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602 23. Tone Reproduction
range images is therefore generally larger as well, although at least one standard
(the OpenEXR high dynamic range file format (Kainz et al., 2003)) includes a
very capable compression scheme.
A different approach to limit file sizes is to apply a tone reproduction operator
to the high dynamic data. The result may then be encoded in JPEG format. In
addition, the input image may be divided pixel-wise by the tonemapped image.
Figure 23.6. Dynamic
range of 2.65 log
2
units.
Figure 23.7. Dynamic
range of 3.96 log
2
units.
Figure 23.8. Dynamic
range of 4.22 log
2
units.
Figure 23.9. Dynamic
range of 5.01 log
2
units.
The result of this division can then be subsampled and stored as a small amount of
Figure 23.10. Dynamic
range of 6.56 log
2
units.
data in the header of the same JPEG image (G. Ward & Simmons, 2004). The file
size of such sub-band encoded images is of the same order as conventional JPEG
encoded images. Display programs can display the JPEG image directly or may
reconstruct the high dynamic range image by multiplying the tonemapped image
with the data stored in the header.
In general, the combination of smallest step size and ratio of the smallest and
largest representable values determines the dynamic range that an image encoding
scheme affords. For computer-generated imagery, an image is typically stored as
a triplet of floating point values before it is written to file or displayed on screen,
although more efficient encoding schemes are possible (Reinhard et al., 2005).
Since most display devices are still fitted with eight-bit D/A converters, we may
think of tone reproduction as the mapping of floating point numbers to bytes such
that the result is displayable on a low dynamic range display device.
The dynamic range of individual images is generally smaller, and is deter-
mined by the smallest and largest luminances found in the scene. A simplistic
approach to measure the dynamic range of an image may therefore compute the
ratio between the largest and smallest pixel value of an image. Sensitivity to out-
liers may be reduced by ignoring a small percentage of the darkest and brightest
pixels.
Alternatively, the same ratio may be expressed as a difference in the logarith-
mic domain. This measure is less sensitive to outliers. The images shown in the
margin on this page are examples of images with different dynamic ranges. Note
that the night scene in this case does not have a smaller dynamic range than the
day scene. While all the values in the night scene are smaller, the ratio between
largest and smallest values is not.
However, the recording device or rendering algorithm may introduce noise
which will lower the useful dynamic range. Thus, a measurement of the dynamic
range of an image should factor in noise. A better measure of dynamic range
would therefore be a signal-to-noise ratio, expressed in decibels, as used in signal
processing.