| mkfftfilter - builds 2D frequency-domain filters |
transfer_function = mkfftfilter(image,filtername,frequency1[,frequency2]) |
| image |
| A gray-level image. |
| filtername |
| a string, the name can be 'binary', 'butterworth1', 'butterworth2', |
| frequency1, frequency2 |
| 1st and 2nd cut-off frequencies which set the filter characteristics. |
| transfer_function |
| is a matrix with values between 0 and 1. These values can then be applied on the fft spectrum of an image. |
| This function gives some popular filters to be applied on the spectrum (fft) of an image. |
| The Fourier Transform gives informations about which frequencies are present in a signal (=spectrum). |
| A great property of the spectrum is that the original image can be reconstructed from it. Of course, modifications in the spectrum will result in a modified image, but spectrum modifications can be easier and more intuitive. |
| A combination of several filters is possible. |
| All these filters are cylindrical and act only on amplitude (not on phase). The following filters are available (h is the trasfer function): |
| h=1/(1+(f/frequency1)^(2*n)) n=1,2 or 3 for 'butterworth1', 'butterworth2' or 'butterworth3'. |
| 'exp': The exponential filter: h=exp(-(f/frequency1)^1); |
| The gaussian filter which is a particular case of the exponential: h=exp(-(f/frequency1)^2); |
| 'trapeze': h=1 if f<=frequency1 h=-(f-frequency2)/(frequency2-frequency1) h=0 if f>=frequency2 |
stacksize(4e7); // increase the stack size because
// images are very much memory consumming
image=gray_imread(SIPDIR+'images/ararauna.png');
xset("window",0);xbasc();imshow(image);
xtitle("Original Image");
IM=fft(image,-1);
//calculate the power spectrum
spectrum=real((IM).*conj(IM));
//for visualisation: the low frequencies are moved to the center of the image
//with sip_fftshift,
//the use of log(spectrum+1) allows to observe great amplitude variations.
xset("window",1);xbasc();imshow(sip_fftshift(log(spectrum+1)),[]);
xtitle("Power Spectrum");
//transfer function
h=mkfftfilter(image,'binary',20);
xset("window",2);xbasc();imshow(h);
xtitle("Transfer Function");
IM2=IM.*sip_fftshift(h);//spectrum modification
//reverse transform
im2=real(fft(IM2,1));
xset("window",3);xbasc();xselect();imshow(im2,[]);
xtitle("Low-pass binary filtering");
//High-pass filter
IM3=IM.*sip_fftshift(1-h);//spectrum modification with (1-h)
im3=real(fft(IM3,1));
xset("window",4);xbasc();xselect();imshow(im3,[]);
xtitle("High-pass binary filtering");
//Combination of 2 filters
h1=mkfftfilter(image,'binary',30);
h2=mkfftfilter(image,'binary',5);
h=h1-h2;
IM4=IM.*sip_fftshift(h);//spectrum modification
im4=real(fft(IM4,1));
xset("window",5);xbasc();xselect();imshow(im4,[]);
xtitle("Band-pass binary filtering");
|
| Jocelyn DRUEL <jocelyn.druel1@libertysurf.fr> |
| The latest version of the Scilab Image Processing toolbox can be found at |
| http://siptoolbox.sourceforge.net |
| fft, gsm2d, imconv |