Volume Rendering for High Dynamic Range Displays

Volume Rendering for High Dynamic Range Displays
Volume Graphics (2005)
E. Gröller, I. Fujishiro (Editors)
Volume Rendering for High Dynamic Range Displays
Abhijeet Ghosh, Matthew Trentacoste, Wolfgang Heidrich
The University of British Columbia†
Abstract
Dynamic range restrictions of conventional displays limit the amount of detail that can be represented in volume
rendering applications. However, high dynamic range displays with contrast ratios larger than 50, 000 : 1 have
recently been developed. We explore how these increased capabilities can be exploited for common volume rendering algorithms such as direct volume rendering and maximum projection rendering. In particular, we discuss
distribution of intensities across the range of the display contrast and a mapping of the transfer function to a
perceptually linear space over the range of intensities that the display can produce. This allows us to reserve several just noticeable difference steps of intensities for spatial context apart from clearly depicting the main regions
of interest. We also propose generating automatic transfer functions for order independent operators through
histogram-equalization of data in perceptually linear space.
Categories and Subject Descriptors (according to ACM CCS): I.3.3 [COMPUTER GRAPHICS]: Picture/Image
Generation - Display algorithms; I.4.10 [COMPUTER GRAPHICS]: Image Representation - Volumetric.
1. Introduction
Direct volume rendering has proven extremely useful for the
visualization of medical and scientific data sets. One of its
advantages is that transfer functions can be used to segment
out interesting parts of the volume, while in principle keeping other information present to provide context useful for
navigation.
Unfortunately, the low dynamic range of conventional displays limits the usefulness of this approach: for optimal contrast in the regions of interest, one has to adjust the transfer
function such that most of the available intensity and opacity levels are used for very specific density values. Consequently, very little precision remains for other density values to provide spatial context. The non-linear gamma curve
of such display devices helps, but the problem remains as
there are not enough addressable intensity values.
Recently developed display technology with a much
higher dynamic range promises to be useful for solving this
problem. Seetzen et al. [SHS∗ 04] describe two such systems,
one with projector-based illumination at a contrast ratio of
† E-mail: {ghosh, mmt, heidrich}@cs.ubc.ca
c The Eurographics Association 2005.
50, 000 : 1 and a peak intensity of 2, 700cd/m2 , and one with
LED illumination reaching a contrast ratio of > 150, 000 : 1
and a peak intensity of 8, 500cd/m2 Typical desktop displays
have a contrast of about 400 : 1 with a maximum intensity of
300cd/m2 , although special medical displays can perform a
factor of 2-3 times better.
In this paper, we investigate the use of this HDR technology for volume rendering (color-plate: Figure 7). In particular, we describe the use of transfer functions in perceptually
linear space over the range of intensities representable by
the display. We also describe adaptations of transfer functions to better represent spatial context and automatic generation of transfer functions based on JND space histogramequalization. Finally, we explore related techniques for order
independent volume rendering algorithms such as maximum
intensity projection and summation, both of which are useful
for x-ray style rendering.
The remainder of this paper is organized as follows: Section 2 briefly recounts previous work in volume rendering,
HDR display technology, and the aspects of human visual
perception that are relevant to our work. Section 3 discusses
methods for deriving transfer function that yield in a perceptually linear usage of the contrast range, while Section 4
explores the possibilities for automatically adapting user-
A.Ghosh, M. Trentacoste, W. Heidrich / Volume Rendering for High Dynamic Range Displays
defined transfer functions to provide spatial context for navigation.
array. This is possible since the local contrast that the human
eye can perceive is limited. This second setup achieves a top
intensity of 8, 500cd/m2 with a contrast of over 150, 000 : 1.
2. Related Work
Seetzen et al. describe the image processing operations
necessary to factorize floating point images (representing
absolute luminances) to drive the front panel and the back
lighting of the HDR displays. These operations can be implemented on GPUs for integration into interactive rendering
systems. In our work, we use the same algorithms as a backend for our volume renderer.
A lot of recent work has focused on deriving transfer functions automatically from volume data. Much of this work
analyzes the histogram of the volume densities, sometimes
combined with gradients [KD98] or curvature [KWTM03].
Several different user interfaces have been proposed, namely
[MAB∗ 97, KG01, KKH02].
Very recently, Mora and Ebert have argued that traditional
direct volume rendering may not be the best way to visualize volume data since important features may be occluded by
less important parts of the volume. They propose order independent volume rendering, a framework that generalizes
both maximum intensity projection and summation based
methods, which roughly correspond to x-ray style rendering. They propose stereo as a way to compensate for the loss
of depth cues arising from order independent methods, and
argue that stereo is, in fact, more effective for order independent methods than for direct volume rendering.
Independent of a specific volume rendering method, it
is important to evenly distribute information across the
range of contrasts that can be shown on a given display. A
first step in this direction was recently taken by Potts and
Möller [PM04], who proposed to specify transfer functions
for direct volume rendering on a logarithmic scale. However, for modern display devices (especially the high dynamic range displays that have recently evolved), it is also
necessary to take into account the limitations of human contrast perception for various intensity levels. In this paper we
analyze the intensities generated on the screen by various
rendering algorithms, and propose to adapt transfer functions to take these perceptual effects into account. The goal
is therefore to optimize the perceptible contrast generated in
the final image.
2.2. HDR Displays
Conventional desktop display systems such as CRTs or LCD
panels have dynamic ranges of about 400 : 1 and a maximum intensity of about 300cd/m2 . In recent work, Seetzen
et al. [SHS∗ 04] describe two setups that combine conventional low dynamic range display technology to form a high
dynamic range display. In the first setup, a video projector
replaces the backlight of a conventional LCD panel. This
way, the light arriving from the projector is filtered by the
semi-transparent LCD panel. Seetzen et al. measured a dynamic range of about 50, 000 : 1 with a maximum intensity
of 2, 700cd/m2 for this setup.
The same authors also developed a second system in
which the projector is replaced with a low-resolution LED
2.3. Human Perception and HDR Imaging
In recent experiments, Muka and Reiker [MR02] have determined that over the dynamic range of conventional displays the perceptual difference between an 8-bit digital display and a 10-bit or higher bit depth is minimal, and in some
cases even non-existent. From this result, we can conclude
that HDR display technology such as the one described in
Section 2.2 is essential for displaying more visually distinct
intensity levels.
# Just Noticeable Difference Levels for Different Maximum Luminance Levels
100000
10000
1000
Luminance in cd/m2
2.1. Direct Volume Rendering
100
10
1
0.1
0.01
0
200
400
600
JND index
800
1000
1200
Figure 1: The number of just noticeable difference (JND)
steps for different maximum intensities according to the DICOM standard.
Over the range of illumination levels representable by the
HDR displays mentioned above, the sensitivity of the human
visual system is highly non-linear: at low luminance levels,
smaller differences are perceivable than at high luminance
levels. This property is formally described by the notion of
just noticeable differences (JND). One JND is the smallest
detectable intensity difference for a given illumination level.
For the intensity range covered by the HDR display technology mentioned above, Barten [Bar92, Bar93] has derived
a psychophysically validated model to characterize JNDs.
Based on this work, an analytical function for computing
JNDs was included in the DICOM Grayscale Standard Display Function [DIC01]. A plot of the JND curve over the
relevant intensity range is shown in Figure 1.
For the projector-based HDR display of Seetzen et
c The Eurographics Association 2005.
A.Ghosh, M. Trentacoste, W. Heidrich / Volume Rendering for High Dynamic Range Displays
al. [SHS∗ 04], this model predicts 962 JND steps, while for
the LED-based display it predicts 1139 JND steps. Both display technologies can produce intensities at a finer granularity, but the human visual system cannot discriminate between those. To make optimal use of the contrast of a display,
the intensities produced by an algorithm therefore must be
linear in JND space, not the physical space. This is the focus
of our work.
3. Transfer Functions for HDR Displays
In the following we describe how to perceptually optimize
user specified transfer functions for the different rendering
algorithms. We start by discussing the case of direct volume
rendering, and then move on to order independent methods
(summation and maximum intensity projection).
−1
−1
I perceived (a, b) = fJND
(I(a, b)) = fJND
Cα
.
τ
(3)
The densities ρ should therefore be specified as
−1
ρ := log( fJND
(ρ0 )),
(4)
where ρ0 , the original volume densities, are now mapped approximately linearly to just noticeable intensity differences
in the final image (Figure 2).
1
opacity transfer function
data histogram
0.9
0.8
Percieved−1
intensity
ρ = log(f
(ρ’))
0.7
0.6
JND
3.1. Direct Volume Rendering
To derive an approximately perceptually linear formulation
of the transfer function for direct volume rendering, consider
the emission absorption volume rendering equation in the
notation of Sabella [Sab88]:
0.5
0.4
0.3
0.2
0.1
0
0
50
100
150
Original data
200
1
I(a, b) =
Z b
a
Cρ(u) · e
−
Ru
a
τρ(t)dt
du
300
opacity transfer function
data histogram
0.9
(1)
250
0.8
If we assume that the density is constant over a segment
of the integral, we get
Actual Intensity ρ’
0.7
Here, ρ is the volume density at point u, C is an emission
constant (i.e. C · ρ is the emitted energy per unit length), and
τ is the absorption constant (i.e. τ · ρ is the absorption per
unit length).
0.6
0.5
0.4
0.3
0.2
0.1
0
I(a, b) =
Cα
τ
with α := 1 − e−τ
Ru
a
ρ(t)dt
,
(2)
as described by Max et al. [MHC90]. In other words, the
transparency α of the integral varies exponentially with the
volume density. For this reason, Potts and Möller [PM04] argue that the transfer function that is used to derive densities
from volume data values should be specified on a logarithmic scale.
However, as described in Section 2.3, the intensities themselves are not perceived linearly by the human observer. In
order to make optimal use of the intensity range delivered
by the HDR displays, the just noticeable differences have
to be taken into account. In particular, let f JND be the JND
−1
function from the Dicom standard [DIC01], and fJND
be its
inverse (i.e. the function mapping intensity values to just noticeable differences). The perceived intensity level in JND
space is then:
c The Eurographics Association 2005.
0
50
100
150
Original data value
200
250
300
Figure 2: Perceptually linear transfer function specification
for the tooth dataset (Figure 8). Top: perceived intensity levels ρ specified in JND space. Bottom: actual intensity ρ0 used
in volume rendering.
Of course the volume densities are not constant along the
ray in practice. As a consequence, if a segment of the transfer
function is changed, but others remain the same, then the
actual intensity change on the screen can still be non-linear.
However, we find that the correspondence between transfer
function and response of the display is much more direct and
easy to control if we use the mapping described above (see
Section 5).
3.1.1. Color
The discussion so far has only considered just noticeable differences in intensity, and has ignored color. In practical volume rendering applications, color is, however, an important
A.Ghosh, M. Trentacoste, W. Heidrich / Volume Rendering for High Dynamic Range Displays
3.2. Order Independent Operators
A similar analysis can be performed for the order independent operators. In the case of the summation operator, it is
easy to see that a change in the transfer function contributes
linearly to a change in pixel intensity. For maximum intensity projection, a change only occurs if the value changed
is actually the maximum along a given viewing ray. If this
is the case, however, then the effect is again linear. In both
cases, the transfer function should therefore only be modified by the inverse of the JND curve.
In addition to this simple perceptual adjustments, order independent methods are also amenable to more sophisticated
methods for automatically generating transfer functions. In
practical volume rendering applications, a linear ramp transfer function is often used as a starting point for exploration.
Mora and Ebert [ME04] showed that this can be a reasonable choice for order independent methods, although it does
not tend to work very well for direct volume rendering.
Several researchers have focused on deriving transfer
functions automatically from volume data [PLB∗ 01]. The
primary focus has been on analysis of the distribution of histogram values and sometimes combined with other features
in the volume such as gradients [KD98] [EMRY02] or curvature [KWTM03].
We propose to perform histogram equalization on the
JND-corrected volume data to generate the intensity transfer function. This equalization is done by first constructing
the normalized cumulative histogram. We then normalize the
histogram of the data values such that the intensity distribution is uniform in JND space. This allows us to generate a
perceptually linear transfer function which maps most of the
interesting data into the visible range (Figure 3). The generated transfer function can also be used as an intuitive starting
point to explore the data and segment it in a more customized
manner.
We find that this method works well for the summation
0.9
0.8
0.7
0.6
intensity transfer function
data histogram
0.5
0.4
0.3
0.2
0.1
0
0
50
100
150
200
250
300
Original data
1
Intensity from histogram equalization in JND space
In the absence of more perceptual models that take both
color and high contrast into account, the best we can do at the
moment is to treat the two aspects as being independent. This
can be achieved by using a color space that separates intensity from chromaticity, for example the L∗ a∗ b∗ space. The
user can then specify two transfer functions for the chrominance channels (a and b), while the luminance is computed
using the algorithm introduced for the monochromatic case.
Intensity from histogram equalization in JND space
1
means of visually segmenting volume data sets into different parts. Unfortunately, knowledge about human perception
in environments with both color and high contrast is at this
point limited: most of the perception experiments dealing
with color differences were performed in low contrast settings, while the intensity JND work is based on monochromatic experiments.
0.9
intensity transfer function
gradient magnitude histogram
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
50
100
150
Gradient magnitude
200
250
300
Figure 3: Automatic transfer function generation based
on JND space histogram equalization for the CT engine
dataset. Top: transfer function based on equalization of data
density values. Bottom: transfer function based on equalization of gradient magnitude (as used in Figures 5 and 6).
operator. For the maximum operator, however, the histogram
of the volume densities is not always a good predictor for
the histogram of the pixel values, since the maximum operator is strongly view-dependent. For this reason, we also consider performing the histogram equalization in image space
after projection. This is easy to implement for the maximum
operator since it requires only one unnormalized value to
be stored per pixel. In Section 5 we show several examples using the six order independent operators proposed by
Mora and Ebert [ME04]: summation and maximum applied
to original data values, to their gradient magnitude and to the
product of data value and gradient magnitude.
Unfortunately, the theoretical motivation behind JND
space histogram equalization does not apply to volume rendering. This is because the perceptually linear mapping of
the data goes through another non-linear mapping in the
form of exponential fall-off due to the volume rendering integral (Equation 1). In practice, however, we find that the
method can often still be used to provide a good starting
point for a transfer function. We provide several examples
of results for direct volume rendering in Section 5.
4. Automatically Providing Spatial Context
Something we might want to do on a HDR display is to reserve a small range of density values for parts of the volume
c The Eurographics Association 2005.
A.Ghosh, M. Trentacoste, W. Heidrich / Volume Rendering for High Dynamic Range Displays
Given a user provided transfer function that segments out
the object of interest and sets the densities of all other regions to 0, we can adapt this transfer function in the following way: all non-zero entries in the old transfer function
are linearly mapped to JND steps reserved for focus (in our
case 400 . . . 962). The regions that were zeroed out previously are replaced by piecewise linear segments mapping
gradient magnitude values to the range 0 . . . 400 (Figure 4).
5. Results and Discussion
We use the perceptually linear mapping described in Section 3.1 to specify the opacity transfer function for various
medical and scientific datasets. We present results on the
projector based HDR display as well as comparisons with
tone mapped versions on a regular display device. Here, we
used a log-linear tone-mapper with gamma correction as implemented in HDRShop [HDR]. The CT tooth dataset has
many distinct isosurfaces very close together in intensity
space and a logarithmic transfer function (Figure 2) significantly aids in isolating these isosurfaces (color-plate: Figure 8, left). Note that the HDR display clearly shows a lot
more detail in the tooth than the tone-mapped version on the
regular display. The same non-linear mapping was used to
isolate the sinuses and a thin layer of skin around the skull
in the CT head dataset (color-plate: Figure 8, right). Again
note the details in the eye sockets and the skull surface as
shown on the HDR display compared to the version shown
on the regular display device. The HDR sequences also convey a better sense of relative depth for various features. In
this case, the tooth and the head datasets were both rendered
with lighting and shading.
Reserving JNDs for context as described in Section 4 can
be very useful as a semi-automatic way of generating transfer functions. We use the gradient magnitude of the data
c The Eurographics Association 2005.
0.8
User selected opacity
in percieved intensity space
For example, on the projector-based HDR display [SHS∗ 04], we can set aside a portion of the 962
displayable JND steps for providing spatial context in this
form. In our implementation, we use information from the
data itself, in the form of gradient magnitude, to highlight
context. Volume areas of high gradient magnitude correspond to distinctive isosurfaces that can be rendered dimly
to provide context for navigation. We found that setting
aside about 400 JNDs for providing this context is a good
tradeoff for the projector based HDR Displays. We expect
that the best choice will depend on the contrast and intensity
range of the individual display used. For our display, this
choice leaves more than 560 JNDs for depicting the data
values the user is currently interested in, which is still more
than twice the precision of conventional displays.
1
0.9
0.7
opacity transfer function
data histogram
0.6
0.5
0.4
0.3
0.2
0.1
0
0
50
100
150
Original data value
200
250
300
1000
900
800
opacity TF for gradient magnitude
opacity TF for data
gradient magnitude histogram
data histogram
700
Opacity mapped to JNDs
that are not directly the focus of attention, but can provide
context for navigation within the volume. A perceptually linear space for specifying transfer functions is useful in this
regard, since it allows us to directly estimate what contrast
range will be used for this purpose.
600
500
400
300
200
100
0
0
50
Gradient magnitude
100
150
200
250
300
Original data
Figure 4: Automatic context generation for the CT head
dataset (Figure 9). Top: User specified opacity transfer function for data (dark histogram). Bottom: Automatic context
for unselected data in the form of gradient magnitude (light
histogram) being mapped to 0 . . . 400 JNDs, while the selected data is mapped to 400 . . . 962 JNDs reserved for focus.
for visualizing context since gradient magnitude defines object boundaries. We selected a threshold of 0 . . . 400 JNDs
with the projector-based display for visualizing context as
this nicely separated out the various isosurfaces for most of
the datasets. This threshold can also be set in a data-driven
way, for example by examining the histogram of the gradient magnitude. The context generated in this way for the CT
tooth and head datasets (color-plate: Figure 9, left and right)
results in semi-automatic isolation of interesting isosurfaces,
such as the sinuses, ear and skin in the CT head dataset and
the roots in the tooth, similar to that obtained from full user
selection in Section 3.1. Also note how the context is mostly
saturated in the long exposure shots as it occupies only a
small portion of the intensity space in order to retain details
in the focus. The tooth and head datasets were rendered without lighting and shading in this case to clearly illustrate the
effect of JND space context generation. Note that the JND
space mapping for focus and context was applied only to the
opacity transfer function and color was manually assigned.
Our proposed JND space histogram equalization in Section 3.2 provides a way to automatically generate a perceptually linear transfer function which maps most of the interesting data into the visible range. It also serves as an improved
A.Ghosh, M. Trentacoste, W. Heidrich / Volume Rendering for High Dynamic Range Displays
Figure 5: JND space histogram equalization for generating automatic transfer functions for the sum operator. The left-right
image pairs were captured at 4 f-stops apart. Top: transfer function generation by histogram equalization; Bottom: JND space
linear ramp transfer function. Left-pairs: CT engine dataset and CT head using gradient magnitude; Right-pairs: CT engine
dataset and CT tooth using product.
starting point for further exploration of the data. As pointed
out previously, this is directly applicable for automatically
generating transfer functions for order independent operators in volume rendering. The histogram equalization is applied in data space for the summation operator and in image
space for the maximum operator. We apply it to the six order
independent models [ME04]: summation and maximum applied to original data values, to the gradient magnitude and
to the product of the data value and gradient magnitude. We
present comparisons of renderings with automatically generated transfer functions through histogram equalization in
JND space with those using a linear ramp in JND space for
these operators.
With summation, the operator applied to gradient magnitude and the product provides the most compelling visualizations as both cases highlight the distinct isosurfaces in the
data. Figure 5 presents both results for the CT engine dataset,
c The Eurographics Association 2005.
A.Ghosh, M. Trentacoste, W. Heidrich / Volume Rendering for High Dynamic Range Displays
Figure 6: JND space histogram equalization for generating automatic transfer functions for the max operator. The left-right
image pairs were captured at 4 f-stops apart. Top: transfer function generation by histogram equalization; Bottom: JND space
linear ramp transfer function. Top-left: CT engine dataset using gradient magnitude; Top-right: CT engine dataset using product; Bottom-left: CT visible human male dataset using data density; Bottom-right: CT visible human male dataset using product.
as well as gradient magnitude image for the CT head, and
product for the CT tooth.
Figure 6 presents the results of applying the maximum
operator to both gradient magnitude and the product for the
CT engine dataset, as well as to original data and the product for the CT Visible Human Male dataset. Note that here
we compare results of JND space histogram equalization in
image space to a linear ramp in JND space. In the case of
both summation and maximum intensity projection, the JND
c The Eurographics Association 2005.
space equalization leads to a better visualization of various
features in the volume.
6. Conclusions
One of the main advantages of direct volume rendering for
visualization of medical and scientific datasets is the usage
of transfer functions in order to segment out interesting parts
of the volume, while in principle keeping other information
present to provide context useful for navigation.
A.Ghosh, M. Trentacoste, W. Heidrich / Volume Rendering for High Dynamic Range Displays
Conventional displays with low dynamic range provide
very little precision for spatial context as most of the precision is used up for visualizing specific segmented regions of
the volume. In this paper, the use of recently developed HDR
display technology for volume rendering is investigated. In
particular, we examine the creation of transfer functions in
perceptually linear space over the range of intensities representable by the display. This is done by mapping intensity values to just noticeable differences and defining transfer function in JND space. Also described is the adaptation
of transfer functions to better represent spatial context by
reserving JND levels for both focus as well as context. Automatic transfer function generation in perceptually linear
space is also presented through histogram equalization in the
JND space.
There are a number of opportunities for future work. In
particular, the treatment of color is presently based on the
assumption of independence between just noticeable differences in luminance and chrominance. The availability of the
HDR display technology would now allow the design of perceptual experiments to verify this assumption, or to derive
better models, which could, in turn, be used to improve the
methods presented here.
Our current analysis does not account for the changes
of the intensities by lighting and shading computations. If
shading is to be included into the contrast optimization, one
would probably not want to give the same priority to these
shading-based differences as to differences based on actual
data values. A possible compromise could be to limit the influence of the shading operations to a small number of JNDs,
similar to the way we currently create navigational context.
7. Acknowledgments
The first author was supported by an ATI Technologies Fellowship. We would like to thank Helge Seetzen and Sunnybrook Technologies for providing the HDR display as well
as technical support and feedback.
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c The Eurographics Association 2005.
A.Ghosh, M. Trentacoste, W. Heidrich / Volume Rendering for High Dynamic Range Displays
Figure 7: Screen photographs of volume rendering of the CT head dataset on a HDR display, captured at 2 f-stops apart,
illustrating the representable dynamic range.
Figure 8: Screen photographs of volume rendering of the CT tooth and the CT head datasets. The left-right image pairs were
captured at 4 f-stops apart. Top row: As displayed on the HDR display; Bottom row: tone-mapped version displayed on a
regular LCD panel.
Figure 9: Automatic context generation for both the CT tooth and the CT head datasets by adapting the transfer function and
remapping the intensities in JND space. The left-right image pairs were captured at 4 f-stops apart. Top row: User selected
focus; Bottom row: Automatically generated context.
c The Eurographics Association 2005.
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