Exploration Of Volumetric Datasets Through Interaction In .
Exploration of Volumetric Datasets through Interaction in Transfer FunctionSpaceFrancisco de M. Pinto and Carla M. D. S. FreitasInstituto de Informática – Universidade Federal do Rio Grande do Sulfmpinto@inf.ufrgs.br, carla@inf.ufrgs.brAbstractDirect volume rendering techniques allowvisualization of volume data without extractingintermediate geometry. The mapping from voxelattributes to optical properties is performed by transferfunctions which, consequently, play a crucial role inbuilding informative images from the data. Onedimensional transfer functions, which are based onlyon a scalar value per voxel, often do not provideproper visualizations. On the other hand, multidimensional transfer functions can perform moresophisticated data classification, based on vectorialvoxel signatures. The transfer function design is a nontrivial and unintuitive task, especially in the multidimensional case, and its controlled modificationallows the user to selectively enhance differentstructures in the volume. In this paper we discuss theinteractive approach of a transfer function designtechnique that allows the user to explore volumetricdatasets by interacting with a derived space as well aswith voxels in the volume space.1. IntroductionIn direct volume rendering (DVR), transferfunctions (TFs) are used for emphasizing regions ofinterest inside the volumes. The most common type oftransfer function is the one-dimensional TF, whichassigns optical properties (usually color and opacity) tovoxels based only on their scalar value.Notwithstanding, one-dimensional TFs have a verylimited classification power because they can not makedistinction between volume regions defined by scalarvalues within the same range. On the other hand, multidimensional transfer functions can perform betterclassification because they can take into account notonly the scalar value of a voxel [8], but also otherattributes like gradient magnitude, directional secondderivative, curvature [7] and statistical measures [23].Figure 1. The sheep heart dataset viewed with two TFs,represented as circle in the color map. The circlerepresents a Gaussian opacity function with peak –maximum opacity – at the center. The color maps arefixed, with red, green and blue representing scalar value,gradient magnitude and directional second derivative,respectively.Designing an appropriate transfer function, even aone-dimensional TF, is a difficult task and muchattention has been given to this issue in the literatureafter Pfister et al.[15]. As the domain dimensionincreases, the visualization of the transfer functionbecomes more difficult, and so the interaction with it.Controlled modifications of color and opacity transferfunctions allow enhancing parts of the datasets, thushiding features and revealing others that the user istrying to isolate. This way, the representation of theThis paper is based on the M.Sc. dissertation named "Especificação de Funções de Transferência Unidimensionais eMultidimensionais para Visualização Volumétrica Direta" by the first author.
transfer functions and the ways the user can interactwith them play an important role in the exploration ofinner structures in volumetric datasets.In this paper we present an interactive technique forthe design of multi-dimensional transfer functions.With our approach the user can interact with asimplified representation of the TFs obtaining differentinformative visualizations in a very easy and fast way(Figure 1). We discuss the resulting method comparedto a previous interface for specifying one-dimensionaltransfer functions.The paper is organized as follows. Next sectionspresent the closest related works, including a briefreview of our previous work. Section 3 describes ourapproach in detail, while main implementation aspectsare discussed in Section 4. Section 5 discusses theresults obtained with our method, and finally, inSection 6 we draw some conclusions and point outfuture work.2. Related work2.1. ional approaches for TF specification rely onthe user's effort in adjusting control points of a graphicplot mapping voxel values to opacity level and/or colortone. The control points are then interpolated in orderto build the TF. But, with no clues or prior knowledgeabout the data, this is a “blind process”. Some datadriven approaches provide to the user higher-levelinformation [2][14] that helps in obtaining insightabout the data distribution as well as supports themanual TF design. Other methods build abstractions ofthe TF specification process - the transfer functions canbe hidden from the user [24] or a simplified space canbe presented [6].Kindlmann and Durkin [6] proposed a derived spacefor specification of opacity transfer functions in whichthe user specifies opacities for voxels as a function ofthe distance between the voxel and the nearestboundary. Informative histograms are built relatingvoxel values with the first and second derivative valuesassociated to each voxel in the volume. From thesehistograms, the mean first and second derivative valuesassociated to each voxel value are used to estimate thedistance to the nearest border. Since the boundariesmust be emphasized, voxel values with small estimateddistances should receive larger opacity values.Prauchner et al. [18] used Kindlmann’s method toclassify the voxel values by the estimated distance tothe nearest border. A set of voxel values with thesmallest distances is elected and random subsets arethen built. The values of each subset are used as controlpoints for the TF specification. Each of these pointsreceives a random color and a random opacity valuedifferent from zero. The transfer functions are obtainedby interpolating the control points. Consequently, eachsubset of the “best'” voxel values derives a transferfunction to be presented in a gallery of thumbnails,similar to the Design Galleries method [13]. This is thefirst level of the two-level interaction interfaceproposed by Prauchner et al. In the second level, theuser can visualize a selected thumbnail in betterresolution and refine its TF by adjusting the controlpoints manually. The thumbnails can be randomly regenerated any time at interactive rates.Following this two-level interaction interfaceapproach, we [16] also adopted the gallery to presentseveral thumbnails generated initially through aboundary emphasis technique, following Kindlmannand Durkin [6]. At this level, the user can generate newthumbnails (TFs) by either reapplying the boundaryemphasis or selecting thumbnails as parents of a nextgeneration of TFs, which are generated using anstochastic approach by He et al.[4]. The user can alsoselect a specific thumbnail, and go to the second-levelof interaction. At this level, looking at the renderedvolume in high resolution, the user can modify the TFmanually either by interacting with the TF graphic plot(Figure 2) or by picking voxels – to be emphasized byincreasing the opacity for its scalar value – from acutting plane (Figure 3). This work was published inSIBGRAPI 2006 and its extended version is to appearin a Computer and Graphics special issue.2.2. Multi-dimensionalspecificationtransferfunctionThe design of multi-dimensional transfer functionsbrings challenges regarding both the visualization ofthe TF as well as the exploration of the TF domain.It is possible to explicitly define a multi-dimensionaltransfer function by interacting in its domain withproper tools. Kniss et al. [8] proposed a volumerendering environment containing a set of directmanipulation widgets for volume inspection,visualization of data distribution and design of threedimensional transfer functions, using dual domaininteraction.However, the difficulty of exploring the transferfunction domain increases with its dimensionality;therefore some approaches for transfer function designprovide interfaces based on interaction in a simplifiedspace. Region growing techniques were used by Huang
and Ma [5] to segment volume data from seed pointsspecified by the user; voxel signatures of the segmentedregion were used to automatically design a transferfunction.Tzeng and Ma [25] clusterized voxel's signatures bysimilarity allowing the user to specify the desiredclassification by successively splitting and merging theclusters. The user sees the results by associating visualproperties to each material class. The same authors[26] implemented multi-dimensional transfer functionsusing neural networks and support vector machines.They evaluate a classification function learned fromtraining sets selected through a slice painting interface.The user paints the voxels of interest with a specificcolor, and the undesired ones with a different color.This way they implement a binary classificationscheme.Sêreda et al. [20] used hierarchical clustering togroup voxels according to their LH signatures [21].The user navigates through the hierarchy searching forthe branches corresponding to regions of interest.Takanashi et al. [22] used independent componentanalysis (ICA) of multi-dimensional voxel signatures inorder to represent them in a space where theclassification is performed by moving axis alignedseparation planes. Rezk-Salama et al. [19] createdmodels of transfer functions that are carefully adjustedby specialists for several data sets of the same type inorder to reveal the desired structures. Then, theyapplied PCA to represent the parameter set of eachmodel by a single variable with an associated semantic.The models can be reused for new data sets by settingonly that variable.In order to have a generic design technique, we canconsider designing a one-dimensional transfer functionas a case of designing a multi-dimensional TF wherethe user selects only one variable to represent the voxelsignature. In [17], we reported a method for designingnD-TFs, where voxel signatures are extracted from thevolumetric dataset to be visualized, 2D or sphericalself-organizing maps are built from the voxelssignatures, and a dimensional reduction step results invoxels signatures being replaced by their coordinates inmap space. These processes are performed off-line andperform non-linear dimensional reduction of voxelsignatures. The result can be thought as a non-discrete,non-linear voxel classification scheme that groupvoxels by similarity and map them to a twodimensional space: a square or a spherical surface.During rendering the user can specify color and opacitytransfer functions by navigating on the map with acursor that is the peak of a Gaussian opacity function.Next section presents this method in detail.Figure 2: Manual design of one-dimensional opacity andcolor transfer functions.Figure 3. Top image: dataset1 rendered using the TFshown at the left side. Bottom images: the voxel pointedby the cursor has the value marked as a white square inthe TF plot. Opacity associated with this value can beinteractively increased by the user.3. Design of multi-dimensional transferfunctionsFigure 4 shows the process of obtaining meaningfultransfer functions for nD signatures. Our work on thissubject [17] was published in EuroVis 2007.1Dataset “Laçador” kindly provided by LACEM-UFRGS.
3.1. Map building processThe map building process starts with apreprocessing phase, when complex voxel's signatures(like derivative values, statistical measures, etc.) areextracted from the volume data and normalized. Thisway, each voxel has an nD signature (a set of scalarvalues represented as a vector) that can be used as atraining case for the self-organizing (Kohonen) mapbuilding algorithm. It is important to mention that,depending on the source of volume data, there aremany background voxels which do not carry usefulinformation (air around scanned objects in CT/MRIvolume data, for example), and would influence themap due to their high occurrence. Upon user decision,they can be partially removed from the input set of thetraining process by a very simple region growingtechnique using as seeds the voxels identified asbackground in the most exterior regions of the volume.The signatures of all non-background voxels areemployed as training cases presented in random orderto the self-organizing map, and two types ofneighborhood functions are applied. In a first stage wedefine the overall aspect of the map by training it usinga Gaussian neighborhood function, and then, wecontinue the map training with a modifiedneighborhood function that depends not only on thetopological distance, but also on the distance betweenthe training case and the weight vector of the winnercell (refer to [17], for further details). This modifiedneighborhood function is designed in order to allow avoxel with a signature far from the weight vector of thecorresponding winner cell (according to the distancemetric) to have more influence on the map. Withoutthis strategy, large homogeneous regions of the volumewould tend to dominate the map, while importantregions with fewer voxels would be badly represented(signatures far from their respective winner cells).We use as topological distance the Euclideandistance between the integer 2D coordinates of twocells in the map grid. For spherical maps, thetopological distance is the number of edges in theshortest path connecting two cells.At the end of this process, we have a Kohonen (orspherical) map where each cell has an associatedweight vector that represents a class of voxels, beingthe most similar weight vector for all elements in thatclass.3.2. Dimensional reductionDimensional reduction was motivated by the need ofproviding a simplified space for the user to interactwith the multi-dimensional transfer functions. Whenusing Kohonen maps, two-dimensional map spacecoordinates in the interval from zero to one can beassociated to cells according to their position in the 2Dgrid. Dimensional reduction can be performed byreplacing each voxel signature by the coordinates of itsrespective winner cell. However, this would causeunnecessary discretization. To avoid this, we createtwo multiquadric radial basis functions (multiquadricRBFs), for x and y map space coordinates, based on theweight vectors of all cells. For spherical maps we adoptx, y and z position coordinates ranging from -1 to 1,and use three RBFs to obtain the coordinates of voxel'ssignatures. Thus, the RBFs supports the final step indimensional reduction of voxel signatures byproducing, through interpolation, the proper x and y(and z) map coordinates for each nD voxel signature.Figure 4. Distribution of processes between CPU andGPU for obtaining opacity and color TFs from nD voxelsignatures.Dimensional reduction normally implies loss anddistortion of information, but volumetric data usuallyhave properties that reduce this problem. The voxelssignatures are usually not uniformly distributed in theirdomain (they form clusters, which are well representedin the map), and elements of the voxel signatures areoften not completely independent [22]. Moreover,voxel signatures that are not present in the training setdo not require space in the map.3.3. Transfer functions specificationAfter the dimensional reduction step, the continuousmap space defined by the RBFs becomes the TFdomain. The user can interactively define the mappingfrom map coordinates (which represent voxel'ssignatures) to optical properties. We propose an
interface for specification of color and opacity transferfunctions that provides dual domain interaction [8] aswell as visualizations of the transfer function and of thevoxel signatures.3.3.1. Interaction in TF-domain. The visualization ofvoxel's signatures in our interface is obtained bydirectly mapping up to three elements of the weightvectors of the map cells (which actually are elements ofthe voxel signature) to the three color channels. Theuser decides which element of the nD signatures shouldbe mapped to each basic color. One element can beassociated to more than one color channel and a colorchannel may have no elements mapped to it. Thisinterface feature illustrates the distribution of voxel'ssignatures on the map and can be used to build colorTFs as described below. Figure 5 (a and b) shows thedistribution of voxel's signatures of the well knownengine data set. The same regions (clusters ofsignatures) can be found in both maps.The transfer function is represented as an RGBAimage and is displayed by blending it with acheckerboard pattern. The blending function allowsTFs with small opacities to be clearly visualized.Figure 5 displays TFs on a Kohonen map (c) and on aspherical map (d) generated for visualizing the enginedata set. The volumetric rendering of the data set usingthe TF in Figure 5c is shown in Figure 7a.Transfer functions are composed by blendingseveral 2D Gaussian opacity TFs, each one having anassociated 2D color TF. We provide three types ofcolor transfer functions that can be associated to aGaussian opacity function: a constant color chosenfrom a colorpicker; map coordinates directly mapped tocolor channels; and elements of weight vectors of mapcells mapped to color channels (for each mapcoordinate the weight vectors of the near cells areinterpolated and mapped to colors). At each step a newGaussian TF is specified and then blended with thecurrent TF, for opacity and color. The result becomesthe current transfer function and the compositioncontinues until the desired TF is reached. At start, thecurrent TF has zero opacity and RGB colors for all themap space.In our interface, by clicking or dragging the mouseon the map representation, the user moves a circlewhose center is the peak of a Gaussian function andwhose radius is its standard deviation ı. The GaussianTF is scaled by a constant k between zero and onewhich is linearly mapped to the circle color, with bluebeing zero and red, one. The parameters ı and k can beincreased or decreased using the keyboard. In order tofully explore the spherical maps, they can be rotated bydragging the mouse using the right button. TheGaussian opacity transfer function is defined in termsof the distance to the center of the circle.Figure 5. Maps of 3D voxel's signatures (a and b). Scalarvalue is mapped to red, gradient magnitude to green andsecond derivative in the gradient direction to blue.Transfer functions displayed on a Kohonen map (c) andon a spherical map (d).The transfer function used for rendering is thecomposition of the current TF and the Gaussianfunction represented by the circle. This schemeprovides interactive previewing of the effect of thecomposition while the user explores the map bymoving the circle on it. When the desired effect isreached, the user can set the composition as the currentTF using the space bar, and other Gaussian functioncan be further experimented.Our interface (Figure 8) keeps track of all transferfunctions defined during a session, and provides a treerepresentation of this evolution using static thumbnailsof the volume rendered with the corresponding TF.This allows simple recovering of previous TFs byclicking on the thumbnails.3.3.2. Interaction in TF-domain. At any time the usercan rotate and translate the volume and place a clippingplane to better explore inner structures. The volumeslice defined by the clipping plane is textured bymapping to color channels the map coordinates of thevoxels sampled by the slice. This causes an interestingcoloring effect that helps in inspecting the volume. Theslice is blended with the rendered volume using anopacity value controlled by the user, as shown inFigure 6. When Kohonen maps are employed, the xand y map space coordinates of the voxels are mapped
to red and green. When using a spherical map the x, yand z map space coordinates are mapped to RGBcolors.The user can also click on the clipping plane to setthe position of the Gaussian opacity function peak tothe map coordinates of the voxel pointed by the mousecursor, emphasizing that region. By moving the mouseon the clipping plane, the user can see the position ofthe pointed voxel
self-organizing maps are built from the voxels signatures, and a dimensional reduction step results in voxels signatures being replaced by their coordinates in map space. These processes are performed off-line and perform non-linear dimensional reduction of voxel signatures. The result can be thought as a non-discrete,
2. Vision-and-Language Tasks 2.1. Task Groups and Datasets We consider 12 popular vision and language datasets. These datasets cover a wide range of tasks and require di-verse grounding granularity and reasoning skills. We group related datasets into four groups to facilitate our analysis: Vocab-basedVQA.Givenanimageandanatural-language
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The Analysis Data Model Implementation Guide (ADaMIG) v1.1 defines three different types of datasets: analysis datasets, ADaM datasets, and non-ADaM analysis datasets: Analysis dataset - An analysis dataset is defined as a dataset used for analysis and reporting. ADaM dataset - An ADaM dataset is a particular type of analysis dataset that .
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Reservoir engineering datasets comprise a large fraction of these data and their analysis is the subject of this report. Volumetric models being developed at the surface exploration stage can give an indication of the power potential at hand. Here a few examples are given, from three different countries. The Corbetti resource
Table XV. Weld Surface and Volumetric Acceptance Criteria - Aluminum Alloys . 65 Table XVI. Surface and Volumetric Acceptance Criteria - Steels, Heat Resistant Alloys. 71 Table XVII. Weld Surface and Volumetric Acceptance Criteria - Titanium Alloys . 72 Table XVIII.
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All volumetric glassware for quantitative work requires calibration. 6. Range All volumetric glassware used for accurate delivery or to contain specific volumes needs to be calibrated. 7. Apparatus and Equipment 7.1 Analytical balance accurate to 0.1mg (0.001g) Analytical balance accurate to 0.1g. (For volumes of 100 mL or less, the balance .
