high dynamic range imaging -...

MotivationRecovering HDR Radiance Maps

Tonemapping

High Dynamic Range Imaging

Mathias Eitz, Claudia Stripf

TU Berlin

January, 16th 2007

Mathias Eitz, Claudia Stripf High Dynamic Range Imaging


Tonemapping

Outline

1 Motivation

2 Recovering HDR Radiance MapsIdeaComputing Camera Response CurveConstructing HDR Radiance Map

3 TonemappingIdeaGlobal OperatorsReinhard Local Operator



Tonemapping

Very High World Dynamic Range

10 −6 10 6

illuminance human

high dynamic range

10 −6 10 6

illuminance picture

low dynamic range

Figure: High dynamic vs. low dynamic range

Human can discern very high range of brightness values

Photography limited to much lower dynamic range


Exposure Series

Figure: From left to right: underexposed, correct exposure, overexposed


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Tasks

Compute a HDR picture from multiple exposures

But: Dynamic range of display usually very limited, cannotdisplay HDR pic

Two tasks

1 Compute HDR image

2 Tonemapping to compress contrast into displayable range



Tonemapping

What We Have Done

To solve those two tasks, we have implemented two papers:

P. Debevec - Recovering HDR Radiance Maps fromPhotographs - SIGGRAPH’97Reinhard et al - Photographic Tone Reproduction for DigitalImages - SIGGRAPH’02



Tonemapping

IdeaComputing Camera Response CurveConstructing HDR Radiance Map

Outline

1 Motivation





Tonemapping


Idea

Take multiple exposures of the same scene

Vary exposure time from small to long to capture completedynamic range

Compute HDR image from those exposures



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Multiple Exposure Photography

10 −6 10 6

illuminance scene

dynamic range of photographed scene

10 −6 10 6

illuminance picture



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Outline

1 Motivation





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Computing Camera Response Curve

Camera response curve f tells us, how scene radiance E ismapped to pixel brighness Z

Using the inverse of f allows us to reproduce actual sceneradiance E

f is different for each camera

compute f from a series of exposures

Camera response curve

Non-linear mapping f from scene radiance Ei and exposuretime ∆tj to pixel brightness Zi

Zij = f (Ei∆tj)

We want to determine f



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Camera Response Curve - Mathematical

Define equation system

Zij = f (Ei∆tj)

f −1 (Zij) = Ei∆tj

ln f −1 (Zij) = ln Ei + ln∆tj

Set g = ln f −1

Solve for g

Solve overdetermined system of equationsg (Zij) = ln Ei + ln∆tj

Solved in a least-squared error sense

Result: Camera response function f



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Computation of Response Curve of Canon EOS 350D

Computed from a series of 9 exposures

Exposure time from 14000 to 15

Each exposure two stops apart (i.e. 14000 , 1

1000 , 1250 ,...,15)

λ = 50


Exposure Series

Figure: Exposure series used to compute camera response curve

Response Curve of Canon EOS 350D

−6 −4 −2 0 2 40

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−8 −6 −4 −2 0 2 40

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log Exposure X

Pix

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−6 −4 −2 0 20

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Pix

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−8 −6 −4 −2 0 2 40

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Figure: Recovered response curve f

Response Curve of Canon EOS 350D

−7 −6 −5 −4 −3 −2 −1 0 1 2 30

50

100

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Pix

el V

alue

Z

Figure: Recovered response curve f


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Outline

1 Motivation





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Idea

What we know

Camera response curve

Multiple exposures of same scene at know exposre times

Each pixel in the scene is correctly exposed at least once

Use this information to assemble HDR image

Each pixel is a weighted combination from the correspondingpixels of all exposures



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Assemble HDR Radiance Map - Mathematical

Radiance

lnEi = g (Zij) − ∆tj

Weighted average

Use weighted average of all exposures to create HDR map

lnEi =sumP

j=1(w(Zij)(g(Zij)−∆tj))sumP

j=1(w(Zij))



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How to Display a HDR Image

We have now generated a HDR image

Dynamic range of resulting HDR image: ≈ 1 : 100000

Dynamic range of computer screen: much lower

Problem We cannot directly display the resulting HDR image

Solution Tone mapping



Tonemapping

IdeaGlobal OperatorsReinhard Local Operator

Outline

1 Motivation





Tonemapping


Idea

Compress high dynamic range to displayable low dynamicrange

Need to preserve details and colors

10 −6 10 6

illuminance scene

dynamic range of photographed scene

10 −6 10 6

illuminance picture

Figure: Tone mapping



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Luminance Map

Tone mapping is usually done on the luminance map

Then colors are reapplied

Luminance map

L (x , y) = 0.2 ·Red (x , y) + 0.7 ·Green (x , y) + 0.1 ·Blue (x , y)



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Outline

1 Motivation





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Global Operators

Definition

Tone mapping operator Maps a HDR image into displayable range[0, 1]

Linear Linear mapping of HDR image into range [0, 1]

Logarithmic Logarithmic mapping of HDR image into [0, 1]

Reinhard Global Reinhard operator L (x , y) = L(x ,y)1+L(x ,y)


Global Operators - Results

Figure: Linear Mapping


Figure: Logarithmic Mapping


Figure: Global Reinhard Mapping


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Outline

1 Motivation





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Local Operators

Adapt to the luminance in the current local neighbourhood

Reinhard local operator

L (x , y) = L(x ,y)1+V (x ,y)

V is the average luminance of a local neighbourhood of acertain size

Find biggest local neighbourhood with fairly even contrast

Done with a Difference of Gaussians approach at multiplescales s



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Reinhard Local Operator

Search the biggest pixel neighbourhood s where|V (x , y , s)| < eps

V is a function of the Difference of Gaussians, telling us wherestrong contrast changes occur


Some Results

Figure: Hackesche Hoefe, Berlin - Reinhard global

Some Results

Figure: Hackesche Hoefe, Berlin - Reinhard local

Some Results

Figure: Desk - Reinhard local

Some Results

Figure: Hackescher Markt, Berlin - Reinhard global


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Questions

Any questions?

Slides can be downloaded at http://user.cs.tu-berlin.de/˜eitz


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