Digital Image Processing - Frequency Filters
- 1. 2- Frequency Filtering Aly Abdelkareem
- 4. Transform (Spatial to Frequency ) • Fourier Transform • It allows a frequency content (spectral) analysis of a signal. • FT is suitable for periodic signals. • If the signal is not periodic then the Windowed FT or the linear integral transformation with time (spatially in 2D) localized basis function, e.g., wavelets, Gabor filters can be used
- 5. Any Function can be “Odd + Even” parts
- 6. FT Examples
- 8. DFT (2D)
- 9. Low pass filter vs High pass filter
- 10. Resources DFT • http://people.ciirc.cvut.cz/~hlavac/TeachPr esEn/11ImageProc/12FourierTxEn.pdf • http://madebyevan.com/dft/?fbclid=IwAR1 wTWCGeYO- jymhSkPG6f883xEJbnpLmFtDOyZCvcQZXOV swO8E5G6Cj0Y
- 11. Sheet 2 – Frequency Filters
- 12. Uniform pattern Noisy with random freq Cosine Diagonally
- 13. LPF -> Radius decrease (more blur ) HPF -> Remove low frequency
- 14. Ideal High passLow pass Band pass
- 15. • The main cause of ringing artifacts is due to a signal passed through a low-pass filter; this is the frequency domain description. • In terms of the time domain, the cause of this type of ringing is the ripples in the sinc function which is the impulse response (time domain representation) of a perfect low-pass filter.
- 16. Ideal Loss pass filter • It suppresses all frequencies higher than the cut-off frequency D0 • Ringing As mentioned earlier, multiplication in the Fourier domain corresponds to a convolution in the spatial domain. Due to the multiple peaks of the ideal filter in the spatial domain, the filtered image produces ringing along intensity edges in the spatial domain.
- 17. Bonus: How to avoid ringing effect ?
- 18. Avoid Ringing Effect • Butterworth filter: The Butterworth filter is a type of signal processing filter designed to have as flat frequency response as possible (no ripples) in the pass-band.
- 20. Q-5)a
- 21. Q-5)b • Another Solution form • Because of the cosine terms, this filter has a gain of +1 at the center or zero frequency, a gain of zero at u = v = N/4, and a gain of -1 at u = v = N/2. • N/2 is the maximum valid frequency for an N x N image. Since the gain decreases with increasing frequency, the filter is a low pass filter
- 22. Quiz 1 out of 5
- 23. Pop Quiz (1) Model A • Q1 (2 marks ) • A)Answer each of the following questions with true or false and justify your choice (include neat diagrams if needed): 1. The optimal way to remove Salt only noise is to use median filter. 2. Butterworth filter can be used to avoid ringing effect.
- 25. Solution 1 • Q1 (2 marks ) 1. The optimal way to remove Salt only noise is to use median filter. 1. False, Min Filter 2. Butterworth filter can be used to avoid ringing effect. 1. True
- 26. Pop Quiz (1) Model B • Q1 (2 marks ) Answer each of the following questions with true or false and justify your choice (include neat diagrams if needed): 1. The optimal way to remove pepper-only noise is to use minimum filter. 2. Ideal low pass filter is used to avoid ringing effect. Q2 (2 marks )
- 27. Solution 1) 1. The optimal way to remove pepper-only noise is to use minimum filter. • False -> Max Filter 2. Ideal low pass filter is used to avoid ringing effect • False -> it causes ringing effect • the cause of this type of ringing is the ripples in the sinc function which is the impulse response (time domain representation) of a perfect low-pass filter.
- 28. Solution (2)