1. Lecture 7
Spatial filtering

2. Image denoising Additive noise model:
Noise usually assumed to be uncorrelated

3. Image averaging for noise removal
Examples of noise added to the same image
Averaging 10, 50 and 128 noisy images

4. Spatial filtering Linear Space Invariant filters. 1D convolution:

5. Discrete Convolution 1D Discrete case: 2D discrete case:
Length of output:
If x is of length M and h is of length L, then y is of length M+L-1

6. Discrete Convolution

7. How to handle image borders
No data to convolve!

8. Zero Padding
Original image
Impulse response array
Area with 0s

9. Do not process border pixels
Input image
Impulse response array
Output image

10. Smoothing spatial filters
Used for noise removal/blurring an image. h1 h2
Usual average
Weighted average

11. Averaging filter Noisy image 3x3 averaging mask (h1) output Note:
The smoothing effect removes the noise, but also blurs the image
Notice the black frame on the image boundary

12. Averaging filter 3x3 averaging mask (h1) output
Note:
Less blur in the center image
Larger black frame in the third image
More blur in the third image

13. Averaging filters to remove details
Test Image contains details of different resolution
Note:
Some small squares disappear.
Noisy rectangles are blurred to remove noise
Vertical bars details are mixed up.