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High dynamic range imaging
Camera pipeline
12 bits 8 bits
Short exposure
10-6 106
10-6 106
Real worldradiance
Pictureintensity
dynamic range
Pixel value 0 to 255
Long exposure
10-6 106
10-6 106
Real worldradiance
Pictureintensity
dynamic range
Pixel value 0 to 255
Varying shutter speeds
Recovering High Dynamic Range Radiance Maps
from PhotographsPaul E. Debevec Jitendra Malik
SIGGRAPH 1997
Recovering response curve
12 bits 8 bits
Dt =1/4 sec
Dt =1 sec
Dt =1/8 sec
Dt =2 sec
Image series
Dt =1/2 sec
Recovering response curve
• 1• 1
• 1• 1
• 1• 1
• 1• 1
• 1• 1
• 3• 3
• 3• 3
• 3• 3
• 3• 3
• 3• 3
• 2• 2
• 2• 2
• 2• 2
• 2• 2
• 2• 2
0
255
Idea behind the math
ln2
Idea behind the math
Each line for a scene point.The offset is essentially determined by the unknown Ei
Idea behind the math
Note that there is a shift that we can’t recover
Math for recovering response curve
Recovering response curve
• The solution can be only up to a scale, add a constraint
• Add a hat weighting function
Recovered response function
Constructing HDR radiance map
combine pixels to reduce noise and obtain a more reliable estimation
Reconstructed radiance map
Gradient Domain High Dynamic Range Compression
Raanan Fattal Dani Lischinski Michael Werman
SIGGRAPH 2002
The method in 1D
log derivative
atte
nuat
e
integrateexp
The method in 2D
• Given: a log-luminance image H(x,y)• Compute an attenuation map
• Compute an attenuated gradient field G:
• Problem: G may not be integrable!
H
HyxHyxG ),(),(
Solution
• Look for image I with gradient closest to G in the least squares sense.
• I minimizes the integral:
22
2,
yx Gy
IG
x
IGIGIF
dxdyGIF ,
y
G
x
G
y
I
x
I yx
2
2
2
2Poissonequation
Attenuation
gradient magnitudelog(Luminance) attenuation map
1),(
),(
yxHyx k
kH 1.0
8.0~
Multiscale gradient attenuation
interpolate
interpolate
X =
X =
Bilateral[Durand et al.]
Photographic[Reinhard et al.]
Gradient domain[Fattal et al.]
Informal comparison
Informal comparison
Bilateral[Durand et al.]
Photographic[Reinhard et al.]
Gradient domain[Fattal et al.]
Bilateral[Durand et al.]
Photographic[Reinhard et al.]
Gradient domain[Fattal et al.]
Informal comparison
Local Laplacian Filters :Edge-aware Image
Processingwith a Laplacian PyramidSylvain Paris Samuel W. Hasinoff Jan
KautzSIGGRAPH 2011
Background on Gaussian Pyramids• Resolution halved at each level using
Gaussian kernel
level 0
level 1
level 2level 3(residual)
27
Background on Laplacian Pyramids• Difference between adjacent Gaussian
levels
level 0
level 1
level 2level 3(residual)
28
Discontinuity
Intuition for 1D Edge
= + +
Input signal Texture Smooth
29
• Decomposition for the sake of analysis only– We do not compute it in practice
Discontinuity
Intuition for 1D Edge
= + +
Input signal Texture SmoothDoes not
contribute toLap. pyramidat that scale(d2/dx2=0)
30
Discontinuity
Ideal Texture Increase
Texture
Keep unchanged
Amplify
31
Our Texture Increase
“Locally good”version
Input signal
σ σ
σ
σ
user-defined parameter σ defines texture vs. edges
32
Local nonlinearity
DiscontinuityUnaffected
Our Texture Increase
= + +
“Locally good”Only left side
is affected
TextureLeft side is ok,right side is not
SmoothDoes not
contribute toLap. pyramidat that scale(d2/dx2=0)
33
= + +
SmoothDoes not
contribute toLap. pyramidat that scale(d2/dx2=0)
Discussion
Negligible because
collocated with discontinuity
Negligible because
Gaussian kernel ≈ 0
DiscontinuityUnaffected
“Locally good”Only left side
is affected
TextureLeft side is ok,right side is not
34
Good approximation to ideal case overall
(formal treatment in
paper)
Texture ManipulationInput
35
Texture ManipulationDecrease
36
Texture ManipulationSmall Increase
37
Texture ManipulationLarge Increase
38
Texture ManipulationInput
39
Texture ManipulationLarge Increase
40