Portofolio 3

Posted by: megabangetz on: May 18, 2008

• In: Portofolio3
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Merekonstruksi foto diri dengan menggunakan freqcomp.m

Listing program freqcomp.m

function recon = freqcomp(im, Npts, delay)

if ndims(im) == 3

% mengubah image jadi grayscale

im = rgb2gray(im);

warning(‘converting colour image to greyscale’);

end

if nargin < 2

Npts = 50;

end

[rows,cols] = size(im);

% If necessary crop one row and/or column so that there are an even

% number of rows and columns, this makes things easier later.

if mod(rows,2) % odd

rows = rows-1;

end

if mod(cols,2) % odd

cols = cols-1;

end

im = im(1:rows,1:cols);

rc = fix(rows/2)+1; % Centre point

cc = fix(cols/2)+1;

% The following code constructs two arrays of coordinates within the FFT

% of the image that correspond to complex conjugate pairs of points that

% spiral out from the centre visiting every frequency component on

% the way.

p1 = zeros(Npts,2); % Path 1

p2 = zeros(Npts,2); % Path 2

m = zeros(rows,cols); % Matrix for marking visited points

m(rc,cc) = 1;

m(rc,cc-1) = 1;

m(rc,cc+1) = 1;

p1(1,:) = [rc cc-1];

p2(1,:) = [rc cc+1];

d1 = [0 -1]; % initial directions of the paths

d2 = [0 1];

% Mark out two symmetric spiral paths out from the centre (I wish I

% could think of a neater way of doing this)

for n = 2:Npts

l1 = [-d1(2) d1(1)]; % left direction

l2 = [-d2(2) d2(1)];

lp1 = p1(n-1,:) + l1; % coords of point in left direction

lp2 = p2(n-1,:) + l2;

if ~m(lp1(1), lp1(2)) % go left

p1(n,:) = lp1;

d1 = l1;

m(p1(n,1), p1(n,2)) = 1; % mark point as visited

else % go sraight ahead

p1(n,:) = p1(n-1,:) + d1;

m(p1(n,1), p1(n,2)) = 1; % mark point as visited

end

if ~m(lp2(1), lp2(2)) % go left

p2(n,:) = lp2;

d2 = l2;

m(p2(n,1), p2(n,2)) = 1; % mark point as visited

else % go sraight ahead

p2(n,:) = p2(n-1,:) + d2;

m(p2(n,1), p2(n,2)) = 1; % mark point as visited

end

end

% Having constructed the path of frequency components to be visited

% we take the FFT of the image and then enter a loop that

% incrementally reconstructs the image from its components.

IM = fftshift(fft2(im));

recon = zeros(rows,cols); % Initialise reconstruction matrix

if max(rows,cols) < 150

fontsze = 7;

else

fontsze = 10;

end

figure(1), clf

subplot(2,2,1),imagesc(im),colormap gray, axis image, axis off

title(‘Original Image’,’FontSize’,fontsze);

subplot(2,2,2),imagesc(log(abs(IM))),colormap gray, axis image

axis off, title(‘Fourier Transform + frequency component pair’,’FontSize’,fontsze);

warning off % Turn off warnings that might arise if the images cannot be

% displayed full size

truesize(1)

for n = 1:Npts

% Extract the pair of Fourier components

F = zeros(rows,cols);

F(p1(n,1), p1(n,2)) = IM(p1(n,1), p1(n,2));

F(p2(n,1), p2(n,2)) = IM(p2(n,1), p2(n,2));

% Invert and add to reconstruction

f = real(ifft2(fftshift(F)));

recon = recon+f;

% Display results

subplot(2,2,2),imagesc(log(abs(IM))),colormap gray, axis image

axis off, title(‘Fourier Transform + frequency component pair’,’FontSize’,fontsze);

hold on, plot([p1(n,2), p2(n,2)], [p1(n,1), p2(n,1)],’r.’); hold off

subplot(2,2,3),imagesc(recon),colormap gray, axis image, axis off, title(‘Reconstruction’,’FontSize’,fontsze);

subplot(2,2,4),imagesc(f),colormap gray, axis image, axis off

title(‘Basis function corresponding to frequency component pair’,’FontSize’,fontsze);

if nargin == 3

pause(delay);

else

fprintf(‘Hit any key to continue \n’); pause

end

end

Dengan jumlah komponen frekuensi 30, hasilnya seperti dibawah ini:

Dengan jumlah komponen frekuensi 50, hasilnya seperti dibawah ini:

Dengan jumlah komponen frekuensi 120, hasilnya seperti dibawah ini:

Filter Gausian

function tugasgausian = Gausian(images);

% mendapatkan image

i = imread(images);

% image grayscale

im = rgb2gray(i);

% filter gausian

gausianfilter = fspecial(‘gaussian’, size(im), 5);

% FFT image

imagefft = fft2(im);

% FFT dari filter gaussian

gausianfilterfft = fft2(gausianfilter);

% perkalian FFT image dengan FFT filter gaussian

result = gausianfilterfft.*imagefft;

figure,imshow(im);

figure,imagesc(gausianfilter),colormap gray;

figure,imagesc(fftshift(log(abs(imagefft)+eps))),colormap gray;

figure,imagesc(fftshift(log(abs(gausianfilterfft)+eps))),colormap gray;

figure,imagesc(fftshift(log(abs(result)+eps))),colormap gray;

% menampilkan hasil smoothing

figure,imagesc(fftshift(real(ifft2(result)))),colormap gray;

Filter Average

function tugasaverage = average(images);

% mendapatkan image

i = imread(images);

% image grayscale

im = rgb2gray(i);

[row col] = size(im);

averageFilter = zeros(row,col);

if (mod(row,2)==0 && mod(col,2)==0)

pusatx = row/2;

pusaty = col/2;

averageFilter(pusatx-10:pusatx+11, pusaty-10:pusaty+11) = 1;

elseif (mod(row,2)==0 && mod(col,2)==1)

pusatx = row/2;

pusaty = (col-1)/2;

averageFilter(pusatx-10:pusatx+11, pusaty-10:pusaty+10) = 1;

elseif (mod(row,2)==1 && mod(col,2)==0)

pusatx = (row-1)/2;

pusaty = col/2;

averageFilter(pusatx-10:pusatx+10, pusaty-10:pusaty+11) = 1;

elseif (mod(row,2)==1 && mod(col,2)==1)

pusatx = (row-1)/2;

pusaty = (col-1)/2;

averageFilter(pusatx-10:pusatx+10, pusaty-10:pusaty+10) = 1;

end

% filter average

averageFilter = averageFilter/(sum(sum(averageFilter)));

% FFT image

imagefft = fft2(im);

% FFT dari filter average

averagefilterfft = fft2(averageFilter);

% perkalian FFT image dengan FFT filter average

result = averagefilterfft.*imagefft;

figure,imshow(im);

figure,imagesc(averageFilter),colormap gray;

figure,imagesc(fftshift(log(abs(imagefft)+eps))),colormap gray;

figure,imagesc(fftshift(log(abs(averagefilterfft)+eps))),colormap gray;

figure,imagesc(fftshift(log(abs(result)+eps))),colormap gray;

% menampilkan hasil smoothing

figure,imagesc(fftshift(real(ifft2(result)))),colormap gray;

Pertukaran Nilai Fase

Image1

Image2

informasi amplitudo dari image1 dan informasi fase dari image2, hasilnya lebih mirip image2

Informasi amplitudo dari image2 dan informasi fase dari image1, hasilnya lebih mirip image1

Fase dari image1

Fase dari image2

Listing program pertukaran nilai fase

% mendapatkan 2 gambar yg berbeda

image1 = imread(‘polka.jpg’);

image2 = imread(‘sok imut1.jpg’);

% image1 dirubah ke bentuk grayscale

image1 = rgb2gray(image1);

% image2 dirubah ke bentuk grayscale

image2 = rgb2gray(image2);

% FFT image1

image1fft = fft2(image1);

% FFT image2

image2fft = fft2(image2);

% mendapatkan informasi fase dari image1

image1fase = angle(image1fft);

% mendapatkan informasi fase dari image2

image2fase = angle(image2fft);

% mendapatkan amplitudo dari image1

image1amp = abs(image1fft);

% mendapatkan amplitudo dari image2

image2amp = abs(image2fft);

% informasi amplitudo dari image1, informasi fase dari image2

newimfft1 = image1amp.*(cos(image2fase) + i*sin(image2fase));

% informasi amplitudo dari image2, informasi fase dari image1

newimfft2 = image2amp.*(cos(image1fase) + i*sin(image1fase));

figure,imagesc(real(ifft2(newimfft1))),colormap gray;

figure,imagesc(real(ifft2(newimfft2))),colormap gray;

% mendapatkan fase dari image1 saja

image1faseaja = image1fft./image1amp;

% mendapatkan fase dari image2 saja

image2faseaja = image2fft./image2amp;

figure,imagesc(real(ifft2(image1faseaja))),colormap gray;

figure,imagesc(real(ifft2(image2faseaja))),colormap gray;

figure,imagesc(image1),colormap gray;

figure,imagesc(image2),colormap gray;