Method of performing fast bilateral filtering and using the same for the display of high-dynamic-range images
A method of performing bilateral filtering and using the method for displaying high-dynamic-range images is presented. The method reduces the contrast of the image while preserving detail of the image. The presently disclosed method incorporates a two-scale decomposition of the image into a base layer encoding large-scale variations, and a detail layer. The base layer has its contrast reduced, thereby preserving detail. The base layer is obtained using an edge-preserving bilateral filter. The bilateral filter is a non-linear filter, where the weight of each pixel is computed using a Gaussian in the spatial domain multiplied by an influence function in the intensity domain that decreases the weight of pixels with large intensity differences. The bilateral filtering is accelerated by using a piecewise-linear approximation in the intensity domain and appropriate subsampling.
1. A method of performing piece-wise linear bilateral filtering comprising:
computing a weight of each of a plurality of pixels of an image using a Gaussian in a spatial domain; and
multiplying said weight by an influence function in the intensity domain wherein a weight of a pixel with a large intensity difference from weights of other pixels of said plurality of pixels is reduced.
2. The method of claim 1 wherein said computing and said multiplying are done in accordance with the formula:
J
s
=
1
k
(
s
)
∑
ρ
∈
Ω
f
(
p
-
s
)
g
(
I
p
-
I
s
)
I
p
wherein J s is the output for pixel s, k(s) is a normalization term, f is the Gaussian in the spatial domain, g is the Guassian in the intensity domain, I p is the intensity for the image, and I s is the intensity for the pixel.
3. The method of claim 2 where k(s) is determined in accordance with the formula:
k
(
s
)
=
∑
ρ
∈
Ω
f
(
p
-
s
)
g
(
I
p
-
I
s
)
where f is the Gaussian in the spatial domain, g is the Guassian in the intensity domain, I p is the intensity for the image, and I s is the intensity for the pixel.
4. The method of claim 1 wherein said multiplying comprises utilizing a piecewise-linear approximation in the intensity domain.
5. The method of claim 1 wherein said piecewise-linear approximation comprises discretizing a set of signal intensities into segment values and computing a linear filter for each said segment value.
6. The method of claim 5 wherein said computing includes utilizing a Fast Fourier Transform(FFT).
7. The method of claim 1 wherein said computing comprises down-sampling in the spatial domain.
8. The method of claim 7 wherein said down-sampling is done in accordance with the formula:
J
s
j
=
1
k
j
(
s
)
∑
ρ
∈
Ω
f
(
p
-
s
)
g
(
I
p
t
-
I
j
)
I
p
=
1
k
j
(
s
)
∑
ρ
∈
Ω
f
(
p
-
s
)
H
p
j
wherein the final output of the filter for a pixel s is then a linear interpolation between the output J s j of the two closest values i j of I s .
9. The method of claim 8 wherein
k
j
(
s
)
=
∑
ρ
∈
Ω
f
(
p
-
s
)
g
(
I
p
-
i
j
)
=
∑
ρ
∈
Ω
f
(
p
-
s
)
G
j
(
p
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.
10. The method of claim 9 wherein said down-sampling comprises dividing said image in sub-images and when a difference between a maximum intensity and a minimum intensity is more reduced in said sub-image than said image then using fewer segments for said sub-images.
11. The method of claim 10 wherein said down-sampled version of said image is obtained using nearest-neighbor down-sampling.
12. The method of claim 11 wherein the output of the linear filters on said down-sampled image are linearly recombined at the full resolution.
13. The method of claim 1 further comprising detecting dubious pixels and fixing said dubious pixels.
14. The method of claim 13 wherein said fixing comprises:
providing a low-pass version of the output of the bilateral filter; and
assigning a value of a linear interpretation to the pixel depending on the log of the uncertainty normalization value.
15. A method for reducing contrast while preserving detail comprising:
selecting a high dynamic range digital image;
decomposing said image into an intensity layer and a color layer;
running said intensity layer through a bilateral filter to obtain a base layer;
dividing said intensity layer by said base layer to obtain a detail layer;
reducing contrast in said base layer; and
recombining said base layer having reduced contrast with said detail layer and said color layer to obtain a reduced contrast image.
16. The method of claim 15 wherein said running said intensity layer through a bilateral filter comprises:
computing a weight of each of a plurality of pixels of an image using a Gaussian in a spatial domain; and
multiplying said weight by an influence function in the intensity domain wherein a weight of a pixel with a large intensity difference from weights of other pixels of said plurality of pixels is reduced.
17. The method of claim 16 wherein said computing and said multiplying are done in accordance with the formula:
J
s
=
1
k
(
s
)
∑
ρ
∈
Ω
f
(
p
-
s
)
g
(
I
p
-
I
s
)
I
p
wherein J s is the output for pixel s, k(s) is a normalization term, f is the Gaussian in the spatial domain, g is the Guassian in the intensity domain, I p is the intensity for the image, and I s is the intensity for the pixel.
18. The method of claim 17 where k(s) is determined in accordance with the formula:
k
(
s
)
=
∑
ρ
∈
Ω
f
(
p
-
s
)
g
(
I
p
-
I
s
)
where f is the Gaussian in the spatial domain, g is the Guassian in the intensity domain, I p is the intensity for the image, and I s is the intensity for the pixel.
19. The method of claim 16 wherein said computing includes utilizing a Fast Fourier Transform (FFT).
20. The method of claim 16 wherein said multiplying comprises utilizing a piecewise-linear approximation in the intensity domain.
21. The method of claim 16 wherein said computing comprises sub-sampling in the spatial domain.
22. The method of claim 16 wherein said sub-sampling comprises discretizing a set of signal intensities into segment values and computing a linear filter for each said segment value.
23. The method of claim 21 wherein said sub-sampling is done in accordance with the formula:
J
s
j
=
1
k
j
(
s
)
∑
ρ
∈
Ω
f
(
p
-
s
)
g
(
I
p
t
-
I
j
)
I
p
=
1
k
j
(
s
)
∑
ρ
∈
Ω
f
(
p
-
s
)
H
p
j
wherein the final output of the filter for a pixel s is then a linear interpolation between the output J s j of the two closest values i j of I s .
24. The method of claim 23 wherein
k
j
(
s
)
=
∑
ρ
∈
Ω
f
(
p
-
s
)
g
(
I
p
-
i
j
)
=
∑
ρ
∈
Ω
f
(
p
-
s
)
G
j
(
p
)
.
25. The method of claim 24 wherein said sub-sampling comprises dividing said image in sub-images and when a difference between a maximum intensity and a minimum intensity is more reduced in said sub-image than said image then using fewer segments for said sub-images.
26. The method of claim 16 wherein said computing is done using a down-sampled version of said image.
27. The method of claim 26 wherein said down-sampled version of said image is obtained using nearest-neighbor down-sampling.
28. The method of claim 16 further comprising detecting dubious pixels and fixing said dubious pixels using a normalization factor.
29. The method of claim 28 wherein said fixing comprises:
providing a low-pass version of the output of the bilateral filter; and
assigning a value of a linear interpretation to the pixel depending on the log of the uncertainty normalization value.