Pulsating Uncertainties: Visualization and Highlighting of Uncertainty in

3D Data Using Animated 2D Transfer Functions

Viktor Leonhardt

1 a

, Tobias Neeb

2 b

, Christoph Garth

1 c

and Alexander Wiebel

2 d

Scientiﬁc Visualization Lab, Department of Computer Science, RPTU Kaiserslautern, Kaiserslautern, Germany

UX-Vis group and ZTT, Hochschule Worms University of Applied Sciences, Worms, Germany

Keywords:

Highlighting, Uncertainty Visualization, Direct Volume Rendering, Animated Transfer Function.

Abstract:

While data with uncertainties arises in many scientiﬁc domains and engineering applications, the visualization

of such data remains challenging as uncertainty information must be included in an accessible and compre-

hensible manner.In this paper we present pulsating uncertainties as a novel way to highlight uncertainties by

animated two-dimensional transfer functions (2DTF) for uncertain scalar data sets. It allows for a ﬂexible

classiﬁcation by 2DTFs and an effective and pre-attentive highlighting of uncertainty by animating the 2DTFs

while enabling users to simultaneously explore the 3D scene.In addition, we present the isosurface variability

widget to highlight the variability of isosurfaces for data with uncertainty.We demonstrate the characteristics

of the new approach by experiments using climate simulation and medical data.

1 INTRODUCTION

Direct volume rendering (DVR) is a common visu-

alization method to explore and visualize volumetric

data sets emerging in medicine, engineering and nat-

ural sciences. Due to a lack of precise measurements,

a lack of prediction accuracy, a lack of completeness,

to name only a few examples (Kamal et al., 2021),

such data can be affected by uncertainty. Thus, almost

all types of visualization methods, among them DVR,

have been adapted or extended to be able to deal with

uncertainty (e.g. (Athawale et al., 2021; Sakhaee and

Entezari, 2017; Liu et al., 2012)) or to allow visualiz-

ing the uncertainty in the data to some extent (Pang

et al., 1997; Bonneau et al., 2014; H

agele et al.,

2022). The latter is especially important for those

users who want to understand, analyze or at least con-

sider the uncertainty in the data they are working with.

In this paper, we present pulsating uncertainties, a

novel DVR approach combining animation and two-

dimensional transfer functions (2DTFs) in order to

pre-attentively highlight more uncertain areas in the

dataset and to automate the exploration and illustra-

tion of these areas. This deliberately contrasts with

https://orcid.org/0000-0002-3888-6156

https://orcid.org/0009-0005-3032-8677

https://orcid.org/0000-0003-1669-8549

https://orcid.org/0000-0002-6583-3092

numerous state-of-the-art methods that employ trans-

parency to illustrate uncertainty and thus rather hide

data points with higher uncertainty instead of high-

lighting them.

Our approach addresses and solves four tasks

) focus on highlighting the uncertainty and two

tasks (I

) focus on assisting users in the interactive ex-

ploration in the context of DVR-based visualization

of uncertainty in 3D scalar ﬁelds which have not been

addressed in previous work: H

As uncertainties in

the data often require special attention, regions with

higher uncertainty should be highlighted to enable

their intuitive and pre-attentive identiﬁcation. H

Iso-

surfaces are one of the prevalent visualization meth-

ods for 3D scalar data, and prior research has explored

their application in uncertain datasets (P

othkow and

Hege, 2011; P

othkow et al., 2011; Pfaffelmoser et al.,

2011). As the position of the surfaces is unsure, their

possible distributions should be illustrated in a way

that allows to be recognized pre-attentively. I

The

pre-attentive highlighting of the uncertainty should

be retained, while allowing users to manually explore

the three-dimensional scene by manipulating the view

(rotate, pan, scale). I

Allow for an automated ex-

ploration of the data values (e.g. mean) for speciﬁc

uncertainty ranges, while allowing users to manually

explore the three-dimensional scene. Pulsating un-

certainties support these tasks using a combination of

2DTFs, animations and a speciﬁc 2DTF widget which

Leonhardt, V., Neeb, T., Garth, C. and Wiebel, A.

Pulsating Uncertainties: Visualization and Highlighting of Uncertainty in 3D Data Using Animated 2D Transfer Functions.

DOI: 10.5220/0013088500003912

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 20th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2025) - Volume 1: GRAPP, HUCAPP

and IVAPP, pages 799-806

ISBN: 978-989-758-728-3; ISSN: 2184-4321

799

we call isosurface variability widget (IVW).

We do not aim to replace well-established DVR-

based uncertainty visualization techniques by pul-

sating uncertainties, but rather see our approach as

a complementary technique in cases where existing

techniques are tedious to use or do not sufﬁciently

guide the attention of the users to the uncertainty in

the data. We note that our method is aimed at uncer-

tainty present in the data itself (data uncertainty (Ka-

mal et al., 2021)) and does not treat uncertainty re-

sulting from the visualization process or being propa-

gated through the pipeline (visualization uncertainty).

2 RELATED WORK

As mentioned above, many methods for the visual-

ization of uncertainty have been proposed in the last

decades. Surveys by Kamal et al. (Kamal et al.,

2021), Pang et al. (Pang et al., 1997) and Bonneau

et al. (Bonneau et al., 2014) summarize this work.

While past work includes techniques for many differ-

ent types of data, we concentrate on methods dealing

with scalar ﬁelds. More speciﬁcally, our method is

related to work in the three areas:

a) visualization of scalar ﬁelds with uncertainty,

b) direct volume rendering and transfer functions (es-

pecially two-dimensional transfer functions), and

c) visualizations employing animations.

In the following, we summarize the related work

in sections considering different combinations of the

above listed areas.

Visualization of Uncertainty of Scalar Fields In-

cluding DVR and transfer functions (TFs). [a+b]

One of the earlier works regarding the visualization

of uncertainty in scalar ﬁelds using DVR has been

presented by Djurcilov et al. (Djurcilov et al., 2002).

While Djurcilov et al. use predeﬁned colored regions

on a scatter plot to specify a 2DTF for the volume ren-

dering, the approach we propose uses an interactive

2DTF editor with different widgets and color-scales to

classify regions of interest. Other work, e.g. Sakhaee

et al. (Sakhaee and Entezari, 2017) and Athawale et

al. (Athawale et al., 2021), included the uncertainty

into the volume rendering process itself, allowing to

explore volumetric data with uncertainty using prob-

ability density functions (PDFs) and non-parametric

representations. None of these works however con-

siders the effect of animations applied to 2DTF clas-

siﬁcation widgets in the context of uncertainty visual-

ization of scalar ﬁelds.

Visualization of Uncertainty of Scalar Fields Us-

ing Animations. [a+c] Gershon (Gershon, 1992)

proposed one of the few approaches to visualize un-

certainty, here fuzziness, using animation. Later,

Ehlschlaeger et al. (Ehlschlaeger et al., 1997) look

into the visualization of positional uncertainty in el-

evation models using an animation-based sequence of

possible surface realizations. Brown (Brown, 2004)

introduced a new approach for visualizing uncertainty

using animated visual vibrations through oscillation

functions.

Our approach follows these works in targeting hu-

man motion perception to highlight areas with higher

uncertainty using DVR and pulsating 2DTFs to visu-

alize the volume data directly while integrating uncer-

tainty information into the rendering.

Visualization with DVR and TFs Including Ani-

mations. [b+c] Correa et al. (Correa and Silver, 2005)

present a method for data set traversal by moving a

region in which a TF is applied along a pre-speciﬁed

skeleton path in order to provide focus-plus-context

(F+C) views. Another F+C visualization approach

has been introduced by Woodring et al. (Woodring

and Shen, 2007), proposing the concept of animat-

ing TFs to incorporate animations in volume render-

ing. Yet another work presenting F+C visualization

has been presented by Sikachev et al. (Sikachev et al.,

2010) extending towards a dynamic F+C approach

that highlights features during user interaction. Akiba

et al. (Akiba et al., 2010) presented AniViz, an anima-

tion tool which allows a user to turn the results of data

exploration and visualization into an animation.

While the aforementioned works give insights

about the application of animations in a volume ren-

dering context, this article uses animations of 2DTFs

to investigate their effect with regard to the visualiza-

tion of uncertainty in a spatial data set.

Visualization of Uncertainty with DVR and TFs

Including Animations. [a+b+c] The work of Lund-

str

om et al. (Lundstr

om et al., 2007) is the only one

found related to the investigation of uncertainty (a)

using animations (c) with DVR and TFs (b). In their

approach, they address the uncertainty in the classi-

ﬁcation of a TF by interpreting overlapping classiﬁ-

cations to be uncertain. These fuzzy classiﬁcations

are presented as an animated rendering of the mapped

color/opacity. In comparison to Lundstr

om et al. who

investigate the visualization of uncertainty stemming

from the classiﬁcation, our approach focuses on the

uncertainty in the scalar data using animated 2DTFs

for DVR thus resulting in a different presentations and

implementations.

Others. While not directly related to our approach,

othkow et al. (P

othkow and Hege, 2011) and Pfaf-

felmoser et al. (Pfaffelmoser et al., 2011) presented

approaches to visualize the positional variability of

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isosurfaces in uncertain scalar ﬁelds, to which we

achieve comparable results with a special application

case based on task H

Other authors aimed to incorporate the data un-

certainty into the pipeline stages of DVR (Athawale

et al., 2021; Sakhaee and Entezari, 2017; Liu et al.,

2012). This allows them to preserve the classical,

non-uncertain TF while uncertain data is present. In

contrast to our work, this approach yields visualiza-

tions in which it is impossible to discern the extent

of accumulated uncertainty in the resulting visualiza-

tion. In other words, the uncertainty of the data is

not mapped directly to visual properties which allow

identifying areas of high uncertainty.

3 WIDGETS, MAPS &

ANIMATIONS FOR 2DTFs FOR

UNCERTAINTY

The approach for uncertainty visualization proposed

in this article is based on a set of visualization-related

features that are applied in the context of a 2DTF-

editor. These features are: (i) the use of different

shapes for classiﬁcation widgets; (ii) color and opac-

ity maps applied to classiﬁcation widgets; and (iii)

widget animations inside the 2DTF-editor.

The combination of the features in different ways

results in the ability to create visualizations of scalar

volume data with uncertainty enabling the fulﬁllment

of the tasks presented in the introduction of this arti-

cle. However, the combination of these features im-

ply issues, which we address in separate subsections.

The baseline of our approach lies in the integration

of Djurcilov et al. (Djurcilov et al., 2002) concept of

using 2DTFs for uncertainty visualization into a ba-

sic 2DTF-editor like the one presented by Kniss et

al. (Kniss et al., 2002) and animate the widgets to cre-

ate a highlighting mechanism.

Let a scalar ﬁeld with uncertainty X be given in

with the data at each point i being modeled by

a Gaussian normal distribution X

∼ N (µ

, σ

) with

mean µ

and variance σ

. A 2DTF-setup that presents

the baseline can be seen in Figure 1 where mean µ and

standard deviation σ are used for the two dimensions

of the 2D-histogram, which depicts the frequency of

value pairs in the data set. The x-axis (horizontal) of

the histogram represents the value range of the mean

values, while the range of standard deviation values

are presented on the y-axis (vertical). Due to this

setup, classiﬁcation widgets in the editor, like the red

widget in Figure 1, can be used to facilitate a clas-

siﬁcation of data with uncertainty. The advantage of

Figure 1: Left: Approximation of an isosurface using a rect-

angular widget. Right: Classiﬁcation of the isosurface vari-

ability using a triangular IVW. While the left 2DTF in-

cludes only value pairs that are very close to the isovalue,

the IVW includes value pairs that are further away but might

be close to the isovalue due to uncertainty. Two horizontal

bars (in blue or green) exemplify the value range of two

points (white cross) with a different standard deviation.

this setup is the implicit interpolation of Gaussian dis-

tributions using the Gaussian PDF interpolation in

which the mean and the standard deviation are inter-

polated separately (P

othkow and Hege, 2011).

The combined application of the features listed

above present a toolkit for visualizing the uncertainty

in spatially distributed scalar data. The following sub-

sections discuss the possible effects which each of

these features has on the ﬁnal visualization.

3.1 Classiﬁcation and Widgets

In the context of 2DTF editors, classiﬁcations are

achieved by manipulating widgets inside the GUI. Al-

though other widget shapes could be easily added to

our implementation, we use only two basic widget

shapes for uncertainty visualization: rectangles and

triangles (see Figure 1). Complex classiﬁcations can

be composed of multiple of these basic widgets.

Isosurface Variability Widget (IVW). As the di-

mension in our 2DTFs represent the mean and the

uncertainty an upside-down isosceles triangle widget

can be used to show the variability of an isosurface.

We call this an isosurface variability widget (IVW).

An example of the IVW is shown in Figure 1 (right).

Here, the isovalue is deﬁned by the apex of the tri-

angle and thus by its center. Since points higher in

the 2D histogram have a higher uncertainty, the IVW

effectively includes more value pairs that have a cer-

tain probability to actually exhibit the isovalue. This

is illustrated in Figure 1 for two points represented as

white crosses. The standard deviations of these points

are represented by the green and the blue bar. Kniss

et al. use a similar widget for isosurface visualiza-

tion (Kniss et al., 2002).

Pulsating Uncertainties: Visualization and Highlighting of Uncertainty in 3D Data Using Animated 2D Transfer Functions

801

Figure 2: Widgets using global and local colormapping.

We can deﬁne the width w(σ) of the IVW using a

conﬁdence interval γ. For Gaussian distributed vari-

ables the probability γ, that a value θ is within the

interval of z times the standard deviation σ around the

mean µ is as follows:

γ = P(µ −zσ ≤ θ ≤ µ + zσ) = er f



√



, (1)

while er f (x) is the error function. We can solve Equa-

tion 1 for the z times of a standard deviation in order

to identify the width w of the IVW:

z(γ) =

√

2 er f

−1

(γ), (2)

where er f

−1

is the inverse of the error function. Now,

we can adjust the width w

(σ) = 2z(γ)σ of the IVW,

based on the standard deviation σ to ensure that γ% of

the possible positions of the isosurface are visualized.

The linearity of w

(σ) with respect to σ shows that

the triangle with its straight edges is the perfect shape

for the IVW.

3.2 Colormapping

To apply color maps and opacity maps to enable the

differentiation of values inside scalar data is a com-

mon practice in the ﬁeld of data visualization. Opac-

ity as a visual variable has also been used in the

context of 2DTFs (Djurcilov et al., 2002) and 2DTF

editors (Kniss et al., 2002). In our approach we

apply color maps with different orientations (Fig. 2

vs. Fig. 6) to classiﬁcation widgets in a 2DTF-editor

to enable the differentiation of values of either the

scalar ﬁeld or the uncertainty ﬁeld in the 2DTF-setup.

To enhance visual distinctness in the rendering,

we employ two mapping states for widgets: global

and local mapping, as illustrated in Figure 2. Global

mapping uses the entire value range of the dataset

for color assignment, while local mapping limits the

color map to the value range classiﬁed by the wid-

get’s dimensions, improving clarity for speciﬁc value

ranges of interest. Unlike global mapping, local map-

ping is inﬂuenced by widget size changes and anima-

tions, which are discussed further in the next section.

3.3 Animation

As mentioned, DVR animations have been used for

exploratory tasks and focus+context views of features

in scalar volume data (Woodring and Shen, 2007),

and animating possible surface realizations (Brown,

2004; Ehlschlaeger et al., 1997) has been used for un-

certainty visualization. Going beyond these works,

we integrate animations into the process of uncer-

tainty visualization of volume data by animating the

2DTF-classiﬁcation itself. More speciﬁcally, we ap-

ply scaling animations to differently shaped and col-

ormapped classiﬁcation widgets in a 2DTF-editor.

Some of the possible advantages of scaling widget an-

imations with regard to uncertainty visualization in-

clude: a) Automated exploration (no manual interac-

tion necessary), b) increased comprehensibility of the

connection between rendering and 2DTF, c) visual-

ization of change in the data domain, d) focus+context

highlighting views with animated and static classiﬁca-

tion widgets and e) fading in and out of more uncer-

tain or certain regions.

Using 2DTFs editors typically requires manual fo-

cus on creating classiﬁcations with widgets. Intro-

ducing widget animations enables automated data ex-

ploration with consistent speed, overcoming the im-

precision of manual exploration. For scaling ani-

mations, this facilitates automated exploration of the

scalar ﬁeld represented by the x or y axis in the scat-

ter plot. Figure 3 illustrates how scaling animations

progressively include or exclude value pairs based on

metrics like mean or standard deviation, rendering ar-

eas with higher uncertainty increasingly transparent

and invisible.

Animations enable the perception of data domain

changes linked to the direction of scaling, such as

large volume regions becoming transparent or visible,

highlighting the frequency of speciﬁc value pairs. Ad-

ditionally, widget animations aid in forming a seman-

tic connection between the 2DTF classiﬁcation and

the visualization (Kniss et al., 2002).

As mentioned, we deﬁned two colormapping

states for the widgets. While global mapping directly

leads to expected results when applying animations to

colormapped widgets, local mapping is not straight-

forward in the context of animations. This is due to

the fact, that for local colormapping, the color scale is

applied based on the size of the widget. To avoid un-

intended color/opacity changes in the rendering, we

introduce an anchoring mechanism. With this, when a

colormapped widget using local mapping is animated,

the color scale is always applied to the initial size of

the widget (Figure 2 and Figure 3).

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3.4 Implementation

Naive approaches to animated TFs involved updating

and uploading the 2D TF texture to the GPU, causing

performance issues. To address this, we extended the

2D TF texture into a 3D texture, using the third di-

mension to store animation steps. This allows GPU-

based DVR animation through simple frame look-

ups, with Θ as the total frames and T as the animation

duration. A slice θ ∈ [0, Θ −1] of the 3D texture rep-

resents the state of the animation at time t(θ) =

θ.

Figure 4 illustrates this approach for the animation in

Figure 3. Each horizontal, semitransparent slice of the

3D texture is shown separately for the ﬁrst half of the

cyclic bouncing animation. Please note, in this ﬁg-

ure, white areas represent a material color with zero

opacity and the start frame is the most bottom one.

4 RESULTS

To showcase our uncertainty visualization approach,

we applied it using various 2DTF setups to address

previously outlined tasks. The approach was proto-

typed in an open-source tool with modules for DVR,

extended to support colormapping and widget anima-

tions. All renderings and accompanying videos were

produced on a system with an AMD Ryzen 7 3700X

CPU and NVIDIA GeForce RTX 4060 Ti GPU.

4.1 Data Sets

Here, we introduce the data sets we use to illustrate

our results for the different tasks. If not noted other-

wise, the data is given on a regular grid and the val-

ues at the points are deﬁned as Gaussian random vari-

ables. At ﬁrst, to achieve a more analytically compre-

hensible visualizations we use the well known tangle

function (Knoll et al., 2009) (see also Figure 5). Simi-

lar to Athawale et al. (Athawale et al., 2021) the tangle

function is mixed with noise to generate an ensemble

representing uncertain data using a resolution of 512

To demonstrate the effects of our approach on

medical data, we use CT data taken from the CHAOS

(combined [CT-MR] healthy abdominal organ seg-

mentation) challenge (Kavur et al., 2019). We used

Figure 3: Frames of scaling animation applied a col-

ormapped widget. When the top of the widget moves down

samples with higher uncertainty are rendered transparent.

Figure 4: Illustration of the 3D texture of the ﬁrst half of

the cyclic bouncing animation. Each frame θ is shown as a

semitransparent 2D slice.

the registered CT data of 20 patients to compute the

weighted mean and variance. The resulting three-

dimensional scalar ﬁeld with uncertainty has a reso-

lution of 256 ×256 ×81. Due to physical differences

of patients in this data set, we have to weight the ﬁrst

patient 20 times more than the other 19 patients. Oth-

erwise, the mean and variance of the created scalar

ﬁeld with uncertainty would not look valid.

We also demonstrate the use of animated

2DTFs on the climate ensemble of the DEMETER

project (Palmer et al., 2004). This ensemble contains

the daily average hindcast for the temperature for

February 20

, 2000. The data is generated by seven

climate models, where each model produced nine sets

with distinct simulation parameters. We used mean

and variance of the 63 ensemble members to model

the scalar ﬁeld with uncertainty (144 ×73 ×4).

4.2 User Interaction and Highlighting

(Task I

)

In our ﬁrst experiment, we address task I

to explore

the uncertainty of the tangle function. Figure 5 shows

DVR and 2DTF for three frames, where scaling down

the 2DTF progressively excludes points with higher

uncertainty, leaving only those with low mean and

low standard deviation. This simple example high-

lights automated uncertainty exploration for a ﬁxed

mean range, enabling users to interactively examine

3D structures while beneﬁting from the automation.

4.3 Automated Exploration of Mean for

an Uncertainty Range (Task I

)

Our second experiment addresses task I

for the tan-

gle data, focusing on exploring regions with low un-

certainty. Using the 2DTF setup in Fig. 6, animating

the widget to narrow its width highlights low-valued

points. This automated exploration allows users to

investigate features by rotating the visualization or

zooming into interesting regions, as shown in Fig. 6.

Pulsating Uncertainties: Visualization and Highlighting of Uncertainty in 3D Data Using Animated 2D Transfer Functions

803

Figure 5: Using color map and animation: basic visualization of increasingly hiding more uncertain areas in the data. This

leads to the highlighting of uncertainty while allowing manipulating the view for manual exploration as described by task I

Figure 6: Frames of an animation where the values of the mean ﬁeld are explored for a speciﬁc uncertainty range (Task I

The 2DTF-setup uses a rectangular widget with a local colormap in x-direction to enable visual differentiation of the selected

mean values. From left to right the renderings vary in the width of 2DTF widget. Additionally, the later renderings were

interactively rotated during the animation process. Note that between the left and the middle rendering only small changes

occur, but the related 2DTF classiﬁcation widget is already at half its initial size. This illustrated the distribution or rate of

change of mean values throughout the volume dataset..

4.4 Pre-Attentive Highlighting of

Uncertainty (Task H

)

This experiment demonstrates the application of pul-

sating animations of the CT data set in order to high-

light regions with higher uncertainty. The pulsation

allows the intuitive and pre-attentive identiﬁcation of

the uncertainties in the data. The used 2DTF setup

is shown in the insets in Figure 7 alongside with the

resulting rendering. To create a static context, a gray

rectangle widget is used to show points in a narrow

range of mean values with comparatively low uncer-

tainty. An additional rectangle widget colored in ma-

genta is used to show points with higher uncertainties.

This leads to an initial rendering, where more certain

values are rendered gray, while areas of higher uncer-

tainty are prominently visualized using magenta. To

repeatedly fade the uncertain areas in and out, a scal-

ing animation is applied to the widget, so that its top

moves down. The effect of this is visible in the frames

shown in Fig. 7. Due to the fading of uncertain areas

viewers are increasingly presented with more certain

areas deﬁned by the initial 2DTF-setup. Areas with

highly uncertain values are highlighted by the pulsat-

ing animation and can be pre-attentively identiﬁed.

In this case, when comparing the left and the right

rendering, it can be seen that most areas belonging to

the rib cage possess a higher uncertainty as they are

close to invisible in the right rendering showing the

more certain areas. Djurcilov et al. (Djurcilov et al.,

2002) used opacity in this way to highlight uncertain

areas. However, this prevents opacity from being used

as a way to create feature related contexts in the clas-

siﬁcation step of the DVR pipeline. For this reason,

we use color as the primary visual variable and ani-

mation as supporting visual cue to convey uncertainty

to the viewer while using opacity to reduce occlusion.

This can also be seen in the renderings of Figure 7,

where due to a lower opacity of the static context vi-

sualization it is possible to perceive areas with higher

uncertainty that lie inside the shown context regions.

4.5 Visualizing the Variability of an

Isosurface (Task H

)

To address task H

we animate the IVW (Section 3)

and thus continuously fade (in/out) the less probable

isosurface realizations. Figure 8 shows this approach

applied to the climate data set. The initial 2DTF-setup

and rendering can be seen on the left, while the other

renderings and 2DTFs present a progressed state of

the animation horizontally collapsing the IVW. Here,

the mean isovalue of 273.15 K (0° C) has been used.

The entire animation cycle, which also expands the

IVW, can be seen in the video accompanying this ar-

ticle. The effect of this widget animation is a progres-

sive elimination of positions that are most uncertain

to actually be part of the isosurface. Thus, initially,

the visualized region represents potential realizations

of the isosurface for 0° C. Later, e.g. in the third ren-

dering, only more probable realizations are shown.

Note that the thickness of the rendered region at

a speciﬁc location can be an indicator of the uncer-

tainty or the gradient magnitude of the data. High un-

certainty results in a thicker ”surface” because points

with very different mean values can be part of the iso-

surface; lower gradient magnitude results in a thicker

”surface” because similar mean values are spread out

over a larger area. In Figure 8, this is most apparent in

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Figure 7: Frames of a 2DTF-animation for CT dataset. The 2DTF-setup enables fading in/out of areas with higher uncertainty,

while also maintaining a static visualization of the more certain structural context represented by the grayish areas. This results

in an example of how task H

can be performed regarding the visualization of uncertainty in the respective dataset.

Figure 8: DVRs and their respective 2DTFs of an animation of the IVW in the context of the climate dataset. While the initial

rendering (left) presents a region of many possible isosurface realizations based on a wide IVW, the other renderings show

later animation states, where the less probable areas are continuously faded out. Additionally, the thickness of the region at a

position is an indicator of the uncertainty in this area. This can especially be seen on the left vertical part of the renderings.

the change of thickness on the left side of the image,

where in the beginning the vertical area is far wider

than in the last rendering. In addition to this, the col-

ors used in the visualization show the local amount of

uncertainty. The blue and teal areas in the last ren-

dering are the ones where it is the most uncertain that

they actually have a value of approximately 0 °C.

othkow and Hege (P

othkow and Hege, 2011)

created a static visualization of the isosurface vari-

ability for the same data and isovalue. Their visualiza-

tion is comparable to the initial rendering of Figure 8.

The advantage of an animation of the isosurface vari-

ability, is that one is able to see the change between

the more and less certain surface realizations.

5 LIMITATIONS

The presented approach exploits the high sensitiv-

ity of the visual perception to oscillating visual fea-

tures which is captured in the temporal contrast sensi-

tivity function (Ramamurthy and Lakshminarayanan,

2015). While humans are capable of identifying that

two animations differ in speed, it is not possible to

quantify the frequency of an animation. Thus, ani-

mations are not a suitable visual channel to support

comparison tasks (Brown, 2004). Using animations to

highlight time-dependent datasets is impractical, as it

is impossible to distinguish between changes caused

by unsteadiness or by the animation itself.

The observation that animation of the DVR can

cause visual fatigue (Lundstr

om et al., 2007) limits

the time the new method can be used effectively. This,

however, does not impede a central goal of the new

approach, i.e. providing a quick overview with a pre-

attentive highlighting of regions with uncertainty.

Simple DVR performance optimization tech-

niques like progressively resolution during user inac-

tivity (Meyer-Spradow et al., 2009) can not be com-

bined with pulsating uncertainties. The animation

continually alters the content that needs to be ren-

dered. A solution could be to extend such techniques

by pre-computing high resolution renderings of ani-

mation frames as soon as the user interactions stops.

6 CONCLUSION AND FUTURE

WORK

In this article, we presented animated two-

dimensional transfer function widgets as an un-

certainty highlighting mechanism for scalar ﬁelds

with uncertainty. In addition to the highlighting, the

animation serves as a means to automatically explore

the data and its uncertainty while users can focus on

the spatial exploration by manually interacting (e.g.

rotating) with the scene. The constant speed of the

animated TF additionally allows judging the rate of

change of uncertainty between different areas in the

rendered scene. One of the introduced TF widgets,

the isosurface variability widget, enables users to

inspect the variability of isosurfaces. Until now this

has been solved by the literature as specializations of

contouring and volume rendering algorithms for data

Pulsating Uncertainties: Visualization and Highlighting of Uncertainty in 3D Data Using Animated 2D Transfer Functions

805

with uncertainty. As the method is not limited to data

from a certain domain, we were able to demonstrate

its expressiveness on data from diverse domains.

Animated 2DTFs open many avenues for fu-

ture work in uncertainty visualization. Instead of

the standard deviation the level-crossing probability

(LCP) (P

othkow and Hege, 2011) could be used for

the y-axis of the 2DTF. The advantage of the LCP is

its capability to deal with non-parametric models of

uncertainty. The interpretation of the animation and

visualization would be a challenge for this research.

We present only a limited amount of widgets for an-

imation. Further widget designs and animation types

(scale, rotate, translate) could be used to explore the

complex data sets with uncertainty in other meaning-

ful ways. It is obvious that animation works well for

highlighting, nevertheless analyzing which animation

speed is most effective could be interesting.

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