Activity9b

2nd image(658x823)



















1 part of the image (1/12)(256 x 256 pixels)















processed image of the part above. the structuring element used is the same structuring element used in the first part (cross)

average area:

471.8495

pixel counting area:

435.8

error: 8.2 %









rating:9/10 -the error for the 2nd part is quite high, another structuring element might lower the uncertainty for this part.

collaborator: m. maallo

Activity9a

original image (748 x 618 pixels)















(1/9) one part of the original image (256x256, lower right)


















image processed result
the structuring element used was a cross with 5 pixels length and 1 pixel thickness

the process was done 9 times using 9 different parts of the image
average size:

519.8939

calculated average area of 10 full circles from different parts of the image using pixel counting:554.6


error: 6.25%

Activity8 – Morphological Operations (continuation)

hollow square dilated with the corresponding structuring elements.

the thickness of the width in the lower right and upper left images varied depending on the orientation of the corresponding structuring image used.















hollow square eroded with the corresponding structuring elements.














cross dilated with the corresponding structuring elements.




















cross eroded with the corresponding structuring elements.

Activity8 – Morphological Operations

Structuing elements:
upper left:4x4 pixels square
upper right: 2x4 pixels
lower left: 4x2 pixels
lower right: 5pixels length 1 pixel width cross















50 x 50 pixel square dilated with the structuring elements as above.

the 1st square has an area of 2809 (53x53), meaning the original image has expanded by 3 pixels.
the upper right and lower left both have areas of 2703 (53x51 or 51x53). its orientation is dependent on the dimensions of the structuring element.
















50 x 50 pixel square eroded with the structuring elements as above.















50 x 30 triangle dilated with the structuring elements as above.











50 x 30 triangle eroded with the structuring elements as above.
















25-pixel radius circle dilated with the structuring elements as above.
upper right circle elongated vertically while the lower left circle elongated horizontally.the lower right circle has both horizontal and vertical elongation.















25-pixel radius circle eroded with the structuring elements as above.
upper right circle looked like it has been elongated vertically because there more parts have been eroded along the horizontal. same principle applies to the lower left circle. the lower right circle has both horizontal and vertical erosion

Activity7 – Enhancement in the Frequency Domain

2d sinusoids (left) FT(right)

A:original 2d sinusoid with f=4
B:f=40, distance between 2 points in the FT increased
C:f=0.4, distance between 2 points in the FT decreased
D:rotated at 30 degrees: the orientation of the 2 points was tilted
E:rotated at 60 degrees: the orientation of the 2 points was tilted further
F:z = sin(2*%pi*4*X).*sin(2*%pi*4*Y): 4 points with equal distance (square)
G:z = sin(2*%pi*40*X).*sin(2*%pi*40*Y): distance between points increased (expected from (b))
H:z = sin(2*%pi*0.4*X).*sin(2*%pi*40*Y):vertical distance decreased but horizontal distance increased( expected from (b) and (c))








left:original indexed image
right:processed fingerprint









score: 8/10
collaborators:dado, maallo

activity6-Fourier Transform Model of Image

6A)


upper left: original image (circle)
upper right: fft2
lower left: fft shifted
lower right: fft shifted zoomed










upper left: original image ( bigger circle)
upper right: fft2
lower left: fft shifted
lower right: fft shifted zoomed











upper left: original image ("A")
upper right: fft2 (inverted image)
lower left: fft shifted
lower right: fft shifted zoomed









6B

upper left: image (VIP)
upper right: aperture (circle)
down: fft (inverted)















upper left: image (VIP)
upper right: aperture ( smaller circle)
down: fft (iimage not well reconstructed because of the smaller aperture size)






























SCore 8/10: failed to complete the last part of the exercise

Activity5 – Physical Measurements from Discrete Fourier Transforms

a) f=120 Hz signal and FT:
N=256
dt=2/256














b) N=512
dt=2/256
(dt fixed, N increased, T increased)














c) N=256
dt=1/256
(dt decreaased, N fixed, T decreased)















d) N=512
dt=T/256
(dt decreased, N increased, T fixed)














codes:
a)
T = 2;
N = 256;
dt = 2/256;
t = [0:dt:(N-1)*dt];
f = 120;
y = sin(2*%pi*f*t);
f1 = scf(1); plot(t,y);
FY = fft(y);
F = 1/(2*dt);
df = 2*F/256;
f = [-(df*(N/2)):df:df*(N/2 -1)];
f2 = scf(2); plot(f, fftshift(abs(FY)));

b)T = 2;
N = 512;
dt = 2/256;
t = [0:dt:(N-1)*dt];
f = 120;
y = sin(2*%pi*f*t);
f1 = scf(1); plot(t,y);
FY = fft(y);
F = 1/(2*dt);
df = 2*F/512;
f = [-(df*(N/2)):df:df*(N/2 -1)];
f2 = scf(2); plot(f, fftshift(abs(FY)));

c)T = 2;
N = 256;
dt = 1/256;
t = [0:dt:(N-1)*dt];
f = 120;
y = sin(2*%pi*f*t);
f1 = scf(1); plot(t,y);
FY = fft(y);
F = 1/(2*dt);
df = 2*F/256;
f = [-(df*(N/2)):df:df*(N/2 -1)];
f2 = scf(2); plot(f, fftshift(abs(FY)));

d)T = 2;
N = 512;
dt = T/512;
t = [0:dt:(N-1)*dt];
f = 120;
y = sin(2*%pi*f*t);
f1 = scf(1); plot(t,y);
FY = fft(y);
F = 1/(2*dt);
df = 2*F/512;
f = [-(df*(N/2)):df:df*(N/2 -1)];
f2 = scf(2); plot(f, fftshift(abs(FY)));

grade:10/10