1. Digital Image Processing 0909.452.01/0909.552.01 Fall 2001
Lecture 4 October 1, 2001
Shreekanth Mandayam
ECE Department
Rowan University

2. Plan Image Enhancement Spatial Filtering Detection of Discontinuities
Edge detection (Sobel, Prewitt and Laplacian masks)
Image Spectrum
2-D Fourier Transform (DFT & FFT)
Spectral Filtering
Low-pass
High-pass
Low-pass
High-pass

3. DIP: Details

4. Image Preprocessing Enhancement Restoration Inverse filtering
Wiener filtering
Spatial
Domain
Spectral
Domain
Filtering
>>fft2/ifft2
>>fftshift
Point Processing
>>imadjust
>>histeq
Spatial filtering
>>filter2

5. Spatial Filtering (Masking)
Portion of
a digital image
Mask z1 z2 z3 z4 z5 z6 z7 z8 z9 w1 w2 w3 w4 w5 w6 w7 w8 w9
Replace
with R
= w1z1 + w2z2 + ….. +w9z9

6. Low-pass Filters Moving Average Filter 1 (1/9)* Median Filter z1 z2 z3
Replace
with R
= median(z1, z2 , ….. , z9)

7. High-pass Filters Basic HP Filter -1 8 (1/9)* Gradient Filter z1 z2 z3-1 1 -1
demos/demo2spatial_filtering/highpassdemo.m

8. Detection of Discontinuities-1 8
Point Detection
Line Detection (Prewitt’s Gradient) -1 1 -1 1
demos/demo2spatial_filtering/prewitt.m

9. Edge Detection Sobel Masks -1 -2 1 2 -1 1 -2 2 >>edgedemo1 2 -1 1 -2 2
>>edgedemo
>>edge
demos/demo2spatial_filtering/edgegradientdemo.m

10. Recall: 1-D CFT Continuous Fourier Transform (CFT)
Frequency, [Hz]
Amplitude
Spectrum
Phase
Inverse Fourier Transform (IFT)

11. Recall: 1-D DFT Discrete Domains Discrete Fourier Transform
Equal time intervals
Discrete Domains
Discrete Time: k = 0, 1, 2, 3, …………, N-1
Discrete Frequency: n = 0, 1, 2, 3, …………, N-1
Discrete Fourier Transform
Inverse DFT
Equal frequency intervals
n = 0, 1, 2,….., N-1
k = 0, 1, 2,….., N-1

12. How to get the frequency axis in the DFT
The DFT operation just converts one set of number, x[k] into another set of numbers X[n] - there is no explicit definition of time or frequency
How can we relate the DFT to the CFT and obtain spectral amplitudes for discrete frequencies?
(N-point FFT)
Need to
know fs
n= n=N
f= f = fs

13. DFT Properties DFT is periodic X[n] = X[n+N] = X[n+2N] = ………
I-DFT is also periodic!
x[k] = x[k+N] = x[k+2N] = ……….
Where are the “low” and “high” frequencies on the DFT spectrum?
n= N/ n=N
f= fs/ f = fs

14. 1-D FFT Demo
>>fft

15. 2-D Continuous Fourier Transformy x v u
Spatial
Frequency
Domain
Spatial
Domain

16. 2-D Discrete Fourier Transform
u= u=N/ u=N
v=N v=N/ v=0
>>fft2
>>ifft2

17. 2-D DFT Properties Conjugate symmetry Rotation Separability
demos/demo3dft_properties/con_symm_and_trans.m
Rotation
demos/demo3dft_properties/rotation.m
Separability
demos/demo3dft_properties/separability.m
>>fftshift

18. Spectral Filtering: Radially Symmetric Filter
u=-N/ u= u=N/2
D(u,v) D0
v=N/ v= v=-N/2
Low-pass Filter
demos/demo4freq_filtering/lowpass.m

19. Lab 2: Spatial & Spectral Filtering

20. Summary