1. Lecture: Image manipulations (2) Filters and kernels
Alireza Akhavan Pour
CLASS.VISION
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2. Image Manipulations (Part 2)
1. Intro to Convolution
2. Blurring
3.Sharpening
4. Dilation, Erosion, Opening and Closing
5. Edge Detection & Image Gradients
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3. Filter example #1: Moving Average
2D DS moving average over a 3 × 3 window of neighborhood h 1
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4. Filter example #1: Moving Average90 90
Courtesy of S. Seitz
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5. Filter example #1: Moving Average90 90 10 5
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6. Filter example #1: Moving Average90 90 10 20
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7. Filter example #1: Moving Average90 90 10 20 30
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8. 90 10 20 30
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9. Filter example #1: Moving Average90 10 20 30 40 60 90 50 80
Source: S. Seitz
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10. Filter example #1: Moving Average
In summary:
This filter “Replaces” each pixel with an average of its neighborhood.
Achieve smoothing effect (remove sharp features) 1
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11. Filter example #1: Moving Average
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12. 2D convolution
Assume we have a filter(h[,]) that is 3x3. and an image (f[,]) that is 7x7.
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13. 2D convolution
Assume we have a filter(h[,]) that is 3x3. and an image (f[,]) that is 7x7.
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14. 2D convolution
Assume we have a filter(h[,]) that is 3x3. and an image (f[,]) that is 7x7.
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15. 2D convolution
Assume we have a filter(h[,]) that is 3x3. and an image (f[,]) that is 7x7.
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16. 2D convolution
Assume we have a filter(h[,]) that is 3x3. and an image (f[,]) that is 7x7.
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17. 2D convolution
Assume we have a filter(h[,]) that is 3x3. and an image (f[,]) that is 7x7.
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18. 2D convolution example
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19. 2D convolution example Slide credit: Song Ho Ahn
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20. 2D convolution example Slide credit: Song Ho Ahn
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21. 2D convolution example Slide credit: Song Ho Ahn
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23. Slide credit: Song Ho Ahn
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24. 2D convolution example
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25. 1 ? = *
Original
Courtesy of D Lowe
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26. Convolution in 2D - examples1 = *
Original
Filtered
(no change)
Courtesy of D Lowe
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27. Convolution in 2D - examples1 ? = *
Original
Courtesy of D Lowe
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28. Convolution in 2D - examples1 = *
Original
Shifted right
By 1 pixel
Courtesy of D Lowe
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29. ? 1 = *
Original
Courtesy of D Lowe
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30. Convolution in 2D - examples1 = *
Original
Blur (with a
box filter)
Courtesy of D Lowe
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31. - = ? - 2 1 1 1 1 (Note that filter sums to 1) Original2 1
= ?
(Note that filter sums to 1)
Original
“details of the image” - 1 1 1 +
Courtesy of D Lowe
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32. What does blurring take away?
detail – =
original
smoothed (5x5)
Let’s add it back:
original
detail
sharpened
+ a =
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33. Convolution in 2D – Sharpening filter- 2 1 =
Original
Sharpening filter: Accentuates differences with local average
Courtesy of D Lowe
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34. Image support and edge effect
A computer will only convolve finite support signals.
What happens at the edge?
• zero “padding”
• edge value replication
• mirror extension
• more (beyond the scope of this class)
-> Matlab conv2 uses zero-padding f h
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35. Convolution vs. (Cross) Correlation
A convolution is an integral that expresses the amount of overlap of one function as it is shifted over another function.
convolution is a filtering operation
Correlation compares the similarity of two sets of data. Correlation computes a measure of similarity of two input signals as they are shifted by one another. The correlation result reaches a maximum at the time when the two signals match best .
correlation is a measure of relatedness of two signals
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36. What about OpenCV? Convolution or (Cross) Correlation?
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37. https://en.wikipedia.org/wiki/Kernel_(image_processing)
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43. منابع http://vision.stanford.edu/teaching/cs131_fall1718/
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