The Frequency Domain Digital Image Processing – Chapter 8

Topics 8.1Spatial frequency 8.2Fourier theory 8.3The discrete Fourier transform 8.4Investigating spectra 8.5Filtering of images 8.6Deconvolution 8.7Further reading

8.1Spatial frequency

8.2Fourier theory 8.2.1Basic concepts basis functions Fourier series Fourier coefficients 8.2.2Extension to two dimensions

8.2.1Basic concepts أي دالة دورية (periodic function) يمكن تحليلها الى عدد لا نهائي من الدوال الأساسية (basis functions) كل دالة لها معامل (coefficient)، بحيث إذا ما ضربت الدوال كل في معاملها ثم جمعت نواتج المضاريب نحصل ثانية على الدالة الأصلية. The key idea is that any periodic function, however complex it might appear, can be represented as a sum of sinusoidal variations (i.e. sine and cosine waves of the kind depicted in Figure 8.1).

8.2.2Extension to two dimensions

8.3The discrete Fourier transform 8.3.1The spectra of an image 8.3.2The fast Fourier transform 8.3.3Properties of the Fourier transform -Periodicity -Conjugate symmetry -Windowing

The important point of the DFT

8.3.1The spectra of an image Magnitude (amplitude) spectrum Phase spectrum Power spectrum

8.4Investigating spectra 8.4.1Display 8.4.2Interpretation Spectra of simple periodic patterns Spectra of edges Spectra of simple shapes

8.5Filtering of images 8.5.1Low pass filtering 8.5.2High pass filtering 8.5.3Band pass and band stop filtering 8.5.4Removal of periodic noise

8.6Deconvolution 8.6.1Point spread functions 8.6.2The inverse filter 8.6.3The Weiner filter