# High Dynamic Range from Multiple Images Which Exposures to

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"High Dynamic Range from Multiple Images Which Exposures to"

```					High Dynamic Range from Multiple Images:
Which Exposures to Combine?
Michael Grossberg and Shree Nayar

CAVE Lab, Columbia University

ICCV Workshop on CPMCV
October, 2003, Nice, France

Partially funded by NSF ITR Award, DARPA/ONR MURI
Combining Different Exposures
Low Dynamic Range Exposures

+

Combination Yields High Dynamic Range

[Ginosar and Zeevi, 88, Madden, 93,
Mann and Picard, 95, Debevec and Malik, 97,
Mitsunaga and Nayar, 99]
The Camera Response

0       255

Scene       Linear Function          Image      Camera         Image

L                 s                  E           f               B
From Response To Measured Irradiance Levels

Brightness Levels B

Response Function f

Where do you want your bits?
Response Function f

Coarse
Brightness B

quantization

Range

Response Function f

Fine
Brightness B

quantization

Low Dynamic
Range
Effective Camera from Multiple Exposures
Goal        Acquired Images       Image from Effective Camera

Capture
High
Dynamic
Range
+

Capture
Uniformly                      +
Flexible Dynamic Range Imaging:

• Can we create an effective camera with a
desired response?

– How many exposures are needed?

– Which exposures to acquire?

– How to combine the acquired images?
f(E)
3
Exposure e1 = 1    2
1
0
Sum
0             E1               E2            E3
f(e2E)
Exposure e2        3
2
1
0

0       E1 / e1      E2 / e2       E3 / e3
h(E)
6
5
Effective Camera   4
3
2
1
0

^   ^        ^       ^     ^        ^
0    E1 E2        E3       E4 E5         E6
Response of the Effective Camera

Effective Response   Number of exposures     Camera Response

n
h( E )   f ( e j E )
j 1

Theorem: The sum of a set of images of a
scene taken at different exposures includes all
the information in the individual exposures.
Camera Response Emulation
~
h                  Emulated Response
Brightness Levels B

depends on:
h
f , e = (e1, … ,en)
g
Desired Response

• How can we tell if h emulates g well?

Level spacing characterizes similarity
How Response Determines Level Spacing

h
Brightness Levels B

Larger       Observation:
Derivative
Smaller                                   The derivative determines
Derivatives                               the distances between
levels.
Sparse         Dense
Spacing        Spacing

The Objective Function
Spacing Based Comparison:
Number of Exposures             Exposure Values        Desired Response   Effective Response

E MAX

( n, e )            | g   h |2 w dE
E MIN

Weight

Weight prevents penalizing success:
Brightness B

h
g                                       0, g ( E )  h( E )
w(E ) 
{   1, otherwise
Which Exposures and How Many?
• For fixed n, find minimizing exposure values e

• Choose min n such that error within tolerance

• Method: Exhaustive search
– Objective function not continuous
– Only need to search actual settings
– Offline build table of exposures
Flexible Dynamic Range Imaging

Effective   Number of               Exposure Values
Camera      Exposures   1     2        3      4     5     6
Linear          2       1   1.003
3       1   1.003    2.985
4       1   1.015    1.019 3.672
5       1   1.003    1.007 1.166 4.975
6       1   1.003    1.007 1.031 1.078 5.636
Gamma =         2       1   3.094
1/2             3       1   1.003    5.146
4       1   1.003    3.019 11.23
5       1   1.003    1.006 5.049 18.56
6       1   1.003    1.006 2.866 8.564   33.7
2       1   20.24
Constant
contrast        3       1   9.91     88.38
(log)           4       1   4.689    37.23 280
5       1   4.831    29.18 144.9 763.5
6       1   3.979    16.01 64.22 305.4   1130
Flexible Dynamic Range Imaging
Effective   Number of               Exposure Values
Camera      Exposures   1     2        3       4        5        6
Linear          2       1   1.003
3       1   1.003    2.985
4       1   1.015    1.019   3.672
5       1   1.003    1.007   1.166     4.975
6       1   1.003    1.007   1.031     1.078    5.636
Gamma =         2       1   3.094
1/2             3       1   1.003    5.146
4       1   1.003    3.019   11.23
5       1   1.003    1.006   5.049     18.56
6       1   1.003    1.006   2.866     8.564    33.7
2       1   20.24
Constant
contrast        3       1   9.91     88.38
(log)           4       1   4.689    37.23    280
5       1   4.831    29.18   144.9     763.5
6       1   3.979    16.01   64.22     305.4    1130

Desired Response
Constant Contrast
Linear
Linear              Dynamic Range
Gamma 1/2             High   1:16,000
Medium 1:1,000
Low    1:256
Baseline Exposure Values

• Typically exposures are doubled
[Ginosar and Zeevi, 88, Madden, 93,
Mann and Picard, 95, Debevec and Malik, 97,
Mitsunaga and Nayar, 99]

• Baseline:
Combine the exposures e =(1,2,4)
Increased Dynamic Range Linear Camera

• Real Camera: f linear
Brightness Brightness
• Desired Camera: g linear (greater dynamic range)

4-bit real camera                                             8-bit real camera
1.0                                                              1.0
Baseline Response (1,2,4)                                        Baseline Response (1,2,4)

0.8                                                              0.8

Brightness B
Brightness B

0.6                                                              0.6

0.4                         Desired Response
0.4
Desired Response

0.2                                                              0.2
Computed Response
Computed Response
(1, 1.05, 1.11)
(1, 1.003, 2.985)
0.0                                                              0.0
0.0   0.2      0.4    0.6       0.8   1.0                        0.0    0.2      0.4     0.6    0.8       1.0

Linear Camera: Synthetic Ramp Image

High Dynamic Range Linear Camera

From baseline exposures (1,2,4)    From computed exposures (1,1.05,1.11)
Linear Camera: Image of Cloth

Ground Truth (HDR image)

Baseline Exposures (1,2,4)

Computed Exposures (1,1.05,1.11)
Constant Contrast from Linear Cameras

• Real Camera: f linear
• Desired Camera: g log response (constant contrast)

3 Exposures                                                     5 Exposures
1.0                                                        1.0
Desired                                                          Desired
Response                                                         Response
0.8                                                        0.8
Brightness B

Brightness B
0.6                                                        0.6
Baseline Response                                               Baseline Response
(1,2,4)
0.4                                                        0.4

0.2                                                        0.2
Computed Response                                                Computed
(1,9.91,88.38)                                                   Response
0.0                                                        0.0
0.0   0.2      0.4   0.6    0.8    1.0                        0.0     0.2      0.4   0.6   0.8     1.0
Constant Contrast : Image of Tiles

Baseline Exposures

Computed Exposures
Linear Camera from Non-linear Camera

• Real Camera: f non-linear (Nikon 990)
• Desired Camera: g linear

Baseline Input Exposures               Computed Input Exposures

Brightness          Brightness

Combined         Iso-brightness         Combined        Iso-brightness
Summary

• Combine images using summation

• Method finds number of exposures and
exposure values to use

• Emulation of a variety of cameras:
Flexible Dynamic Range Imaging

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