Assignment 5

Assignment 5

1. Find octave commands for constructing a 256x256 matrix with entries of 0 everywhere except inside the circle with radius 50 where the values are 1.

A=zeros(256);
for x=1:256;for y=1:256;
if (x-128)^2+(y-128)^2<=2500;

A(x,y)=1;

endif;

endfor;

endfor;

Imshow(A*256)

2. Give octave commands to draw the top part of figure 6.4 in the book.

A=zeros(256);
B=zeros(256);
C=zeros(256);
for x=1:256;for y=1:256;
if (x-93)^2+(y-128)^2<=2500;

A(x,y)=1;

endif;

if (x-153)^2+(y-93)^2<=2500;

B(x,y)=1;

endif;

if (x-153)^2+(y-153)^2<=2500;

C(x,y)=1;

endif;

endfor;

endfor;

E(:,:,1)=A*255;

E(:,:,2)=B*255;

E(:,:,3)=C*255;

imshow (E)

3. Consider the black and white image from the matrix. Skew the image by a factor of s pixels. Rotate the image theta degrees

bigT=255*ones(256);
bigT(30:79,64:191)=zeros(50,128);
bigT(50:199,111:146)=zeros(150,36);

BIG T

bigT=255*ones(256);
bigT(30:79,64:191)=zeros(50,128);
bigT(50:199,111:146)=zeros(150,36);
function retval=newy(x,y,s)
retval=y+mod(x*s,256)+1;
endfunction
for x=1:256;
for y=1:256;
y1=int32(newy(x,y,1));
if(y1>256)
y1=y1-256;
endif;
bigT1(x,y1)=bigT(x,y);
endfor;
endfor;
imshow(bigT1)

Skew by a factor of 0.9 and 1

Rotation of 5pi/3

bigT=255*ones(256);
bigT(30:79,64:191)=zeros(50,128);
bigT(50:199,111:146)=zeros(150,36);
bigT2=ones(256);
for x=1:256;
for y=1:256;
xnew=int32(mod(x*cos(5*pi/3)-y*sin(5*pi/3),256)+1);
ynew=int32(mod(x*cos(5*pi/3)+y*sin(5*pi/3),256)+1);
bigT2(xnew,ynew)=bigT(x,y);
endfor
endfor; imshow(bigT2)