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