap(gray)
h=fspecial('laplacian',.3);
C3=imfilter(B,h);
figure(2)
imagesc(C3); colormap(gray)
h=fspecial('log');
C=imfilter(B,h);
figure; imagesc(C); colormap(gray)
h=fspecial('log',10,2);
C=imfilter(B,h);
figure; imagesc(C); colormap(gray)
h=fspecial('log',10);
C=imfilter(B,h);
figure; imagesc(C); colormap(gray)
h=fspecial('gaussian');
Cavg=imfilter(B,h);
figure; imagesc(Cavg); colormap(gray)
Cs=B-Cavg;
figure; imagesc(Cs); colormap(gray)
h=fspecial('average')
Cavg=imfilter(B,h);
Cs=B-Cavg;
figure; imagesc(Cs); colormap(gray)
figure; imagesc(-Cs); colormap(gray)
h=fspecial('unsharp')
C=imfilter(B,h);
figure; imagesc(C); colormap(gray)
h=fspecial('laplacian')
C2=imfilter(B,h);
figure; imagesc(C2); colormap(gray)
C3=B+C;
figure; imagesc(C3); colormap(gray)

Class of Mar. 3rd, 2013

x=zeros(1,256);
x(1)=1;
help fft
plot(x,'.')
y=fft(x);
plot(y,'.')
x=zeros(1,256);
x(2)=1;
y=fft(x);
plot(y,'.')
plot(abs(y),'.')
plot(real(y),'.')
plot(imag(y),'.')
plot(phase(y),'.')
x=zeros(1,256);
x(3)=1;
y=fft(x);
plot(real(y),'.')
plot(phase(y),'.')
z=phase(y);
z{1:5)
z(1:5)
x=zeros(1,256);
x(129)=1;
y=fft(x);
plot(real(y),'.')
y(1:5)
plot(phase(y),'.')
x=zeros(1,256);
x(90:140)=1;
plot(x,'.')
y=fft(x);
plot(abs(y),'.')
help fftshift
u=fftshift(y);
plot(abs(u),'.')
plot(real(u),'.')
plot(imag(u),'.')

Back to Gilad Lerman's webpage
Back to current 5467 webpage