1 / 10

Image processing

Image processing. Fourier Transform. Discrete Fourier Transform. Generate signals. t = 0:0.001:0.6; x = sin(2*pi*50*t)+sin(2*pi*120*t); figure, plot(x(1:50)) title('original Signal’) xlabel('time (seconds)') Add a random noise y = x + 2*randn(size(t)); plot(y(1:50))

ambrose
Download Presentation

Image processing

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Image processing Fourier Transform

  2. Discrete Fourier Transform

  3. Generate signals t = 0:0.001:0.6; x = sin(2*pi*50*t)+sin(2*pi*120*t); figure, plot(x(1:50)) title('original Signal’) xlabel('time (seconds)') • Add a random noise y = x + 2*randn(size(t)); plot(y(1:50)) title('Signal Corrupted with Zero-Mean Random Noise') xlabel('time (seconds)')

  4. Obtain FFT of original and noisy signals X= fft(x,512); Y = fft(y,512);

  5. Obtain the power spectrum and plot • The power spectrum, a measurement of the power at various frequencies, is Pxx= X.* conj(X) / 512; Pyy = Y.* conj(Y) / 512; f = 1000*(0:256)/512; figure,plot(f,Pyy(1:257)) title('Frequency content of y') xlabel('frequency (Hz)'); figure,plot(f,Pxx(1:257)) title('Frequency content of x') xlabel('frequency (Hz)')

  6. DFT of image C= imread('pout.tif'); y=fft2(C); mesh(abs(y)); The Fourier transform indicates concentration around low frequencies This is due to the slow variations of the intensities (low contrast).

  7. Template matching with cross correlation

  8. Application • Locate occurrences of the letter "a" in an image containing text. • This is called template matching: Invariant to rotation and shift if performed in Fourier domain • Correlation can be computed by first rotating the image of "a" by 180 and then using the FFT-based convolution technique. • Convolution is equivalent to correlation if you rotate the convolution kernel by 180

  9. Obtain image of letter a bw = imread('text.tif'); a=bw(59:71,81:91); %Extract one of the letters "a" from the image knowing the position imshow(bw); figure, imshow(a);

  10. Find the max correlation point C = real(ifft2(fft2(bw) .* fft2(rot90(a,2),256,256))); % rotate the image of “a” by 180 (2 times by 90) and pad to fit 256 by 256. figure, imshow(C,[]) max(C(:)) thresh = 45; figure, imshow(C > thresh)

More Related