Flexible GPU-Based Multi-Volume Ray-Casting

Ralph Brecheisen, Anna Vilanova i Bartroli, Bram Platel, Bart ter Haar Romeny

Technical University of EindhovenEmail: {r.brecheisen,a.vilanova,b.platel,b.m.terhaarromeny}@tue.nl

Abstract

Using combinations of different volumetric datasetsis becoming more common in scientific applica-tions, especially medical environments such as neu-rosurgery where multiple imaging modalities are re-quired to provide insight to both anatomical andfunctional structures in the brain. Such data setsare usually in different orientations and have differ-ent resolutions. Furthermore, it is often interesting,e.g. for surgical planning or intraoperative appli-cations to add the visualization of foreign objects(e.g., surgical tools, reference grids, 3D measure-ment widgets). We propose a flexible frameworkbased on GPU-accelerated ray-casting and depthpeeling, that allows volume rendering of multi-ple, arbitrarily positioned volumes intersected withopaque or translucent geometric objects. These ob-jects can also be used as convex or concave clippingshapes. We consider the main contribution of ourwork to be the flexible combination of the above-mentioned features in a single framework. As such,it can serve as a basis for neurosurgery applicationsbut also for other fields where multi-volume render-ing is important.

1 Introduction

The acquisition of multiple volumetric datasetsbased on data measurements or simulations isbecoming more common in modern scientificapplications. This is especially apparent in medicalenvironments. Modern hospitals nowadays havea wide range of 3D imaging modalities at theirdisposal. For example, in neurosurgery of thebrain, it is not possible to visualize all structuresof interest using only a single imaging modality.Multiple modalities have to be combined to viewboth anatomical structures and functional areas.Relevant modalities in this case are ComputedTomography (CT), Magnetic Resonance Imaging

(MRI), functional Magnetic Resonance Imaging(fMRI) and Diffusion Tensor Imaging (DTI). Itis also interesting to combine the volume datawith foreign objects that can only be representedwith geometric primitives. For neurosurgeryapplications one can think of virtual surgicaltools, reference grids, 3D measurement widgetsor streamlines to visualize Diffusion Tensor Imag-ing data. To avoid cluttering and occlusion ofunderlying volume data it is useful to be able torender these geometric objects semi-transparently.Furthermore, to explore hidden structures in thevolumetric data both semi-transparency, usingopacity transfer functions, and surface-based clip-ping should be available. For example, a complexand possibly concave clipping shape could be usedfor virtual resection or an extracted surface modelof the brain could be used as a clipping shape.Different datasets acquired for the same patientoften have different resolutions. Also their coordi-nate systems are not always exactly aligned whichrequires them to be registered. To visualize alldatasets simultaneously a common approach is toresample them onto a common grid such that theyall share the same coordinate frame. This allowseasier sampling but also reduces the image qualitydue to double interpolations. Low-resolutiondatasets may need to be inflated thereby increasingmemory consumption. This can become an issuein intraoperative navigation where the difference inresolution between preoperative and intraoperativeimages can be large. For this reason, we believethat resampling should be avoided.Several multi-volume rendering frameworks exist,however to our knowledge none of these imple-mentations fulfill all the points specified above.Especially, thecombination of multiple volumeswith transparent geometry and concave clippingis not supported by any existing framework. Forthis reason, we propose a GPU-based multi-volumeray-casting framework with the goal of being

VMV 2008 O. Deussen, D. Keim, D. Saupe (Editors)

as flexible as possible with respect to the pointsspecified above, that is, allowing independent,volume-local sampling of multiple volumetricdatasets possibly intersected with opaque ortranslucent geometric shapes and convex or con-cave clipping shapes. Registration of the datasetsis assumed as a pre-processing step that gives usthe coordinate transformations needed to positionvolumes and geometry in space.

The outline of this paper is as follows: Section 2discusses related work in the field of multi-volumerendering. In Section 3 we explain the conceptsof our multi-volume depth peeling algorithm, vol-ume/geometry intersections, different options forrendering intersection regions and depth-based clip-ping. In Section 4 we illustrate how our multi-volume rendering framework could benefit the plan-ning of brain tumor resections. In this Section wealso discuss memory and performance issues. Fi-nally, we end with conclusions and future work inSection 5.

2 Related Work

Several implementations for multi-volume render-ing have been proposed in the past. Due to thecomputational complexity of rendering multiplevolumes, software-based methods require advancedacceleration techniques such as using segmentationinformation [22] and efficient memory addressingand multi-threading [17]. Without such tech-niques software-based multi-volume rendering isrestricted either to non-intersecting volumes [4] ornon-interactive, static images [34, 23].With the advent of harware acceleration andprogrammable GPU’s interactive and high-qualitymulti-volume rendering has become much morefeasible. Hadwiger et al. [13] propose a two-levelvolume rendering method that allows differentparts of the dataset to be visualized with differentrendering modes such as MIP, DVR and isosurface.However, they do not explicitly support multiplevolumes or intersecting geometry.As mentioned in the introduction, we considerthe combination of volume data with geometricshapes to be an important feature of a multi-volume rendering framework. However, mostmulti-volume rendering frameworks do not supportthis [8, 24, 9, 16, 19]. Those that do, are mostly

limited to convex, opaque geometry [10, 7, 6].Translucent geometry intersections are reported byLevoy [2] and Kreeger et al. [5]. However, theray tracing framework proposed by Levoy onlyproduces still images. Kreeger et al. mention thatthey support multiple volumes with translucentgeometry, however they discuss only the single-volume case. Futhermore, their implementationrequires a specialized hardware architecture.In our algorithm we use depth peeling [33] incombination with GPU-accelerated ray-casting[29, 27] to allow flexible volume/geometry in-tersections. A similar approach has been usedby others [14, 11, 35, 30] although these imple-mentations are restricted to single-volume scenes.Borland et al. [30] propose a technique calledvolumetric depth peeling, however it is not relatedin any way to depth peeling as an algorithm fordepth-sorting translucent polygons. It does imposea layered structure on the volume data by restartingray-casting after some threshold is reached, but thisis a purely volumetric technique with no supportfor intersecting geometry.One of the most challenging issues in multi-volumerendering is how to deal with overlapping materials(or tissues). This remains a largely unsolvedquestion but several implementations exist thatoffer a range of mixing strategies at different levelsin the rendering pipeline. They are either basedon opacity-weighted mixing [3, 20, 21, 19, 24],successively applying compositing on each sample(in some order) [10, 17] or other operators such asminimum, maximum, negative, sum, product andblend [9].Most implementations simplify sampling bymapping all volumes onto a common coordinateframe [6, 16, 10, 15]. However, if volumes arenot axis-aligned and only partially overlappingthen this requires resampling. This introducesnumerical inaccuracies and may also increasememory consumption significantly if resolutionsdiffer greatly. Only a few implementations sampleeach volume locally within its own coordinateframe [17, 4, 8, 9], however neither of these supportvolume/geometry intersections or complex clippingshapes.Finally, many existing methods for multi-volumerendering were proposed with a clear applicationin mind such as seismic data exploration [9]. Inthe medical area, Beyer et al. [10] propose a

framework for planning key-hole neurosurgery.Hardenbergh et al. [6] added DTI fiber geometryto an already existing functional MRI visualizationsystem. However, they do not support translucentgeometry or complex clipping shapes. Koehn etal. [26] present a system for neurosurgery planningthat has features very similar to ours. However,they do not support multi-volume rendering at thesampling level. They can combine multiple volumerenderers and mix their outputs at the image-level.

Much work has been done for multi-volume ren-dering. However, we conclude that most frame-works do not have the flexibility to combine mul-tiple volumes in arbitrary orientations without re-sampling or deal with intersecting geometric shapesand clipping. We believe that this is especiallyneeded in neurosurgery applications. We intendto offer this flexibility by using (1) GPU ray-casting, which allows interactive, high-quality ren-dering and perspective projections, and (2) depthpeeling, which allows a natural integration betweenvolumes, opaque or translucent geometric surfaces(e.g. for visualizing surgical tools) and complexclipping combinations (e.g. for virtual resection).

3 Method Overview

Sampling multiple volumes independently in a sin-gle rendering pass is problematic, especially if thevolumes are intersected by arbitary and possiblytranslucent or concave geometric surfaces. To cor-rectly include the geometry colors and opacities inthe volume compositing along each ray, intersectioncalculations would have to be performed at eachsample step for all possible surfaces. Computa-tionally this is not feasible in real-time, especiallyfor more complex object shapes. For this reason,we propose a multi-pass approach where we ren-der the scene in separate layers usingdepth peel-ing [33]. This subdivides the scene into regionswhere sampling conditions do not change and weonly have to determine our sampling position withrespect to each volume at the beginning of such aregion. As we will describe later, surface geometryrequires no special intersection calculations. Fig-ure 1 gives a high-level overview of our algorithmand the functional steps performed during asingleiteration of the algorithm. Rendering the completevolume/geometry scene consists of repeatedly exe-

cuting these steps for each iteration after which thefinal result is rendered to screen.

Figure 1: Overview of the algorithm subdividedover two fragment shaders, one for depth peeling(shader 1) and one for ray-casting (shader 2). Illus-trated are the different functional steps taken duringa single iteration of the algorithm.

In short, our algorithm alternates depth peeling witha ray-casting pass until all depth layers of the vol-ume/geometry scene have been processed. The useof depth peeling and ray-casting is not new in itself[14, 11, 35]. However, their application to multiplevolumes intersected by translucent geometry andconcave clipping shapes is novel and our main con-tribution. In the following subsections we explainour multi-volume ray-casting algorithm in more de-tail.

3.1 Depth Peeling

Depth peeling is a well-known technique for view-independently depth sorting a collection of poly-gon surfaces and originally used for renderingtranslucent polygons correctly. It is a multi-pass, fragment-level technique that was initially de-scribed by Mammen [12] and Diefenbach et al. [25]and implemented by Everitt [33] using hardware-accelerated shadow mapping. Depth peeling can beapplied to any scene consisting of polygon surfaces.This means it can also be applied to GPU-basedray-casting because it is initiated by rasterizing thefront faces of a geometric bounding box. If we havemultiple, partially overlapping volumes, rasterizingtheir bounding boxes while performing depth peel-

ing over multiple passes will sequentially give usaccess to the fragments of each volume’s bound-ary. This is precisely what we need for efficientlycomputing sample positions with respect to eachvolume. To implement depth peeling for multi-volume ray-casting we use an approach that is simi-lar to the algorithm proposed by Everitt [33]. How-ever, he uses a shadow mapping technique that re-lies on relatively slow and obsolete buffer-to-texturecopies. We use the OpenGL Framebuffer extensionand programmable fragment shaders to extract thedifferent depth layers and store them directly in a setof high-precision depth textures without the needfor expensive copy operations.

3.2 Multi-Volume Ray-Casting

Our multi-volume ray-casting algorithm starts byrendering the front-most faces of the scene andstoring the fragment depths and colors in offscreenbuffersDnear andCnear. This is illustrated in Figure2A. In the second pass the scene is rasterized againexcept now a fragment shader is activated, withDnear as input parameter, that compares the raster-ized fragment depths to the corresponding depthvalue in bufferDnear. If, for a given fragment, itsdepth isless or equal to the Dnear value then thefragment is discarded. Since depth test LESS isstill applied, this will result in the second-nearestfragments being stored in a second set of offscreenbuffersD f ar andC f ar. This is illustrated in Figure2B.

After depth peeling the first two depth layers,stored inDnear andD f ar, we initiate a ray-castingpass by rasterizing the scene again with a depthtest EQUAL. The depth test only passes fragmentsthat have a depth equal to those inDnear. For thesefragments a second fragment shader is activated,with Dnear, D f ar and color bufferCnear as inputparameters. This fragment shader performs directvolume ray-casting starting at the layer correspond-ing toDnear and stopping at the layer correspondingto D f ar. The composited color and opacity arewritten to an offscreen accumulation bufferCaccwhich is updated and passed as an input parameterto the next ray-casting pass.

Sampling corrections: When doing ray-casting ina multi-volume scene, special care should be takento preserve equidistant step sizes as we cross vol-

ume boundaries from one iteration to the next. Thedistance between two depth layers will almost neverbe an exact multiple of the ray step size.

A

B

C

Figure 2: (A) Use depth test LESS to extract firstdepth layer and store in textureDnear. (B) Peelaway first depth layer by using fragment shader todiscard fragments with depth equal toDnear, thenuse depth test LESS again to extract second depthlayer and store in textureD f ar. (C) GPU ray-castingis started at the fragments corresponding toDnear.A depth test EQUAL is used to select these frag-ments. The output of the ray-casting shader is writ-ten to the color accumulation bufferCacc.

Therefore, to preserve equidistant steps along theray through all volumes we need to add a slightoffset ∆d at the beginning of each region (exceptthe first). This offset is computed in the previous

pass.

Intersecting geometry: Due to our depth peelingapproach it is relatively easy to implement intersec-tions with geometry because it is depth-peeled justlike any other layer. We store the color and opac-ity of each layer inCnear so it is straightforward toinclude this color and opacity in the compositingequation before we do ray-casting for any given re-gion. In this way, geometry is naturally taken intoaccount. Whether the geometry is opaque or semi-transparent makes no difference.

3.3 Volume Entry/Exit States

To keep track of which volumes the viewing rayenters and exits in a flexible way, we introducea scheme to maintain a list of bitflags, one flagfor each volume, that is toggled each time wepass a volume’s boundary. A similar approachto store state variables across multiple renderingpasses is used by Beyer et al. [10]. While theyuse a 1D lookup texture to keep track of which(anatomical) objects map to which volume ID, weuse a 2D texture to store a list of bitflagsfor eachviewing ray or pixel. It is illustated in Figure 3. Allbitflags are initialized to zero at the beginning ofray traversal. Each volume has an associated indexwhich is used to retrieve the corresponding bitflagfrom the list. To implement this feature, we usean additional, screen-sized texture, which we callthe objectInfo texture, that is queried and updatedin each ray-casting pass. Each texture elementcontains a floating-point value that encodes thelist of bitflags. Encoding and decoding of bitflagsas floating-point values is done using themodulooperator. IfEi is the bitflag value for volumeVi,T is the floating-point texture value to be decodedandN is the number of volumes then we have,

Ei = mod

(

T2i ,2

)

,0≤ i < N (1)

Given a volume indexi and bitflag valueEi we cantoggle the bitflag, without using IF-statements, asfollows,

Ei = mod(Ei +1,2) (2)

Finally, re-encoding the bitflags into the floating-

point value is done as follows,

T =N

∑i=0

2i·Ei (3)

Figure 3: Bitflag values for traversing two volumes(least significant bit on the right, only 2 out of 4bitflags used). The indices (0,1,2,3) refer to the vol-ume index.

3.4 Depth-based Clipping of Selected Vol-umes

Volume clipping is an essential part of any 3D view-ing toolbox because it helps to reduce clutteringwhen a lot of information has to be visualized. Also,if the sample values of an object differ only slightlyfrom the objects occluding it, it will be difficult toexpose it using a basic opacity transfer function. Inthat case, clipping becomes the only way to showthe object by cutting away the occluding data.In our multi-volume rendering algorithm we offersupport for depth-based clipping. We keep track ofclipping states in a similar manner as for volumesexcept we do not use ’entry/exit’ (1/0) bitflags butsimply ’clip/no-clip’ (1/0) bitflags. These bitflagsare encoded in a second channel of theobjectInfotexture which we introduced for the volume bitflags.Depending on the clipping mode, volumeprobingor volumecutting [11], theobjectInfo texture is ini-tialized with ’1’ or ’0’ respectively. This is illus-trated in Figure 4.Using these volume and clipping bitflags we canquickly determine for each volume whether to ren-der it or not in a given region. We are able to handleall the different combinations of volumes, clippingshapes and clipping modes (probing or cutting) in a

Figure 4: Clipping modes: volume cutting (left) re-quires clip object bitflag to start with ’0’, volumeprobing (right) requires bitflag to start with ’1’.

flexible way without using multiple IF-statements.For this, we precompute a 2D lookup table to con-tain this logic. The integer-encoded volume andclipping bitflags are used as lookup indices. Theoutput of the table is another integer-encoded bit-flag list which specifies for each volume whether torender it or not. Figure 5 shows an example sce-nario consisting of two volumes and a single clip-ping shape set forvolume cutting on volume 0 only.

Figure 5: ExampleclipInfo lookup table for a sceneconsisting of two volumes and one clipping shapeset for volume cutting. PointP is associated withvolume bitflags ’0011’ and clip bitflags ’0001’. Per-forming lookup in table results in ’0010’ mean-ing volume 1 should be rendered, while volume 0should not be rendered.

3.5 Data Intermixing

One of the most challenging aspects of multi-volume rendering is to decide how to render over-lapping volume regions. The difficulty lies not somuch in finding different mixing schemes, as indeciding which schemes result inuseful visualiza-tions. In our algorithm we limit ourselves to of-fering a number of data mixing options withoutproposing to solve the general problem. GivenNvolumes inside an intersection, the options we offerare:

• Priority selection: Select one volume for ren-dering based on apriority ID.

• Opacity-weighted average: Apply transferfunction classification and shading to each vol-ume sample, pre-multiply the colors with theirassociated opacity and compute the averagecolor.

• 2D intersection transfer function: Apply a 2Dtransfer function to the intersection between atmost two volumes.

• Intersection color: Apply a single color andopacity to the intersection region. This can beused for visual collision detection.

Figure 6 illustrates these mixing schemes. We ap-plied them to four abstract cube datasets to clearlyconvey the difference between each scheme. The2D intersection transfer function takes gray valuesfrom two volumes and returns a color and opacity.In the example, the 2D transfer function returns ayellow color wherever two volume samples haveequal value (+/- an offset). We limit ourselves to 1Dand 2D transfer functions, however the algorithmcould easily be extended to 3D if memory availabil-ity allows it. Note that it is far from trivial to definehigh-dimensional transfer functions [7].

4 Results and Discussion

Our multi-volume rendering algorithm can be usedfor any application that involves multiple volumet-ric datasets possibly intersected with geometric sur-faces. However, our work was mainly motivated bymedical applications that require visualization of in-formation from many different imaging modalitiesand where resolutions may differ significantly be-tween datasets. Tumor resection planning in neu-rosurgery is such an application where the surgeonneeds to visualize general anatomical context, suchas the brain, and specific focus objects such as tu-

A B

C D

Figure 6: Different intermixing schemes: (A) pri-ority selection where volume 1 has priority, (B)opacity-weighted average, (C) intersection color(magenta) and (D) 2D intersection transfer functionwhich highlights regions where sample values areequal (+/- an offset).

mor, cortical activations, fiber tracts and surgicaltools. Figure 7 illustrates what this could looklike using our framework. In this example, differ-ent representations are chosen for different objects.The DTI fiber tracts are represented as stream tubes(128×128×52, 16 directions) while the tumor andcortical activations are volume data.Figure 8 shows an example of a CT datasetwith one clipping shape used for simulating anaccess hole in the skull through which a virtualsurgical tool is inserted. Another clipping shapeis used to offer a free view of the access holefrom an alternative viewing direction. Figure 9illustrates an example of a concave surface modelof the brain used as a complex clipping shape toextract the brain as a volume representation. Theperformance and memory requirements of thesescenarios are discussed in the following paragraphs.

Performance: In most scenarios our algorithmruns at interactive framerates (NVIDIA GeForce8800 GTX, 512×512 window, 1mm stepsize). De-pending on scene complexity however frameratesmay drop significantly. For example, the CT dataset

Figure 7: Multimodal view of head, tumor (T1-weighted MRI), cortical activations (fMRI) andfiber tracts (DTI). Brain, tumor and activations areall separate volumes. DTI fiber tracts are visualizedas stream tubes.

in Figure 8 renders at 12.6 fps which includes a256×256×225 CT dataset, a 64×64×64 tumordataset and two clipping shapes. The MRI datasetin Figure 7 renders at 2.5 fps and includes a256×256×200 MRI dataset, a 64×64×64 tumordataset, a 64× 64× 64 fMRI dataset, DTI fibersas streamtubes, a surgical tool and a clipping box.This is the most complex scenario we rendered.The MRI dataset in Figure 9 runs at 2.8 fps. andincludes the 256× 256× 200 MRI dataset and aconcave brain model consisting of around 450Kpolygons. As can be seen the flexibility of ourframework comes at a cost. The performance dropswhen the number of depth layers increases becauseeach depth layers is associated with an additionalray-casting pass.

Memory consumption: Our algorithm requiresall volumes to fit inside GPU texture memory. Thismeans that there is a physical limit to the numberand dimensions of volumes that can be simultane-ously visualized. However, due to our volume-localsampling scheme there is no need for inflating lowresolution datasets. This keeps memory consump-tion at acceptable levels. If 8-bit datasets are used,the multi-volume scenario of Figure 7 requires only15.4 MBytes (1 x 13Mb for head, 1 x 0.2Mb for tu-

Figure 8: Multiple clipping shapes applied to a CTskull. The larger clipping shape allows an alterna-tive view on the access hole with virtual tool.

mor, 1 x 0.2Mb for fMRI). For 16-bit datasets thiswould be twice as much but still well within the lim-its of GPU memory (768 MBytes).

5 Conclusions and Future Work

Our multi-volume depth peeling algorithm offers aflexible way to visualize multiple, partially overlap-ping volumes intersected with an arbitrary numberof opaque or translucent geometric shapes. Vol-umes are sampled locally in their native resolutionwhich keeps memory requirements to a minimum.Together with support for multiple, convex orconcave clipping shapes this makes our frameworkespecially suitable for neurosurgery applicationswhere volumetric datasets of differing resolutionsoften need to be combined with geometric dataderived from DTI fiber tracking or additionalsurface models. We also offer several options forrendering the intersection between two or morevolumes.

Figure 9: Top: semi-transparent geometric modelof brain combined with tumor and f-MRI data. Bot-tom left: geometric brain model embedded in MRIdataset. Bottom right: brain model used as con-cave clipping shape to clip away surrounding tissuethereby resulting in a volumetric representation ofthe brain based on MRI data.

A number of points remain that need to be ad-dressed in the near future. First, performancecould be improved by incorporating empty-spaceskipping techniques and using the depth peelingalgorithm only when necessary. Most importantlyhowever, we wish to implement a neurosurgicalplanning and navigation tool based on this frame-work and evaluate its usability in a clinical setting.

References

[1] H. Hauser, L. Mroz, G.I. Bischi, M.E.Groeller. Two-Level Volume Rendering.IEEETransactions on Visualization and ComputerGraphics, 7(3), 242–252, 2001.

[2] M. Levoy. A Hybrid Ray Tracer for RenderingPolygon and Volume Data.IEEE ComputerGraphics and Applications, 2(4):33–40, 1990.

[3] W. Cai, G. Sakas. Data Intermixing and Multi-Volume Rendering.Computer Graphics Fo-rum, 1999

[4] A. Leu, M. Chen. Modeling and RenderingGraphics Scenes Composed of Multiple Vol-umetric Datasets.Computer Graphics Forum,159–171, 1999.

[5] K.A. Kreeger, A.E. Kaufman, MixingTranslucent Polygons with Volumes.IEEETransactions on Visualization and ComputerGraphics, 191–198, 1999.

[6] J. Hardenbergh, B.R. Buchbinder, S.A.M.Thurston. Integrated 3D Visualization offMRI and DTI Tractography.IEEE Transac-tions on Visualization and Computer Graph-ics, 2005.

[7] S. Bruckner, E. Groeller. VolumeShop: An In-teractive System for Direct Volume Illustation.IEEE Transactions on Visualization and Com-puter Graphics, 671–678, 2005.

[8] S. Bruckner, E. Groeller. Exploded Views forVolume Data.IEEE Transactions on Visual-ization and Computer Graphics, 2006.

[9] J. Plate, T. HoltKaemper, B. Froehlich. AFlexible Multi-Volume Shader Frameworkfor Arbitrarily Intersecting Multi-ResolutionDatasets.IEEE Transactions on Visualizationand Computer Graphics, 2007.

[10] J. Beyer, M. Hadwiger, S. Wolfsberger, K.Buehler. High-Quality Multimodal VolumeRendering for Preoperative Planning of Neu-rosurgical Interventions.IEEE Transactionson Visualization and Computer Graphics,2007.

[11] D. Weiskopf, K. Engel, T. Ertl. InteractiveClipping Techniques for Volume Visualizationand Volume Shading.IEEE Transactions onVisualization and Computer Graphics, 2003.

[12] A. Mammen. Transparency and Antialias-ing Algorithms Implemented with the Vir-tual Pixel Maps Technique.IEEE ComputerGraphics Applications, 43–55, 1989.

[13] M. Hadwiger, C. Berger, H. Hauser. High-Quality Two-Level Volume Rendering of Seg-mented Data Sets on Consumer GraphicsHardware. Proceedings of IEEE Visualiza-tion,, 2003

[14] M.A. Termeer, J. Olivan Bescos, A.C. Telea.Preserving Sharp Edges with Volume Clip-ping. In Proceedings of Visualization, Model-

ing and Vision,, 2006.[15] T. Schafhitzel, F. Roessler. Simultaneous Vi-

sualization of Anatomical and Functional 3DData by Combining Volume Rendering andFlow Visualization. InSPIE Medical Imaging2007, 2007.

[16] F. Roessler, E. Tejada, T. Fangmeier, T. Ertl.GPU-based Multi-Volume Rendering for theVisualization of Functional Brain Images. InProceedings of SimVis, 315–318, 2006.

[17] S. Grimm, S. Bruckner, A. Kanitsar, E.Groeller. Flexible Direct Multi-Volume Ren-dering in Interactive Scenes. InVision, Mod-eling, and Visualization, 386–379, 2004.

[18] T. Hendler, P. Pianka, M. Sigal, M. Kafri.Two are Better Than One: Combining fMRIand DTI-based Fiber Tracking for EffectivePre-Surgical Mapping. InProceedings of In-ternational Society for Magnetic ResonanceMedicine, 2003.

[19] B. Wilson, E. Lum, K. Ma. Interactive Multi-Volume Visualization. InWorkshop on Com-puter Graphics and Geometric Modeling,2002.

[20] M. Ferre, A. Puig, D. Tost. Rendering Tech-niques for Multimodal Data. InProc. SIACG2002 1st Ibero-American Symposium on Com-puter Graphics, 305–313, 2002.

[21] I. Manssour, S. Furuie, L. Nedel. A Frame-work to Visualize and Interact with Multi-modal Medical Images. InVolume Graphics,385–398, 2001.

[22] K.J. Zuiderveld, M.A. Viergever. Multi-modalVolume Visualization using Object-OrientedMethods. InProceedings of the 1994 sympo-sium on volume visualization, 59–66, 1994.

[23] D.R. Nadeau. Volume Scene Graphs. InPro-ceedings of the IEEE Symposium on Volumevisualization, 49–56, 2000.

[24] A. Ghosh, P. Prabhu, A.E. Kaufman, K.Mueller. Hardware Assisted MultichannelVolume Rendering. InProceedings of Com-puter Graphics International, 2003.

[25] P.J. Diefenbach, N.I. Badler. Multi-passPipeline Rendering: Realism for Dynamic En-vironments. InProceedings of the Symposiumon Interactive 3D Graphics, 59–ff, 1997.

[26] A. Koehn, F. Weiler, J. Klein, O. Konrad,H.K. Hahn, H.-O. Peitgen. State-of-the-ArtComputer Graphics in Neurosurgical Planning

and Risk Assessment. InProceedings of Euro-graphics, 2007.

[27] S. Stegmaier, M. Strengert, T. Klein, T.Ertl. A Simple and Flexible Volume Render-ing Framework for Graphics-Hardware-basedRaycasting. InProceedings of Volume Graph-ics, 2005.

[28] R. Westermann, T. Ertl. Efficiently UsingGraphics Hardware in Volume Rendering Ap-plications. In Proceedings of the 25th SIG-GRAPH, 1998.

[29] J. Krueger, R. Westermann. AccelerationTechniques for GPU-based Volume Render-ing. In Proceedings of IEEE Visualization,2003.

[30] D. Borland, J.P. Clarke, J.R. Fielding, R.M.Taylor II. Volumetric Depth Peeling for Medi-cal Image Display. InProceedings of SPIE Vi-sualization and Data Analysis, 2006.

[31] K. Engel, M. Hadwiger, C. Rezk-Salama, J.M.Kniss.Real-Time Volume Graphics. A.K. Pe-ters, 2006.

[32] B. Preim, D. Bartz.Visualization in Medicine.Morgan Kaufmann Publishers, 2007.

[33] C. Everitt. Interactive Order-IndependentTransparency. Technical report NVIDIAOpenGL applications engineering, 2001.

[34] A. Koenig, H. Doleisch, E. Groeller. Multi-ple Views and Magic Mirrors - fMRI Visual-ization of the Human Brain.Technical reportVienna university of technology, institute ofcompute graphics, 1998.

[35] K. Eide. GPU-Based Transparent PolygonalGeometry in Volume Rendering.Technical re-port Norwegian University of Science andTechnology, 2005.