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 Filtering in 2-dimensional Signals using 2D FFT

Reklamy Google

Quick presentation of 2-dimensional Fast Fourier Transform. Frequency analysis is very important in Image Coding. 2D FFT is similar to DCT (Discrete Cosine Transform) - used in JPEG image compresion format.
Better method to image coding is Wavelet Transform - used in JPEG 2000 format.

FFT of Image

Identically as in 1-dimensional signals (soudns, etc.) you transform signals from Time Domain convert to a Frequency Domain - you can also transform 2-dimensional signals. Simpe example of 2D signal is an image.
Example of 2D FFT on Image is below :

   
Original image and FFT Spectrum of Image

As you expect the zeros frequencies are located on the borders of image. In center of image is located maximum frequency. If you want reverse minimum and maximum frequencies by places then use a Shift function.

Filtering on Images using FFT

Four steps how filtering 2-dimensional signals :

Open an original image

Make a FFT of the image

Fill by zeros any area in 2D FFT Spectrum

Make an Inverse FFT on zeros-filled area

        
Original image (1), FFT of Image (2), Filled area of Spectrum (3) and final image after IFFT (4)

Application for testing 2D FFT

I made a simple application for seeing and testing 2D FFT with filtering. View of FFTImage.exe is below :

Simple application for testing ImageFFT Delphi Component

Pliki do pobrania:

FFTImage.exe (535 kB) - alikacja testująca komponent TImageFFT (599 pobrań)

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Reklamy Google

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