Flexible Direct Multi-Volume Rendering in Dynamic Scenes

Soren Grimm†, Stefan Bruckner†, Armin Kanitsar‡, Eduard Groller†

† Vienna University of Technology, Austria‡Tiani Medgraph AG, Austria

Email: {grimm, bruckner, gr oller }@cg.tuwien.ac.at , kanitsar@tiani.com

Abstract

In this paper we describe methods to efficiently vi-sualize multiple intersecting volumetric objects. Weintroduce the concept of V-Objects. V-Objects rep-resent abstract properties of an object connected toa volumetric data source. We present a method toperform direct volume rendering of a scene com-prised of an arbitrary number of possibly intersect-ing V-Objects. The idea of our approach is to distin-guish between regions of intersection, which needcostly multi-volume processing, and regions con-taining only one V-Object, which can be processedusing a highly efficient brick-wise volume traversalscheme. Using this method, we achieve significantperformance gains for multi-volume rendering. Weshow possible medical applications, such as surgi-cal planning, diagnosis, and education.

1 Introduction

Direct volume rendering is an important and flexi-ble technique for visualizing 3D data. It allows thegeneration of high quality images without a need ofan intermediate interpretation. Traditionally, medi-cal volume visualization systems feature only sim-ple scenes consisting of a single volumetric data set.It has been proposed to extend these scenes to amore complex description [13]. In this paper we in-troduce a flexible data structure called V-Objects forrepresenting scenes containing multiple volumetricobjects. We present an efficient approach to ren-der a scene composed of V-Objects. Furthermore,by presenting practical examples for possible appli-cations we demonstrate that medical visualizationsystems can take advantage of V-Objects. The maincontributions of this paper are an efficient techniqueto render V-Objects and to show that common medi-cal volume visualization systems can greatly extendtheir flexibility by supporting concurrent display of

multiple volumetric objects.The presentation of the paper is subdivided as

follows: Section 2 surveys related work. In Sec-tion 3 we present as a new data-structure V-Objectsand an approach to efficiently render a scene com-posed of multiple V-Objects. In Section 4 wepresent possible medical applications. Finally, inSection 5 we give ideas for future work and con-clude our work.

2 Related Work

The past decade has seen significant progress involume visualization, driven by applications suchas medical imaging. A number of different vol-ume rendering algorithms have been developed, im-proved, and extended [8, 6, 12]. Today, it is possi-ble to perform interactive high-quality volume ren-dering on commodity hardware [15, 2]. Hybrid al-gorithms have been designed, which allow concur-rent display of intersecting volumetric and polygo-nal objects [9, 5]. Direct rendering of scenes con-sisting of multiple volumetric objects, however, hasreceived less attention. With the increasing per-formance of modern hardware, we feel that thistopic will become more important in the future.Our work was inspired by Leu and Chen, who in-troduced a two-level hierarchy for complex scenesof non-intersecting volumes [7]. While their ap-proach allows multi-volume rendering, the individ-ual volumes cannot intersect. However, the dis-play of intersecting semi-transparent objects can bea powerful visualization technique. In the workof Nadeau [13] intersecting volumes are possi-ble, however, the whole scene description has tobe re-sampled every time a volume’s transforma-tion changes. The idea behind our approach is toallow multiple intersecting volumetric objects tobe rendered directly, without requiring costly re-

VMV 2004 Stanford, USA, November 16–18, 2004

sampling. Thus, our algorithm is well-suited foranimations.

3 V-Objects

A V-Object is an element of a scene descriptionwhich is connected to one volumetric data source.The V-Object comprises the following visual prop-erties:

• Illumination: This includes the selected Illu-mination model and its parameters. For exam-ple, for the Phong-Blinn Illumination modelthe ambient, diffuse, specular, and emissivematerial coefficients are specified.

• Transfer Functions:For each defined region inthe attached volumetric data source a mappingfunction between scalar values and colors aswell as opacities is stored.

• Region of Interest:An arbitrary number ofplanes define a convex region of interest.

• Transformation: An affine transformationdefining position, orientation, and scaling ofthe V-Object.

The separation of visual properties and volumetricdata sources allows an arbitrary number of varyingrepresentations of the same data source within onescene, as illustrated in Figure 1. This is achieved byassigned several V-Objects to the same volumetricdata source. To take full advantage of the V-Objectswe apply direct volume rendering to simultaneouslyvisualize a scene consisting of several V-Objects.The properties of a V-Object influence the pointsin a scene at which it is defined. For example, re-gions of the volume which are classified as trans-parent due to the transfer function specification arenot part of a V-Object.

The following section briefly describes howmono-volume raycasting can be greatly acceler-ated by a bricked volume layout and an appropriatebrick-wise processing scheme. This performancebenefit is then exploited in Section 3.2 to acceler-ate multi-volume raycasting.

3.1 Mono-Volume Rendering

The discrepancy between processor and memoryperformance is rapidly increasing, making memoryaccess a potential bottleneck for applications whichhave to process large amounts of data. Volume ray-casting is prone to cause problems, as it generally

V-Objects

data sources

Figure 1: Different representations of the same datasource using V-Objects.

leads to irregular memory access patterns. There areapproaches which address this issue, such as Knit-tel et al. [4] or Mora et al. [11]. The basic idea isto employ a spread memory layout. They achievehigh frame-rates. As we are interested in render-ing of multiple volumes these approaches are notwell suited, due to their immense memory require-ments. Therefore we first take a look at an appro-priate memory layout.

The most common way of storing volumetricdata is a linear volume layout, see Figure 2(a).Volumes are typically thought of as a number of

(a) (b)

Figure 2: (a) Linear memory layout. (b) Brickedmemory layout.

two-dimensional images (slices) which are kept inan array. This three-dimensional array has the ad-vantage of a simple address calculation. It hasdisadvantages when used in raycasting, due to itsview-dependent memory access patterns. A muchmore suitable memory layout for raycasting is based

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on the concept of bricking. It has been shownthat bricking is one way to achieve high cache co-herency, without increasing memory usage. Brick-ing supposes the decomposition of data into smallfixed-size data blocks. Each block is stored in lin-ear order, see Figure 2(b). The basic idea is tochoose the block size according to the cache sizeof the architecture so that an entire block fits in afast cache of the system. To take full advantage of abricked memory layout, especially of its very goodcache coherency, a suitable addressing and process-ing scheme must be used. We apply the one pro-posed in [3].

They propose a brick-wise processing scheme,as shown in Figure 3 and present an approach totake full advantage of commodity multi- and hyper-threading technology. Different bricks are pro-cessed in parallel on different physical CPUs, whilesingle bricks are processed in parallel on differentlogical CPUs on the corresponding physical CPU.By this processing scheme, the main memory toCPU transfer is considerably reduced.

5

4 5

53 4

542 3

5431 2

image plane

advancing

ray-front

1110986 7

109876

9876

876

76

6

Figure 3: Brick-wise processing scheme. The num-bers correspond to processing order of the bricks,with respect to the visibility order.

The other important issue is the access of datain a bricked volume layout. Accessing data in abricked volume layout is very costly. One way toavoid the costly address computation is to inflateeach brick by an additional layer. However, thisconsiderably increases the memory consumption.A solution to this issue is the proposed addressingscheme in [3]. They propose to use offset lookup-tables to address the direct neighbors of one sample.The key to efficiency are a small lookup table anda sophisticated indexing of this look-up table. Ba-

sically, they differentiate the possible sample posi-tions, within a brick, by the locations of the neededneighboring samples. This is illustrated in 2D inFigure 4 for a eight- and a 26-neighborhood. Theprinciple can be mapped straightforwardly to 3D.Each shaded area defines a subset. For each subset,the offsets to access the corresponding eight or 26neighbors are constant, assuming that one brick isstored one after the other in memory. With the aidof these subsets, a very small offset lookup table canbe created. This table can then be very efficientlyindexed, as shown in [3]. By using this addressingscheme, the neighbors can be accessed in constanttime, similar to the addressing in a linear volumelayout.

Figure 4: Different brick addressing patterns: Solidlines represent brick boundaries and crosses corre-spond to samples. Left side: 8-neighbor-addressingpattern (4 subsets). Right side: 26-neighbor-addressing pattern (9 subsets).

The next important issue to accelerate volumeraycasting is to efficiently skip empty regions. Aswe are interested in rendering multiple V-Objects,the memory consumption as described earlier is ofgreat importance. We therefore apply the approachpresented in [2], which is based on a hybrid trans-parent region removal and skipping technique. Thework-flow is shown in Figure 5. At first transparentregions are removed on a brick basis (Figure 5a→Figure 5b). Then to support even more refined re-moval of smaller transparent regions they performoctree projection (Figure 5b→ Figure 5c). Dueto efficiency reasons the octree subdivision, con-tained in each brick, does not fully go down to indi-vidual cells. This granular resolution of the octreeleads to approximate rays-volume intersections. Toovercome the resulting performance penalty theyuse a Cell Invisibility Cache to skip the remain-ing transparent cells (Figure 5c→ Figure 5d). Weuse the complete pipeline of the hybrid transparentregion removal and skipping technique. However,

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our main focus is on the octree projection which wewill extend and exploit for multi-volume renderingin Section 3.2.

(a) (b) (c) (d)

fully transparent

brick partially transparent

brick

Figure 5: General work-flow of our hybrid transpar-ent region removal and skipping technique: Thicksolid lines are brick boundaries, thin solid lines areoctree boundaries, / are transparent regions and\ isvisible volume data. (a)→ (b): transparent regionremoval of bricks. (b)→ (c): removal based on anoctree projection. (c)→ (d): removal using a cellinvisibility cache.

3.2 Multi-Volume Rendering

Before describing our approach to accelerate multi-volume rendering, we briefly discuss how we per-form compositing of multiple volumes [1]. The ba-sic idea of volume raycasting is to cast for eachpixel of the image plane a ray through the volume.For a single object we determine the final color andopacity of the image pixel by the over-operator [14]in front-to-back order. That is, at each re-sample lo-cation, the current color and alpha values for a rayare computed in the following way:

cout = cin + c(x)α(x)(1 − αin)αout = αin + α(x)(1 − αin)

(1)

cin andαin are the color and opacity the ray hasaccumulated so far.x is the reconstructed func-tion value andc(x) andα(x) are the classified andshaded color and opacity for this value.

For the simultaneous processing of multiple vol-umes it must be decided how they should be com-bined. We consider volumes as clouds of particlesand take into account all volume simultaneously atthe corresponding sample position. The simultane-ously compositing of multiple volumes is achievedby sequentially applying Equation 1 for each indi-vidual volume. Hereby we obtain an approximationfor compositing multiple volumes at the same loca-tion.

As described in Section 3.1, the key to high per-formance for mono-volume rendering is to optimizethe memory access pattern. This can be achieved byusing a bricked volume layout. However, to findsuch a suitable memory layout for multi-volumerendering is very difficult, due to the unpredictablememory access pattern. Every time multiple vol-umes have to be simultaneously processed, severaldata entities from memory regions far apart have tobe accessed. This leads to enormous cache trash-ing. To keep this cache trashing penalty as low aspossible, we propose to separate multi-volume ren-dering from mono-volume rendering within a scenecomposed of multiple volumes. While the process-ing of the intersection between multiple volumesrequires costly computations, the non-intersectingregions could be efficiently computed by using amono-volume rendering technique. In the follow-ing we will address this issue and present a solu-tion to efficiently decompose the scene in mono-and multi-volume rendering regions.

We start by distinguishing between the conceptsof a mono- and a multi-volume renderer. Both typesof renderers are initially supplied with a list of rays.Each entry in the ray data structure contains, amongother data, a start and an end depth. A mono-volume renderer processes one V-Object using thebrick-wise processing scheme described in the pre-vious section. It operates efficiently by using thecache coherent volume traversal presented in [3].A multi-volume renderer performs compositing inmultiple V-Objects. As the V-Objects can have dif-ferent volumetric data sources and transformations,efficient brick-wise traversal is in general not possi-ble. Thus, the multi-volume renderer performs clas-sical ray traversal. As re-sample positions along aray are likely to lie within totally different memorylocations for different V-Objects, lacking cache co-herence results in considerable performance penal-ties. In our approach, a mono-volume renderer isset up for every V-Object in the scene, while thereis only one global multi-volume renderer.

The main idea is to first identify different seg-ments along a ray’s path in the initialization phase.There are two basic types of segments:

• Mono-object segment:A mono-object seg-ment is a continuous interval along a ray lyingwithin the same V-Object.

• Multi-object segment:A multi-object segmentis a continuous interval along a ray lying

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within one or more V-Objects. Thus, eachmono-volume segment is also a multi-volumesegment.

In our approach, when performing this kind ofsegmentation, the goal is to maximize the combinedlength of mono-object segments, as mono-objectsegments can be processed more efficiently. In gen-eral, for this the intersections between a ray and allV-Objects need to be known. We apply a conser-vative approach by using the octree projection ex-plained in the previous section. For each V-Object,the entry and exit points of all rays can be obtainedby projecting its octree and setting the depth testto either less or greater. By a depth sort of these en-try and exit points mono- and multi-object segmentscan be determined.

All mono-object segments are added to themono-volume renderer which is responsible forthis V-Object. These segments can then be pro-cessed efficiently, as brick-wise traversal is possi-ble. All other segments are added to one globalmulti-volume renderer. This renderer traverses ev-ery ray segment and performs multi-volume com-positing in every step for all V-Objects which aredefined at one re-sample location. This distributionof ray segments between mono- and multi-volumerendering is done in the initialization phase. Afterall ray segments have been assigned to their corre-sponding renderer, the actual raycasting process isstarted. All renderers operate independently. Afterthey have finished, a final compositing step is re-quired which combines the values accumulated ineach segment of a ray.

The distribution of ray segments between mono-and multi-volume renderers is illustrated in Fig-ure 6. Ray A consists only of one mono-object seg-ment (A1). Ray B consists of the mono-object seg-ments B1 and B3 which pass through V-Object II,and the multi-object segment B2 which passesthrough the intersection of the two V-Objects. RayC consists of the mono-object segments C1 andC3 which pass through V-Object II, and the multi-object segment C2 which passes through the inter-section of the two V-Objects. Thus, A1 is the onlyray segment added to the mono-volume renderer forV-Object I. The segments B1, B3, C1, and C3 areadded to the mono-volume renderer for V-Object II.The multi-volume segments B2 and C2 are addedto the global multi-volume renderer. Through thiskind of distribution only a fraction of the ray seg-

ments have to undergo costly multi-volume pro-cessing.

A

B

C

A1

B1 B2 B3

C1 C2 C3

V-Object I

V-Object IIV-Object I

∩

V-Object II

multi-volume renderer

B2

C2

mono-volume renderer

for V-Object I

A1

mono-volume renderer

for V-Object II

B1

B3

C1

C3

Figure 6: Top: Segmentation of three rays, A, B,and C, in a scene consisting of two V-Objects.Bot-tom: Distribution of ray segments among mono-and multi-volume renderers.

The performance gains achieved through ourmulti-volume rendering approach depend on thesize of intersections between the individual V-Objects. Typically, intersections are small, whichallows us to exploit the high performance of mono-volume processing to accelerate the rendering.Moreover, if there is no intersection between anyV-Object, our algorithm evaluates to a pure mono-volume renderer.

We have compared our approach to a standardmulti-volume raycaster where rays are processedsequentially, performing re-sampling and composit-ing in each of the V-Objects defined at every pointalong a ray. Figure 7 shows the speed-ups weachieve for different degrees of intersection. As canbe seen from the figure, the performance gains dueto our algorithm depend on the size of the inter-section between the V-Objects. For typical scenes,where size of intersections is normally not exces-sively large, we achieve speed-ups of about 2.5.

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43.5%

1.93

21.7%

2.43

0.0%

2.78

Scene 1 Scene 2 Scene 3

Figure 7: Obtained speed-ups for different degreesof intersection. The first row displays the ratio be-tween the combined lengths of all ray segmentsand the multi-object ray segments, row two showsthe achieved speed-up of our approach comparedto brute-force multi-volume rendering. The images(512×512) in row three show the rendering results.The last row displays the corresponding octree pro-jections of both V-Objects. Test system specifica-tions: Intel Pentium 4, 2.4 GHz, 1 GB RAM.

4 Exploring the capabilities of V-Objects

In general, in a volume rendering system there existseveral means to enhance visual perception. Suchmeans are for example transfer function specifica-tion, segmentation and clipping. Since their in-troduction to volume visualization by Levoy [8],piecewise linear transfer functions mapping scalarvalues to colors and opacities are featured in vir-tually every volume visualization system. Manyresearchers have proposed to extend transfer func-tions to higher dimensions to increase their usabil-ity, as their specification is a non trivial task. Someapproaches for semi-automatic transfer functiondefinition have been presented, however fully auto-matic transfer function selection remains a widelyunsolved problem. Still, much research needs to bedone to produce results automatically as shown inFigure 8 (color plate), first row, image (a).

One way to simplify the transfer function spec-ification is segmentation. Many methods exists toidentify certain structures within the data. Most ofthese approaches produce a labelling of the data.Different transfer functions can be assigned to iden-tify regions or objects. Figure 8 (color plate), firstrow, image (b) shows an example of segmentation

based on region growing. The main vascular struc-tures and the kidneys have been segmented.

One problem in the visualization of volumetricdata is occlusion. While transparency can be use-ful to simultaneously display different structures ofinterest, it can lead to cluttering when used exten-sively. It is therefore common to cut away opaqueobjects to reveal occluded features. Cutting can beperformed using axis aligned or arbitrarily orientedplanes, convex regions or arbitrarily shaped objects.However complex cutting shapes are often difficultto interpret by the user. Figure 8 (color plate), firstrow, image (c) shows the use of cutting planes toreveal an aneurism. In the following we show howsuch basic tools can be greatly enhanced by the useof V-Objects.

Though many systems allow modification oftransfer functions, and illumination properties canbe specified on a per object basis, certain limitationsapply: objects typically can not intersect, are uniqueand static. By assigning V-Objects to componentsof a data set we can overcome these limitations ina natural way. For example, with V-Objects it ispossible to move an object while keeping a virtualcopy in place. These two objects can have a totallydifferent appearance. This capability can be used inapplications such as surgical planning, education,illustration, and for investigation or exploration ofdata. In the following we give several examples forthe use of V-Objects in combination with the previ-ous described basic tools. We show examples formoving objects, simultaneously changing the ap-pearance of objects, time varying, and multi-modaldata. As some of these concepts are very hard toillustrate using still images, we have produced sev-eral animation sequences. Our application featuresan interactive tool for the generation of animationsequences using key-framing. V-Objects can be in-teractively positioned in the scene and their proper-ties can be modified. Between the key-frames, V-Object states are interpolated. This enables speci-fication of animation paths, transfer function fades,light movement, control of clipping planes, changeof data sources, enabling and disabling of objects,etc. For each of these properties, different interpo-lation schemes can be applied. In the following wepresent our application examples.

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4.1 Advanced Browsing Techniques

Traditional techniques for inspecting volumetricdata like cutting, involve removing portions of thedata. This has the disadvantage of potentially hid-ing important contextual information. McGuffin etal. [10] have presented novel tools for browsingvolume data which employ transformations and de-formations of semantic layers contained in the dataset. In the future, we feel that multi-volume render-ing will be an important tool to improve the visualquality of such interaction techniques. In Figure 8(color plate), second row, we demonstrate that V-Objects can be used to realize this kind of visualiza-tion. Although we support only affine transforma-tions currently, we are confident that we can extentour concept to more complex deformations in thefuture. One the other hand V-Objects can be used toindicate the positions of displaced structures. Mul-tiple V-Objects can be assigned to the same struc-ture in the data, only one of these V-Objects is de-formed, the other objects remain in place to indicatethe original position in space. Transparency is espe-cially useful to indicate the position while not hid-ing surrounding important information. In Figure 8(color plate), third row, we show an example of suchan application of V-Objects. The images representstills of an animation we made. In the animationyou can see, for example, that a kidney is relocatedto the left to reveal an occluded tumor. Other inter-esting features are shown, such as transfer functionfading, moving, and object specific cutting planes.

4.2 Time Varying Data

Visualization of time varying volume data is a verycomplex task. Animations due to their dynamic na-ture often do not allow an in depth analysis of cer-tain data characteristics. Static images on the otherhand, often suffer from cluttering when many time-steps are visualized. Therefore, it has been pro-posed to apply more advanced projection and map-ping techniques to aid the understanding of suchdata. For example, Woodring at al. [16] applyhyper-slicing to a 4D dataset. The flexibility of V-Objects allows to use a variety of different map-pings by combining transfer functions and varyingthe spatial arrangement of objects. We show an ex-ample of a time varying data set, see Figure 8 (colorplate), fourth row. It is a electrocardiogram trig-gered CT scan of beating heart. Time is mapped to

color and opacity. This type of visualization allowsthe three dimensional examination of several timesteps simultaneously. The fanning in time allows toconvey similarities and differences in the progressof time. Furthermore, a topological relationship be-tween different time steps is visualized. In general,V-objects support the explorations of useful layoutsand mappings. In the future, we therefore seek tofurther investigate the application of multi-volumerendering to 4D data visualization.

4.3 Multi-Modal Imaging

Multi-modal imaging is a method for combiningdisparate sets of 3D imaging data that containcomplementary information on overlapping lengthscales. In medicine, for instance, morphologicalmodalities are combined with functional modalitiesin order to increase the information content of theresulting image. The concept of V-Objects inher-ently includes the ability to perform multi-modal vi-sualization of registered data sets. In Figure 8 (colorplate), first row, image (d) we show an example ofa combination of computed tomography (CT) andpositron emission tomography (PET). While the CTmethod supplies high precision, it is difficult to dis-tinguish between tumors and healthy tissue. PET,on the other hand, is a functionally oriented methodthat allows to identify tumors, but only provideslower resolutions.

5 Conclusion and Future Work

We presented V-Objects, a concept of modellingscenes consisting of multiple volumetric objects.We have shown that an efficient volume rendererbased on a brick-wise traversal scheme can be ex-tended to handle scenes comprised of multiple pos-sibly intersecting V-Objects. As regions of inter-section typically do not cover all the objects, weachieve significant performance gains by identify-ing mono-volume regions and performing efficientbrick-wise traversal of these regions. The advan-tage of our approach is that it allows to efficientlyrender multiple intersecting volumetric objects di-rectly from their grid representation. Multi-volumerendering is a promising technique for visualizingmedical data. We showed three examples for its ap-plication: browsing, time varying data, and multi-modal imaging. Each of them emphasized that the

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concept of V-Objects can provide advanced meansto explore and investigate data. In the future, wewill further investigate the topic of multi-volumevisualization as we believe it has great potential toimprove medical applications.

The animation sequences described in this paperand additional material are available at:http://www.cg.tuwien.ac.at/research/vis/adapt/2004vobjects

6 Acknowledgements

The work presented in this publication hasbeen funded by theADAPT project (FFF-804544). ADAPT is supported by TianiMedgraph, Vienna (http://www.tiani.com),and the Forschungsforderungsfonds furdie gewerbliche Wirtschaft, Austria. Seehttp://www.cg.tuwien.ac.at/research/vis/adaptfor further information on this project. Theused data sets are courtesy of AKH Vienna andUniv.-Klinikum Freiburg.

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(a) (b) (c) (d)

Figure 8: First row: (a) Transfer function example. (b) Segmentation example. (c) Clipping example. (d)Fusion of CT and PET scan based on V-Objects. Second row: Stills of animation to illustrate advancedbrowsing of volumetric data based on V-Objects. Virtual dissection of the human skull, uncovering thenervous and vascular system. Third row: Stills of animation to illustrate advanced browsing of volumetricdata based on V-Objects. Enhancing anatomical features by spatial displacement. Fourth row: Stills ofanimation to illustrate 4D visualization based on V-Objects. Fanning in time allows to convey similaritiesand differences in the progress of time.

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