1. A Gentle Introduction to Bilateral Filtering and its Applications
“Fixing the Gaussian Blur”: the Bilateral Filter
Sylvain Paris – MIT CSAIL

2. Blur Comes from Averaging across Edges*
input
output * *
Same Gaussian kernel everywhere.

3. Bilateral Filter No Averaging across Edges
[Aurich 95, Smith 97, Tomasi 98] *
input
output * *
The kernel shape depends on the image content.

4. Bilateral Filter Definition: an Additional Edge Term
Same idea: weighted average of pixels.
normalization factor
new
space weight
not new
range weight I
new

5. Illustration a 1D Image 1D image = line of pixels
Better visualized as a plot
pixel intensity
pixel position

6. Gaussian Blur and Bilateral Filterp q
space
space
Bilateral filter [Aurich 95, Smith 97, Tomasi 98] p
range q
space
range
normalization
space

7. Bilateral Filter on a Height Field
output
input
reproduced from [Durand 02]

8. Space and Range Parameters
space σs : spatial extent of the kernel, size of the considered neighborhood.
range σr : “minimum” amplitude of an edge

9. Influence of Pixels
Only pixels close in space and in range are considered.
space
range p

10. Exploring the Parameter Space
σr = ∞ (Gaussian blur)
σr = 0.1
σr = 0.25
input
σs = 2
σs = 6
σs = 18

11. Varying the Range Parameter
σr = ∞ (Gaussian blur)
σr = 0.1
σr = 0.25
input
σs = 2
σs = 6
σs = 18

12. input

13. σr = 0.1

14. σr = 0.25

15. σr = ∞ (Gaussian blur)

16. Varying the Space Parameter
σr = ∞ (Gaussian blur)
σr = 0.1
σr = 0.25
input
σs = 2
σs = 6
σs = 18

17. input

18. σs = 2

19. σs = 6

20. σs = 18