Online Submission ID: 1180

Scatterplot Matrix Navigation for MultivariateTransfer Function Sculpting

Category: Research

Fig. 1. Transfer function sculpting through a scatterdice interface on the bluntfin dataset.

Abstract — Multi-dimensional transfer functions are often employed as a means of separating and visualizing features in volumetricdata. Unfortunately, the difficulty associated with the creation of such transfer functions is proportional to the dimensionality. As suchcurrent transfer function design widgets typically restrict the user to interacting in a two-dimensional scatterplot. The two dimensionsare typically static, allowing for exploration of only a subset of the feature space. While such transfer function design tools have provento be useful in the interactive extraction and rendering of volumetric features, a more advanced interface is needed to effectively createhigher dimensional transfer functions. In order to overcome these issues, our work focuses on the use of a scatterdice interface fortransfer function design. The scatterdice interface allows users to interactively explore the multi-dimensional feature space of avolume and sculpt transfer functions across dimensions. Our system provides users with a scatterplot matrix view of all possibledimensional combinations for transfer function manipulation. Linked brushing and selection are used to define a volume renderingtransfer function in any scatterplot within the matrix, and users can iteratively build transfer functions using bounding volumes in thefeature space, sculpting the transfer function from different viewpoints and refining it across n-dimensions. Our results illustrate howsuch an interface can provide a more comprehensive understanding of the multi-dimensional feature space and aid in the generationof complex, n-dimensional transfer functions for better visualization, analysis and feature highlighting.

Index Terms —Scatterplot matrix, feature space, transfer function, volume rendering.

1 INTRODUCTION

Multi-dimensional transfer functions have long been established as apowerful means for interacting with volumetric data [10, 12, 14, 19].However, efficiently designing transfer functions has turned out to bea non-trivial problem. Typically, multi-dimensional transfer functionsare shown as a two-dimensional (2D) scatterplot, the axes ofwhichrepresent two variables of the feature space of the data. Users interactin this space, assigning optical properties (color and opacity) to thevoxel data. The volume is then rendered based on these optical prop-erties. In this dual-domain interaction (volume data spaceand transferfunction feature space), users are able to select data properties in thefeature space and see the resultant rendering in the volume space. Thisinteraction improves the user’s ability to understand how the featurespace of the data is reflected in the volumetric data.

While such a method works well when the feature space consistsof only a few dimensions (e.g., CT and MRI data), the extraction andvisualization of features within a high dimensional feature space (e.g.,flow data) is a far more complex problem. Basically, a fundamen-tal drawback of transfer function based methods is that the mappingfrom the domain of the 2D feature space to the volume space is injec-tive, meaning that the separation of features with the same statisticalproperties (within a single feature space view) is impossible in current2D transfer function widgets. Some research (e.g., [12, 22]) has beenperformed on exploring and understanding high dimensionalfeaturespace through the use of a complex multi-dimensional transfer func-tion widgets. However, interacting with and understandingthe links

between high-dimensional transfer functions, the featurespace, andthe resultant volume rendering is difficult. To overcome these difficul-ties, our work expands the 2D scatterplot transfer functionspace to ascatterplot matrix [4] and incorporates the idea of a scatterdice nav-igaton interface [7] introduced by Elmqvist et al. for enhancing 2Dinformation visualization.

In this work, we adapt the scatterdice exploration scheme tointer-activen-dimensional transfer function creation, as shown in Figure 1.This allows us to maintain the simplicity and familiarity ofthe 2D scat-terplot transfer function interface, while increasing theamount of dataavailable for the user to use in refining the transfer function. In doingso, we are able to enhance a user’s understanding of the volume featurespace and allow the user to explore how interactions betweenfeaturesfound in one dimension affect those in another. Furthermore, this in-terface allows for transfer function sculpting acrossn-dimensions, al-lowing the user to refine their transfer function across the various fea-ture spaces. Finally, the dimensions in the transfer function space canbe reordered to highlight correlations amongst them, providing furtherinsight into the data relationships.

2 RELATED WORK

Interactive transfer function design has been addressed with manydifferent approaches, ranging from simple (yet intuitive)one-dimensional (1D) transfer functions (e.g., [8, 17]) in which a scalar

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Fig. 2. Our transfer function sculpting control widgets. 2D transfer functions are edited in the transfer function editing window and the datadistribution across all feature spaces based on the transfer function is updated in the scatterplot matrix. Users are able to refine the transferfunctions based on the selected logical operation and navigate through feature spaces from the scatterdice interface for the next transfer functionsculpting step. Final rendering results based on the n-dimensional transfer functions can be seen in the 3D rendering window.

data value is mapped to color and opacity, to more complex multi-dimensional transfer functions in which color and opacity are mappedacross multiple variables. Early work by Kindlmann et al. [10] andKniss et al. [12] demonstrated the usefulness of a multivariate transferfunction as a means for extracting boundary regions betweenmaterial.This work used a 2D scatterplot consisting of density versusdensitygradient magnitude and three-dimensional (3D) transfer functions forfurther delineating boundaries of volumetric features, and identifiedkey problems in transfer function design, noting that many interactivetransfer function widgets lack information to guide users to appropri-ate selections, making the creation of an appropriate transfer functionessentially a process of trial and error.

Other works on transfer function design have proposed higher-dimensional transfer functions based on mathematical properties ofthe volume. Continued work by Kindlmann et al. [11] employedtheuse of curvature information to enhance multi-dimensionaltransferfunctions. Tzeng et al. [22] focused on higher dimensional transferfunctions that use a voxel’s scalar value, gradient magnitude, neigh-borhood information and the voxel’s spatial location. Workon statisti-cally quantitative volume visualization by Kniss et al. [13] noted thatdata samples tend to be spatially correlated, and focused ona generalstatistical classification for feature extraction. Roettger et al. [20] fur-ther incorporated the spatial information of the volume to present anautomatic color selection to the user, and Lundstrom et al.[15] intro-duced theα-histogram to simplify transfer function design by amplify-ing data ranges corresponding to spatially coherent materials. Recentwork by Correa et al. introduced size based transfer functions [5] thatincorporates the magnitude of spatial extents of volume features intothe color and opacity channels, and visibility based transfer functions[6], where the opacity transfer function is modified to provide betterfeature visibility.

In all of these related works, one can note that various statisticalproperties of the volumes are being used in order to extract features ofinterest and segment properties of the volume, focusing on increasingthe dimensionality of the transfer function. Unfortunately, as the di-mensions get larger, interaction inn-dimensional space becomes cum-bersome to the point that few systems exceed two dimensionaltransferfunctions; instead, the extra dimensionality is incorporated automati-cally, somewhat limiting the user’s control. As such, the applicationof multivariate data exploration techniques has become more preva-lent. Recent work by Akiba et al. [1, 2] utilizes parallel coordinateplots [9] to create a volume rendering interface for temporal volumet-ric data. Our work also incorporates advanced information visualiza-tion techniques, focusing on creating ann-dimensional transfer func-tion through the use of interactions with 2D scatterplots, visualizingthe entirety of the volume feature space through the use of a scatterplotmatrix [4]. We utilize the scatterdice interface developedby Elmqvistet al. [7] allowing users to navigate from one 2D transfer function to

another, sculpting the overalln-dimensional transfer function as theynavigate and filter data across the range of feature space.

3 VOLUME RENDERING SCATTERDICE INTERFACE

The scatterplot is already a commonly adopted method for 2D trans-fer function generation, providing high visual clarity [21]. However,as shown in previous transfer function design work (e.g., [12, 20, 22]),the use of only two data dimensions in transfer function design is oftennot sufficient to extract data features. As such, our system adopts theuse of a scatterplot matrix [4] to display the entire data feature spaceto a user. By arranging multiple plots into a scatterplot matrix with thedata dimensions on the rows and columns and each cell representing anindividual scatterplot, we are able to describe the entire feature spaceof the volume in a series of images that users are familiar with (i.e., 2Dscatterplots). While this approach does lend overview and structure tothe exploration, the individual scatterplots in the matrixappear as aset of image thumbnails with no indication how data points distributebetween scatterplots when compared pair wise. In order to provide theuser with more information about the links between the different fea-ture space components, we have adopted the scatterdice [7] interactiveexploration techniques.

Our work utilizes the techniques developed by Elmqvist et al. [7] tosupport the structural visual exploration of multidimensional featurespace inherent within volumetric data. Instead of forcing the user tocreate and edit a transfer function within the confines of thecommon2D scatterplot, we create one scatterplot for each combination of di-mensions and arrange them in a large scatterplot matrix. This matrixserves as an overview of the volumetric feature space and defines avisual space for transfer function creation and navigation. Transitionfrom one scatterplot to the next is performed using 3D rotation, andwe provide transfer function creation tools as a set of sculpting opera-tions across each scatterplot. Given that the order of the columns androws within the scatterplot matrix can provide further context of therelationships between feature space dimensions, we provide tools forboth manual ordering as well as hierarchical ordering.

3.1 System DesignThe two main transfer function interaction components of our systemconsist of the current scatterplot and the scatterplot matrix. Thesecomponents provide users with a means of interacting withinthe vol-umetric feature space, assigning color and opacity to various proper-ties and exploring their relationship within the rendered volume. Fig-ure 2 shows our current interface for feature space exploration, transferfunction design and volume rendering. In this example, the user hassculpted ann-dimensional transfer function using the scatterplot ma-trix and created a volume rendering of the NASA X38 dataset (seeSection 4 for more details). Our system supports the comparison andcorrelation of feature space dimensions within a volumetric dataset,

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Online Submission ID: 1180

Fig. 3. Dimensional ordering and corresponding scatterplot matrixbased on (top) hierarchical scheme of spatial features versus raw datafeatures and (bottom) user defined feature scheme.

and the animated transitions provide consistency and enhanced seman-tic information when exploring between dimensions. Furthermore,the interactive nature of the scatterdice method and the familiarity ofthe 2D transfer function scatterplot allows users to explore and sculpttransfer functions acrossn-dimensional space while realizing data re-lationships.

The traditional 2D transfer function editor is shown in the middlewindow of Figure 2 with the scatterplot shown as the background. Thedata distribution based on previous sculpted transfer functions is high-lighted and can be used to guide current transfer function sculpting.The feature space of transfer function editing is now directly linkedwith the currently viewed cell in the scatterplot matrix (the rightmostwindow) together with the names and labels of the two displayed axes.Users may then interact with the selected feature space and edit a trans-fer function using box widgets of configurable color and opacity distri-butions in order to begin sculpting a transfer function. Thecoloring ofscatterplot points in one feature space is then automatically reflected inthe scatterplot matrix, allowing users to quickly see the relationshipsbetween other components. The created transfer function isthen ap-plied directly to the volume, displaying the rendered imagein the 3Drendering window. After finishing current transfer function editing,users can combine this transfer function with the previous sculptedtransfer function based on sculpting logic operations (seeSection 4) togenerate(i +1)-dimensional transfer functions, assuming the previoussculpted transfer function isi-dimesional.

Once the transfer function in the current feature space has beendefined, users may then interact with the scatterplot matrixwindowin order to navigate into the next feature space for transferfunctionsculpting. Navigation operations can be generated by usingthe ar-row keys on the keyboard to step through the adjacent cells until thedesired scatterplot cell is reached, or by double clicking the desiredscatterplot cell for automatic feature space transitions.Users can thenstart to edit transfer functions in the new feature space, asdescribed

above, for higher dimensional transfer functions.In addition to our data navigation options and transfer function edit-

ing widgets, we also allow users to probe specific points in the 2Dscatterplot in order to gain an understanding of how these points aredistributed across other feature spaces. Users are able to hover themouse over the interactive 2D scatterplot window and the correspond-ing points are then highlighted across the scatterplot matrix, therebyperforming data brushing [3]. Such interactions allow the user to seehow clusters of points in one feature space view are distributed acrossother views.

3.2 Dimensional Ordering

The scatterdice interface starts off as a 2D matrix, containing only theraw variables. Derived fields (e.g., value gradient magnitude) can beadded onto the scatterplot matrix through our interaface. However, theautomatically generated dimensional order may not reflect the users’interests in the dataset. Therefore, we provide the dimensional order-ing ability to allow users interactively arrange the feature spaces basedon their interests.

We provide two modes for the scatterplot matrix creation: hierar-chical and user-defined. In the hierarchical ordering scheme, we groupblocks of the scatterplot matrix into groups of properties:spatial data,raw measurements, and derived properties. The user may choose toview one group of properties versus another group, for example, spa-tial data versus raw data as shown in Figure 3 (top). Here, thefirstproperty set will become the column axis and the second becomesthe row axis. In the hierarchical mode, users are able to quickly seethe relationships between various properties, allowing for advanceddata exploration. In the user-defined mode, users may interactively re-order the dimensions of the scatterplot matrix. The order inwhich thedimensions are added/removed, determines the final ordering of thescatterplot matrix (i.e., the first feature will be the first row/column,etc.). Figure 3 (bottom) shows the order of feature spaces that reflectthe users’ interests of finding shocks in a flow dataset.

3.3 Animated Transitions

Once the feature space is defined, users may navigate betweenfeaturespace views within the scatterplot matrix by selecting the desired fea-ture space plot in the scatterplot matrix and double clicking. The 2Dtransfer function editor window is then treated to a series of anima-tions as the data space is navigated from the current space tothe newlyselected space. This navigation is restricted to orthogonal movementalong the same row or axis in the matrix, forcing one dimension in thetransfer function editor window to be preserved as the otherchanges.The change is done as an animated 3D rotation giving the user theability to correlate how points in one plot map to points in another.This is particularly efficient because the 3D rotation allows for inter-preting the motion of the points as a shape [23]. Figure 1 illustrates aportion of the animated transition as the feature space is shifting alongthe x-axis. Note that now the user can see the distribution ofthe den-sity vs. density gradient magnitude with respect to the location alongthe X axis of the volume data set. We can see that the higher densitygradients are focused near a specific region in the X space, perhapsindicating that features of interest lie in this area.

4 APPLICATIONS IN TRANSFER FUNCTION SCULPTING

To facilitate n-dimensional transfer function construction using thescatterplot matrix navigation and transfer function widgets describedabove, we define an iterative filtering mechanism that we calltransferfunction sculpting. Transfer function sculpting consists of creating abase transfer function in the interactive 2D scatterplot window usingour interactive widgets. When the user moves to another feature spacedimension, the new interactions in this feature space will be combinedwith the base transfer function in anAND or OR logic operation. Suchinteractions allow for an interactive refinement of the transfer functionin a method similar to high-dimensional brushing [18]. The applica-tion of an n-dimensional transfer function can readily increase dataexploration and enhance the user’s understanding of how various fea-tures are mapped across different volume dimensions. We have ap-

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plied our work to both structured and unstructured grid rendering, andin this section, we illustrate several sample applications.

4.1 Feature Visualization for Multivariate Scientific Data

Scientific simulations often produce multivariate volumetric datasetsand the correlations among multiple fields may reveal features thescientists are interested in. For example, the weather simulation of-ten produce volumetric datasets that contain visible fields(e.g., cloud,rain, ice, snow, and graupel), physical variable (e.g., temperature andpressure), and vector fields (e.g., wind). Visualizing a correlationamong fields can often be done by specifying the feature with certainconstraints, design special visualization process, or develop specificvisualization techniques. However, the feature definitionbeforehandlimits the flexibility of feature detection and visualization. Our scatter-dice user interface removes the limitation by allowing users to designthe field order for the feature they are interested in, navigating throughfeature spaces, sculptingn-dimensional transfer function and examingthe results instantaneously.

We demonstrate the scientific discovery process with a stormdataset that contains visible fields and physical variables. Scientists areinterested in understanding the snow splittering process in the storm,where the process is often located in the regions with high ice and highgraupel mixing ratio while the temperature lies in the rangeof -14 to9.

To locate the regions, users can first order the scatterplot matrixbased on their interests, with Qsum (total density), Qsum gradientmagnitude, cloud, ice, graupel and temperature along the matrix axis,as seen in Figure 4 (left). Second, we start with ice vs. graupel fea-ture space to select the regions with high ice and graupel mixing ratio.The corresponding regions are highlighted in red in Figure 4(middle).Third, we navigate to the feature space of temperature vs. Qsum, andsculpt the previous transfer function with the above temperature range,using AND logical operation. The regions that satify the feature con-straints are visualized in red in Figure 4 (bottom). Note that the stormbody is rendered in while for spatial reference.

This whole process is done by sculptingn-dimensional transferfunction among numerical spaces through our scatterdice user inter-face. No special visualization procedure or techniques need to be de-veloped for every specific feature. Also, scientists are able to viewthe data distribution of all feature spaces while he/she is designing thetransfer functions so that the dataset is better understood.

4.2 Flow Feature Visualization

Flow data (such as the result of a CFD simulation) contains a widevariety of variables for feature exploring. For example, one commonfeature researchers are looking for in the supersonic CFD simulationsis where the shocks are occurring and the location and properties ofshocks. Ma et al. [16] listed three data properties that indicate thepresence of a shock within the data.

1. Regions where the Normal Mach number is close to one

2. Regions that have a positive first directional derivativeand a zerosecond directional derivative

3. Vertices where the density gradient magnitude exceeds theweighted gradient magnitude of its neighbors

However, Ma et al. [16] were only able to explore each criteria sep-arately. By using our transfer function sculpting techniques, we areable to explore the impact of combining these shock data propertiesutilizing a four-dimensional feature space (Normal Mach Number ver-sus First Directional Derivative versus Second Directional Derivative)to classify regions that mutually satisfy these criteria.

We demonstrate the discovery process of the shock wave from theNASA X38 dataset. The NASA X38 dataset records a single timestep of the crew return vehicle during reentry into the atmosphere at a30 degree angle of attack. Scientists are interested in visualizing theprimary shock close to the aircraft nose. To accurately locate the shock

wave, we need to incorporate not only numerical informationbut alsothe spatial information for visualization.

First, we construct the scatterplot matrix (as shown in Figure 5),with the feature ordering defined as density, normal mach number, firstdirectional derivative, second directional derivative, and the space tu-ple (x, y, z). The user first selects the base transfer function in the firstdirectional derivative versus 2nd directional derivativefeature space.The base transfer function is defined such that all points with seconddirectional derivative close to zero and positive 1st directional deriva-tive will be colored yellow, Figure 5-1), thus satisfying the secondcriteria noted by Ma et al. [16].

Next, since it is known that the shock emanate from the body oftheaircraft, the user navigates to the X versus Y feature space.Here, theuser places new transfer function widgets in the feature space, coloringall of the primitives near the nose of X38 aircraft white. Theuserchooses the AND operation such that the data being visualized is datawith positive 1st directional derivative, zero 2nd directional derivativeand close to the nose of the aircraft body. The resultant rendering isseen in Figure 5-3).

Finally, the user navigates to the Density versus Normal MachNumber space, and adds a widget (through an AND operation) tose-lect only the points that have Normal Mach number close to 1.0(corre-sponding to the first criteria of Ma et al. [16]. The resultantrenderingis seen in Figure 5-4). The user then navigates to the DensityversusSecond Directional Derivative space and confirms that the renderedvoxels only have second directional derivative values of zero. In thismanner, the user is able to combine multiple criteria to search for com-plex shocks.

The detection and visualization of the shock wave of the X38dataset shows the flexibility and effectiveness of our user interface formultidimensional transfer function sculpting. Through our interface,users are able to sculpt high dimensional transfer functions that satisfymultiple criteria for more accurate shock wave detection and visual-ization.

4.3 Feature Separation for CT/MRI Data

In contrast to scientific simulation data, CT/MRI data normally con-sists of singular value data (signal strength); however, the derivedfields (e.g., value gradient, Laplacian, etc.) and spatial componentsof the data play a key role in the user’s ability to separate features.Unfortunately, in a regularly sampled grid, a feature spaceview of twospatial components are unable to provide the user with informationabout their data. However, as we illustrate in Figure 6, as the userinteracts in other feature space domains (e.g., value versus value gra-dient magnitude), structures reveal themselves in the cross-sectionalfeature space view.

Figure 6 illustrates the use of transfer function sculptingon the Vis-ible Woman feet CT dataset for feature separation, and demonstratesthe application of both the AND and OR Boolean operators. Initially,the user begins by interacting with the value versus value gradientmagnitude feature space. A 2D rectangular control widget isadded tothe scatterplot feature space, and the user chooses to colorthe data tan.The bones are shown in the 3D rendering window. This user definedtransfer function is now the base transfer function from which all logicoperations will take place. Once the data in the value versusvalue gra-dient magnitude feature space is colored, the spatial structures are re-vealed in both the volumetric rendering and the spatial feature spacesfound in the scatterplot matrix.

Next, the user navigates to the X versus Z feature space. Two rect-angular control widgets are added to the base transfer function andthese widgets are placed such that each widget encompasses one ofthe ankles. From there, the user can choose the OR operation,whichthen results in all the data surrounding the left foot bones to be col-ored white. Alternatively, the user can choose the AND operation thatcreates a resultant rendering showing only the left foot bones. Fo-cus+context effects can be achieved by highlighting skin regions usingOR operator with the previously sculpted transfer function, shown inFigure 6. Clearly our method allows the user to quickly understandthe complex interactions between the various feature spaceviews (as

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Online Submission ID: 1180

High Ice vs. High Graupel

AND Temperature Range

Fig. 4. Multivariate weather data visualization using n-dimensional transfer function sculpted through our scatterdice user interface. (Top) The stormdataset is rendered as a spatial reference; (Middle) Regions that contain high ice and high graupel ratio are highlighted in red; (Bottom) Regionsare refined by the temperature range of -14 to 9.

shown when the spatial slice highlighting occurs after interaction withthe value versus value gradient magnitude space), and sculpt the datain whatever manner is appropriate for their task.

Compared to the high-dimensional classification interfacein [22],our interface employs a scatterplot matrix for more intuitive transferfunction interaction and better global data distribution viewing acrossall data features. The ordering of the feature spaces provides flexibilityfor feature discovery and navigation.

5 CONCLUSION

In this paper, we have proposed a novel interface for easily sculptingn-dimensional transfer functions. Our work takes advantage of advancedinformation visualization techniques for exploring largefeature spacesthrough the use of the scatterdice interface. Users are ableto organizethe scatterplot matrix following hierarchical or self-defined schemesbased on their interests. The design and sculpting of the transfer func-tions are better assisted by our interactive brushing and highlightingabilities.

We have demonstrated the flexibility of our transfer function sculpt-ing scheme through the application of scientific data, flow data (un-structured grid) (Figure), and medical data (structured grid). Flow fea-ture close to the fin that is highlighted with banding effectsis shown inFigure 1. The regions where high ice ratio, high graupel ratio, and lowtemperature are collocated (Figure 4), are easily highlighted throughour scatterdice interface, indicating the snow splitting process in thecloud model. The shock wave of the X38 dataset that satisfies mul-

tiple shock criteria is illustrated in Figure 5. Also, the bone featureseparation on the feet dataset can be easily achieved through our inter-face.

Our results illustrate the ease in which feature separationcan beachieved throughn-dimensional transfer function sculpting. Futurework will focus on enhanced dimensional ordering of the scatterplotmatrix as well as a larger suite of logic operations for advanced transferfunction design.

REFERENCES

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[2] H. Akiba, K.-L. Ma, J. H. Chen, and E. R. Hawkes. Visualizing multi-variate volume data from turbulent combustion simulations. Computingin Science and Engg., 9(2):76–83, 2007.

[3] R. A. Becker and W. S. Cleveland. Brushing scatterplots.Technometrics,29(2):127–142, 1987.

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Zoomed view of step-by-step renderings Final sca�erplot matrix view

Base TF (1st Dir. Der. vs.

2nd Dir. Der.)

AND opera�on with

previous TF (X vs. Y)

AND opera�on (Density

vs. Normal Mach

Number)

1)

2)

2)

1)

3)

2)

4)

Fig. 5. Shock wave detection using n-dimensional transfer functions. Here the user explores the X38 dataset and extracts multi-dimensional shockfeatures near the aircraft body.

[7] N. Elmqvist, P. Dragicevic, and J.-D. Fekete. Rolling the dice: Multidi-mensional visual exploration using scatterplot matrix navigation. IEEETransactions on Visualization and Computer Graphics (Proc. InfoVis2008), 14:1141–1148, 2008.

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[12] J. Kniss, G. Kindlmann, and C. Hansen. Interactive volume renderingusing multi-dimensional transfer functions and direct manipulation wid-gets. InVIS ’01: Proceedings of the conference on Visualization ’01,pages 255–262, 2001.

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[17] J. Marks, B. Andalman, P. A. Beardsley, W. Freeman, S. Gibson, J. Hod-gins, T. Kang, B. Mirtich, H. Pfister, W. Ruml, K. Ryall, J. Seims, andS. Shieber. Design galleries: a general approach to settingparameters forcomputer graphics and animation. InSIGGRAPH ’97: Proceedings ofthe 24th annual conference on Computer graphics and interactive tech-niques, pages 389–400, 1997.

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[19] H. Pfister, B. Lorensen, C. Bajaj, G. Kindlmann, W. Schroeder, L. S.Avila, K. Martin, R. Machiraju, and J. Lee. The transfer function bake-off. IEEE Comput. Graph. Appl., 21(3):16–22, 2001.

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Online Submission ID: 1180

B ase transfe r function :

(D ensity vs. D ensity

G rad ien t)

O rig ina l sca tte rp lo t m atrix . N ote the spatia l v iew fo r regu lar g rid . S catte rp lo t m atrix afte r firs t b rush ing revea ls c ross -sectiona l in fo rm ation .

O R com pared to A N D :

(X vs . Z )

A N DO R

O rig ina l sca tte rp lo t m atrix . N ote the spatia l v iew fo r regu lar g rid . S catte rp lo t m atrix afte r firs t b rush ing revea ls c ross -sectiona l in fo rm ation .

O R com pared to A N D :

(X vs . Z )

A N DO R

Fig. 6. Feature separation using n-dimensional transfer functions on feet dataset. The user is able to visualize the bones using the value vs. valuegradient magnitude 2D transfer function. By sculpting a region in the X vs. Z space, the user is able to separate the bone structure of the left tarsaljoint after the AND operation is applied. A focus+context effect is achieved by highlighting the skin using the OR operation.

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