SLIDE 1
A Gentle Introduction to Bilateral Filtering and its Applications
“Fixing the Gaussian Blur”: the Bilateral Filter
Sylvain Paris – MIT CSAIL
Blur Comes from Averaging across Edges
* * *
input
- utput
Same Gaussian kernel everywhere.
Fixing the Gaussian Blur: the Bilateral Filter Sylvain Paris MIT - - PowerPoint PPT Presentation
Fixing the Gaussian Blur: the Bilateral Filter Sylvain Paris MIT - - PowerPoint PPT Presentation
A Gentle Introduction to Bilateral Filtering and its Applications Fixing the Gaussian Blur: the Bilateral Filter Sylvain Paris MIT CSAIL Blur Comes from Averaging across Edges * output input * * Same Gaussian kernel everywhere.
SLIDE 2
SLIDE 3
Properties of Gaussian Blur
- Does smooth images
- But smoothes too much:
edges are blurred.
– Only spatial distance matters – No edge term
input
- utput
S
I G I GB
q q p
q p || || ] [
space
SLIDE 4
Bilateral Filter No Averaging across Edges
* * *
input
- utput
The kernel shape depends on the image content.
[Aurich 95, Smith 97, Tomasi 98]
SLIDE 5
space weight
not new
range weight
I new
normalization factor
new
Bilateral Filter Definition: an Additional Edge Term
S
I I I G G W I BF
q q q p p p
q p | | || || 1 ] [
r s
Same idea: weighted average of pixels.
SLIDE 6
Illustration a 1D Image
- 1D image = line of pixels
- Better visualized as a plot
pixel intensity pixel position
SLIDE 7
space
Gaussian Blur and Bilateral Filter
space range normalization
Gaussian blur
S
I I I G G W I BF
q q q p p p
q p | | || || 1 ] [
r s
Bilateral filter
[Aurich 95, Smith 97, Tomasi 98] space space range p p q q
S
I G I GB
q q p
q p || || ] [
SLIDE 8
q p
Bilateral Filter on a Height Field
- utput
input
S
I I I G G W I BF
q q q p p p
q p | | || || 1 ] [
r s
p
reproduced from [Durand 02]
SLIDE 9
Space and Range Parameters
- space s : spatial extent of the kernel, size of
the considered neighborhood.
- range r : “minimum” amplitude of an edge
S
I I I G G W I BF
q q q p p p
q p | | || || 1 ] [
r s
SLIDE 10
Influence of Pixels
p
Only pixels close in space and in range are considered.
space range
SLIDE 11
s = 2 s = 6 s = 18 r = 0.1 r = 0.25 r =
(Gaussian blur)
input
Exploring the Parameter Space
SLIDE 12
s = 2 s = 6 s = 18 r = 0.1 r = 0.25 r =
(Gaussian blur)
input
Varying the Range Parameter
SLIDE 13
input
SLIDE 14
r = 0.1
SLIDE 15
r = 0.25
SLIDE 16
r =
(Gaussian blur)
SLIDE 17
s = 2 s = 6 s = 18 r = 0.1 r = 0.25 r =
(Gaussian blur)
input
Varying the Space Parameter
SLIDE 18
input
SLIDE 19
s = 2
SLIDE 20
s = 6
SLIDE 21
s = 18
SLIDE 22
Basic denoising
Noisy input Bilateral filter 7x7 window
SLIDE 23
Bilateral filter
Basic denoising
Median 3x3
SLIDE 24
Bilateral filter
Basic denoising
Median 5x5
SLIDE 25
Basic denoising
Bilateral filter Bilateral filter – lower sigma
SLIDE 26
Bilateral filter
Basic denoising
Bilateral filter – higher sigma