Visualization of Time-Varying Volumetric Data using Differential Time-Histogram Table

Transcription

1 Volume Grphics (5) E. Gröller, I. Fujishiro (Editors) Visuliztion of Time-Vrying Volumetric Dt using Differentil Time-Histogrm Tble Hmid Younesy, Torsten Möller, Hmish Crr Simon Frser University, Simon Frser University, University College, Dublin Abstrct We introduce novel dt structure clled Differentil Time-Histogrm Tble (DTHT) for visuliztion of timevrying sclr dt. This dt structure only stores voxels tht re chnging between time-steps or during trnsfer function updtes. It llows efficient updtes of dt necessry for rendering during sequence of queries common during dt explortion nd visuliztion. The tble is used to updte the vlues held in memory so tht efficient visuliztion is supported while gurnteeing tht the sclr field visulized is within given error tolernce of the sclr field smpled. Our dt structure llows updtes of time-steps in the order of tens of frmes per second for volumes of sizes of.5gb, enbling rel-time time-sliders. Ctegories nd Subject Descriptors (ccording to ACM CCS): I.3. [Computer Grphics]: Grphics dt structures nd dt types - E.1 [Dt]: Dt Structures Keywords: time-vrying dt, volume rendering 1. Introduction As computing power nd scnning precision increse, scientific pplictions generte time-vrying volumetric dt with thousnds of time steps nd billions of voxels, chllenging our bility to explore nd visulize interctively. Although ech time step cn generlly be rendered efficiently, rendering multiple time steps requires efficient dt trnsfer from disk storge to min memory to grphics hrdwre. We use the temporl coherence of sequentil time frmes, the sptil distribution of dt vlues, nd the histogrm distribution of the dt for efficient visuliztion. Temporl coherence [SH99] is used to prevent loding unchnged smple vlues, sptil distribution [WG9] to preserve rendering loclity between imges, nd histogrm distribution to updte for incrementl updtes during dt clssifiction. Of these, temporl coherence nd histogrm distribution hyounesy@cs.sfu.c torsten@cs.sfu.c hmish.crr@ucd.ie re encoded in differentil tble computed in preprocessing step. This differentil tble is used during visuliztion to minimize the mount of dt tht needs to be loded from disk between ny two successive imges. Sptil distribution is then used to ccelerte rendering by retining unchnged geometric, topologicl nd combintoril informtion between successive imges rendered, bsed on the differentil informtion loded from disk. The contributions of this pper re to identify nd nlyze sttisticl chrcteristics of lrge scientific dt sets tht permit efficient error-bounded visuliztion. We unify the sttisticl coherence of the dt with the known sptil nd temporl coherence of the dt in single differentil tble used for updting memory-resident version of the dt. We define coherence nd distribution more formlly in Section, review relted work in Section 3 nd support our definition of coherence nd distribution in Section with cse study. In Section 5 we show how to exploit dt chrcteristics to build binned dt structure representing the temporl coherence nd sptil nd histogrm distribution of the dt, nd how to use this structure to ccelerte interctive explortion of such dt. We then present some results c The Eurogrphics Assocition 5.

2 H. Younesy, T. Möller & H. Crr / Differentil Time-Histogrm Tble in Section nd some conclusions in Section 7, followed by comments on possible future work in Section 7.. Dt Chrcteristics In order to discuss both previous work nd our own contributions, we strt by defining our ssumed input nd the sttisticl properties of the dt tht we will exploit for ccelerted visuliztion: we will support these ssertions empiriclly in our cse study in Section. Formlly, time-vrying sclr field is function f : R R. Such dt is often smpled f t fixed loctions V = {v 1,...,v n } nd fixed times T = {t 1,...,t τ }. Since we exploit this smpling regulrity to ccelerte visuliztion, we ssume tht our dt is of the form F = {(v,t, f (v,t)) v V,t T }, where ech triple (v,t, f (v,t)) is smple. Previous reserchers report [OM1] tht only smll frction of F is needed for ny given imge generted during visuliztion. Thus, ny imge cn be thought of s the result of visulizing subset of F defined by query q. More formlly, given F nd condition q t time t (e.g. trnsfer function), find the set F q of ll smples (v,t, f (v,t)) for which q is true (e.g. the opcity of f (v,t) is non-zero). Thus, F q is the set of smples needed to render q, clled the ctive set of q. To construct query q for isosurfce extrction t isovlue h, F q consists of ll smples belonging to cells whose isovlues spn h. For volume rendering, we bse trnsfer functions on the isovlue, s shown in Figure : the ctive set therefore hs rnge of isovlues. We now restte our observtion: we expect F q F. Moreover, F q is rrely rndom, nor is it evenly distributed throughout the dt set. Insted, F q tends to consist of lrge contiguous blocks of smples, due to the continuity of the physicl system underlying the dt, nd the inherent orgniztion of most physicl systems being studied. We exploit both chrcteristics to ccelerte visuliztion. We lso exploit the fct tht humn explortion of dt usully involves continuous (i.e. grdul) vrition of queries. Formlly, we re interested, not in single query q, but in sequence q 1,...,q k of closely-relted queries, with occsionl brupt chnges to new query sequence q 1,...,q m. We expect tht the ctive sets for ny two sequentil queries will be nerly identicl, i.e. tht F q i+1 F q i. In prticulr, we exploit coherence nd distribution. Let us denote two smples σ 1 = (v 1,t 1, f (v 1,t 1 )) nd σ = (v,t, f (v,t )), nd choose smll vlues δ,λ >. Sptil coherence is coherence with respect to the sptil dimensions x,y,z of the domin of f, nd is bsed on the sptil continuity of the physicl system. Smll sptil chnges imply smll functionl chnges, i.e. if v 1 v < δ nd t 1 = t, then f 1 f < λ for smll λ. Temporl coherence is coherence with respect to the time dimension t of the domin of f nd is bsed on the temporl continuity of the physicl system. Hence, if t 1 t < δ nd v 1 = v, then f 1 f < λ for smll λ. Given two sequentil queries q i,q i+1 which differ only slightly in spce or time, F q i nd F q i+1 will therefore overlp significntly. We exploit this to ccelerte the tsk of updting the ctive set for rendering purposes, focusing principlly on temporl explortion. We lso exploit sttisticl properties of the dt sets in question, which we describe in terms of dt distribution: Histogrm distribution is property of the functionl dimension (i.e. the rnge of f ) nd depends lrgely on the dt being studied. However, it is usully true tht extrcted fetures re chosen t vlues where the rnge of f vries gretly: thus we expect f to be firly well distributed, lthough smpling my ffect this. Sptil distribution is lrge scle form of sptil coherence, nd is bsed (gin) on the physicl phenomen scientists nd engineers study. Although dt is commonly generted over lrge domins, it is often true tht nothing interesting hppens in most of the domin. As result, the ctive sets for queries mde by the user re often clustered in subset of the spce. Histogrm distribution is crucil where two sequentil queries q i nd q i+1 differ only slightly in the functionl dimension. For well-distributed dt vlues, we expect F q i nd F q i+1 to be substntilly identicl: i.e. tht we cn chnge trnsfer functions more rpidly by loding only the new dt vlues required. Moreover, the sptil distribution of the dt llows us to hve sptilly sprse dt structures. 3. Relted Work The difficulty of rendering lrge dt sets is well-recognized in the literture, with successive solutions ddressing progressively lrger dt sets by exploiting vrious dt chrcteristics. Brodly speking, however, the solutions proposed hve delt with isosurfce extrction nd volume rendering s seprte topics, wheres our solution is pplicble to either with suitble modifictions. Modern isosurfce extrction nd volume rendering methods re bsed on the recognition tht the problem is decomposble into smller sub-problems. Lorenson & Cline [LC7] recognized this nd decomposed the extrction of n isosurfce over n entire dt set by extrcting the surfce for ech cell in cubic mesh independently. Almost simultneously, Wyvill, McPheeters & Wyvill [WMW] exploited sptil coherence for efficient isosurfce extrction in their continution method. Sptil coherence hs lso been exploited for volume rendering [WTTL9]. c The Eurogrphics Assocition 5.

3 H. Younesy, T. Möller & H. Crr / Differentil Time-Histogrm Tble Other reserchers [CMM 97, Gl91, LSJ9, WG9] exploit sptil distribution for efficient extrction of isosurfce ctive sets. In prticulr, Wilhelms & vn Gelder [WG9] introduced the Brnch-On-Need Octree (BONO), spce efficient vrition of the trditionl octree. Octrees, however do not lwys represent the sptil distribution of the dt, nd re inpplicble to irregulr or unstructured grids. Livnt et l. [LSJ9] introduced the notion of spn spce - plotting the isovlues spnned by ech cell nd building serch structure to find only cells tht spn desired isovlue. Since this represents the rnge of isovlues in cell by single entry in dt structure, it exploits histogrm distribution. Histogrm distribution hs lso been exploited to ccelerte rendering for isosurfces [CVCK3] by computing ctive set chnges with respect to isovlue. Ching et l. [CSS9] clustered cells in irregulr meshes into met-cells of roughly equl numbers of cells, then built n I/O- efficient spn spce serch structure on these met cells, gin exploiting histogrm distribution. For time-vrying dt, it is impossible to lod n entire dt set plus serch structures into min memory, so reserchers hve reduced the impct of slow disk ccess by building memory-resident serch structures nd loding dt from disk s needed. Sutton & Hnsen [SH99] extended brnch-on-need octrees to time-vrying dt with Temporl Brnch-on-Need Octrees (T-BON), using sptil nd temporl coherence to ccess only those portions of serch structure nd dt which re necessry to updte the ctive set. Similrly, Shen [She9] noted tht seprte spn spce structures for ech time-step re inefficient, nd proposed Temporl Hierrchicl Index (THI) Tree to suppress serch structure redundncy between time-steps, exploiting both histogrm distribution nd temporl coherence. Reinhrd et l. [RHP] binned smples by isovlue for ech time step, loding only those bins required for given query: this form of binning exploits histogrm distribution but not temporl coherence. For volume rendering, Shen & Johnson [SJ9] introduced Differentil Volume Rendering, in which they precomputed the voxels tht chnged between djcent time-steps, nd loded only those voxels tht chnged, principlly exploiting temporl coherence. Shen [SCM99] extended Differentil Volume Rendering with Time-Spce Prtitioning (TSP) Trees, which exploit both sptil distribution nd temporl coherence with n octree representtion of the volume. Binry trees store sptil nd temporl vritions for ech sub-block, nd this informtion is used for erly termintion of ry-trcing lgorithm, bsed on visul error metric. Shen lso cched imges for ech sub-block in cse little or no chnge occurred between frmes. M & Shen [MS] further extended this by quntizing the isovlues of the input dt nd storing them in octrees before computing differentils. Finlly, Sohn nd Bjj [SBS] use wvelets to compress time-vrying dt to desired error bound, exploiting temporl coherence s well s sptil nd histogrm distribution. Our contribution in this pper is to unify temporl coherence in the form of differentil visuliztion with sttisticl distributions in the form of isovlue binning. Before introducing our dt structures, however, we demonstrte the vlidity of coherence nd distribution with some cse studies.. Cse Studies: Dt Chrcteristics of Isbel & Turbulence As noted in the previous sections, our pproch to ccelerting visuliztion depends on mthemticl, sttisticl nd physicl properties of the dt being studied. Before progressing further, it is therefore necessry to demonstrte tht these properties re the cse. We do so by mens of cse studies of three different dt sets. The first nd lrgest dt set is the Hurricne Isbel dt set provided by the Ntionl Center for Atmospheric Reserch (NCAR) for the IEEE Visuliztion Contest nd hs time steps of dimension 5x5x1. It contins 13 different floting point sclr vribles of which we study the temperture nd pressure. We hve lso studied the Turbulent Jets (jets) nd Turbulent Vortex Flow (vortex) dt sets provided by D. Silver t Rutgers University nd R. Wilson t University of Iow to Kwn-Liu M t University of Cliforni, Dvis. The jets dt contins 15 time steps of 1x19x19 flots, while the vortex dt contins 1 time steps of 1 3 floting point sclrs..1. Temporl Coherence We demonstrte temporl coherence by computing the difference between djcent time steps, nd grphing the percentge of differences tht exceed n error bound expressed s percentge of the overll dt rnge. As we see in Figure 1(), t n error bound of %, ll of the voxels differ from one time step to the next. This my be due to numericl inccurcies in the floting point dt. It therefore follows tht 1% of the smples will need to be replced for the memory-resident version of the dt to be ccurte. However, s we see from the second line on the grph, between % nd % of the smples differ by more thn.3%. Thus, for.3% error in the isovlues displyed, we cn sve s much s % of the lod time between queries. As the error bound is incresed further, the number of smples to be loded decreses further: t 1% error, between c The Eurogrphics Assocition 5.

4 H. Younesy, T. Möller & H. Crr / Differentil Time-Histogrm Tble chnged voxels (%) chnged voxels (%) 1 1 λ=% λ=.3% λ=1.% λ=3.% Time step () Isbel - temperture Time step (c) Turbulent Jets λ=% λ=.3% λ=1.% λ=3.% chnged voxels (%) chnged voxels (%) 1 1 λ=% λ=.3% λ=1.% λ=3.% Time step (b) Isbel - pressure λ=% λ=.3% λ=1.% λ=3.% 1 Time step Figure 1: Temporl Coherence: Number of smples tht chnge by more thn n error bound of λ = %,.3%, 1%, 3% for the temperture nd pressure sclrs of the Isbel dt set s well s the jets nd vortex dt sets. % nd 9% of the smples need not be reloded, while t 3% error, over 95% of the smples need not be reloded. Similr effects cn be seen for pressure in Isbel (Figure 1(b)) nd for the jets nd vortex dt sets (Figure 1(c) & (d)). In Figure 1(d), we believe tht the shrp periodic dips indicte tht certin time steps were indvertently duplicted. This side, the overll conclusion is tht reltively smll error bounds permit us to void loding lrge numbers of smples s time chnges... Histogrm Distribution In the lst section, we sw tht the sttistics of temporl coherence permit efficient differentil visuliztion for given error bound. It is nturl to sk whether similr sttistics re true for smll chnges in isovlues defining query. We show in Figure tht this is true by exmining the histogrm distribution for ech dt set. For this figure, we set our error bound to 1% nd computed the size of the ctive set for individul dt rnges (bins) nd for different times, nd lso the number of smples whose vlues chnged in the temporl dimension. For exmple, we see in Figure () tht temperture isosurfces in the Isbel dt set never hve ctive sets of more thn 5% of the size of single slice, nd tht less thn hlf of the ctive set typiclly requires replcement between one time step nd the next. For pressure, lthough nerly 5% of the smples re in the ctive set in the worst cse, these smples chnge little between timesteps, indicting tht the physicl phenomenon mrked by this pressure feture does not move much in spce between time steps. In the jets dt set (Figure (c)), the worst-cse behviour is exhibited: t n isovlue of roughly % of the rnge, nerly 1% of the smples re in the ctive set. Although this hs implictions for the ctul rendering step, we see tht this set chnges little with respect to time. However, s it turns out, these dt vlues constitute most of the ir surrounding the flow under study nd re likely to be ignored during dt explortion. In the vortex dt set (Figure (d)), we see gin tht dt bins involve reltively few smples, nd tht these smples hve lrge degree of temporl coherence..3. Sptil Distribution Unlike histogrm distribution, sptil distribution is hrder to test, s it is best mesured in terms of the sptil dt structure used to store the dt. We therefore defer considertion of sptil distribution to the discussion of Tble 1 in Section Differentil Time Histogrm Tble In the previous section, we demonstrted tht temporl coherence nd histogrm distribution offer the opportunity to reduce lod times drsticlly when visulizing lrge timevrying dt sets. To chieve the hypothesized reduction in lod-time we introduce new dt structure clled the Differentil Time Histogrm Tble (DTHT) long with n efficient lgorithm for performing regulr nd differentil queries in order to visulize the dt set. To exploit temporl coherence nd histogrm distribution, we pply differentil visuliztion in the temporl direction nd binning in the isovlue direction. Since we expect user explortion of the dt to consist mostly of grdul vritions in queries, we precompute the differences between successive queries. We modify temporl coherence by including in the differentil set only those smples for which the error exceeds chosen bound, further reducing the number of smples to be loded t ech time step Computing the DTHT Our DTHT, shown in Figure 3 stores smples in twodimensionl rry of bins defined by isovlue rnge nd time step. In ech bin, we store the ctive set (), nd set of differences (rrows) between the ctive sets of djcent bins. For given dt set with τ time steps, we crete DTHT with τ bins in the temporl direction nd b bins in the isovlue direction. Lrge vlues of b will increse the size of the tble, but decrese the rnge of vlues in ech bin, mking ctive set queries more efficient for one bin, but not necessrily fster for query covering lrge rnge of bins. Also, lrge numbers of bins will result in more storge overhed. We choose number b nd divide the isovlue rnge into b c The Eurogrphics Assocition 5.

5 H. Younesy, T. Möller & H. Crr / Differentil Time-Histogrm Tble Isovlue Bin Active Set Differentils Time () Isbel - temperture Figure 3: The Differentil Time Histogrm Tble (DTHT). Ech bin holds the ctive set () nd differentils between the bin nd djcent bins (rrows). Components not used for our experiments re shown in lighter shde. (b) Isbel - pressure (c) Turbulent Jets Figure : Temporl Coherence + Histogrm distribution: Number of smples tht chnge by more thn n error bound of λ = 1% for the temperture nd pressure sclrs of the Isbel dt set s well s the jets nd vortex dt sets. Ech dt set is divided up into 1 iso-vlue bins. bins. We lso choose λ, the mount of error we will tolerte in isovlues for single smple over time. We compute the DTHT by loding the first time step into memory nd binning the smples. We then lod the second time step into memory longside the first nd compute the difference between the two time steps. Any smple whose difference exceeds the error bound is dded to the differentil set in the time direction. Any smple whose difference does not exceed the error bound is modified so tht the vlue in the second time step is identicl to the vlue in the first time step: this ensures tht, over time, errors do not ccumulte beyond our chosen bound. At the sme time, differentils re computed in the isovlue direction if these re desired. In our experiments, we hve chosen to render using spltting: in this cse ech smple belongs to only one bin nd the ctive sets in djcent bins re disjoint. It follows tht the isovlue differentils re equl to the ctive sets, nd cn be omitted ccordingly, we show them in lighter shde in Figure 3. In cse we wnt to dpt the dt structure to support extrction of isosurfces, ech voxel my belong to rnge of isovlue bins depending on the vlues of its neighbors; therefore the bins will hve overlp nd it would be resonble to hve differentils between neighbor bins to void redundncy. The first time step is then discrded, nd the next time step is loded nd compred to the second time step. This process continues until the entire dt set hs been processed. For ech smple, we store loction, isovlue, nd normlized grdient vector t lef node of brnch-on-need octree. At ll times, the current ctive set is stored in brnchon-need octree, s re the ctive sets nd the differentils for ech bin. Smples re dded or removed from the current ctive octree by tndem trversl with the octrees for the bins. Insted of single smples, however, we store entire bricks of dt (typiclly 3 3 3) t octree leves, either in linked lists (if no more thn % is ctive) or in rrys (if c The Eurogrphics Assocition 5.

6 H. Younesy, T. Möller & H. Crr / Differentil Time-Histogrm Tble Structure List Octree Octree All Active Sets 1st Active Set λ GB %ge GB %ge GB %ge Isbel - temperture.% % % %.3%. 77% %.7 1% 1.% 15. 3% 1. 5%. % 3.% 1. % 9. 9%.59 1% Isbel - pressure.% % % %.3% % %.9 1% 1.% 13. 9% % 1.9 % 3.% 1. % %.7 15% Turbulent Jets.% 7. 73% 5. 55% 3. 33%.3% 3. 31%. 1%.71 7% 1.%. 55% %. % 3.%. 3% 1. 1%. % Turbulent Vortex Flow.%. 731% 3.7 5%.5 39%.3%. 3% 3. 59%. 3% 1.% %. 5% 1. 5% 3.%. 13%.1 33%.93 15% Tble 1: Size (in GB nd percent of originl dt set) of DTHT using lists nd octrees with ll or only the first ctive set stored. more thn % is ctive). We sve spce by storing smple loctions reltive to the octree cell insted of bsolutely, requiring fewer bits of precision. Moreover, octrees re memory coherent, so updtes re more efficient thn liner lists, lthough t the expense of lrger memory footprint, s shown in Tble 1. We note, however, tht the memory footprint is principlly determined by the size of the octrees for the ctive sets. Further reductions in storge re possible depending on the nture of the queries to be executed. We ssume tht brupt queries re few nd fr between, nd dispense with storing ctive sets explicitly except for the first time step. If n brupt query is mde t time t, we cn construct the ctive set by strting with the corresponding ctive set t time nd pplying ll differentil sets up to time t. Doing so reduces the mount of storge required even further, s shown in the third column of Tble 1. As with the isovlue differentils, we indicte this in Figure 3 by displying the unused ctive sets in lighter shde. We cn lso store ctive sets in subset of priorily chosen keyfrmes so tht we lwys strt from the nerest keyfrme insted of strting from the first frme. Another wy of reducing the storge is to remove the ctive sets nd differentils for the non-interesting isovlue rnges (e.g. the empty spces) which cn hve huge impct depending on the nture of the dtset. 5.. Queries in the DTHT For ny query, we first clssify the query s grdul ( smll chnge) or brupt ( lrge chnge): s noted in Section, we expect the nture of user interction with the dt will cuse most queries to be grdul in nture rther thn brupt. We chose to implement volume rendering using pointbsed spltting, in which the ctive set consists only of those smples for which the opcity is non-zero. This ctive set my spn multiple DTHT cells, s shown in Figure, in which cse we use the union of the ctive sets for ech DTHT cell. It is lso possible to use other volume rendering methods s long s they low runtime updte of the dt. For instnce, hrdwre texture slicing would be suitble only if the hrdwre llows texture updtes without requiring to lod the whole texture for ech updte. Abrupt queries re hndled by discrding the existing ctive set nd reloding the ctive set from the corresponding bin or bins on disk. Becuse the dt ws binned, the ctive set is over-estimted for ny given trnsfer function. This is conservtive over-estimte which includes the desired ctive set, but is sensitive to the size of the bin. Too few bins leds to lrge numbers of discrds for prticulr query, while too mny bins leds to overhed in dt structures nd overhed in merging octrees. Isovlue TF Opcity Time Active DTH Cells Figure : Active DTHT Cells For Given Trnsfer Function. Grdul queries in the temporl direction edit the ctive set using differentils for ech bin spnned by the trnsfer function. Since forwrds nd bckwrds differentils re inverse, we only store on ech rrow the set of smples tht needs to be dded in tht direction. The set of smples tht needs to be removed is then the set of smples stored on the opposite-direction rrow between the sme two bins. Grdul queries in the isovlue direction discrd ll smples in bin when the trnsfer function no longer spns tht bin, nd dd ll smples in bin when the trnsfer function first spns tht bin. It should be noted tht rndom ccess to voxels in our octree bsed dt structure is not efficient since it requires top down trversing of ll octrees for to ccess the voxel. Hence, visulizing multimodl dt would be generlly difficult. We hve ddressed tht in our future work. For fster rendering, prtil imges for ech bse level c The Eurogrphics Assocition 5.

7 H. Younesy, T. Möller & H. Crr / Differentil Time-Histogrm Tble block in the current ctive octree re stored, s in the TSP tree [SCM99]. Since we updte bse level blocks in the octree only when chnges exceed the λ-bound, these prtil imges often survive two or more time steps.. Results nd Discussion We implemented our differentil temporl histogrm tble lgorithm nd visulized different sclr time-vrying dtsets introduced in Section, using 3.GHz Intel Xeon processor, GB of min memory nd n nvidi AGP x GeForce grphics crd, with dt stored on fileserver on 1Mb/s Locl Are Network. In our experiments we used b = 1 isovlue bins, set the bse-level brick size in the octrees to 3x3x3, nd tested four different vlues for error bounds (λ = %,.3%,1.%,3.%). In our first experiment we controlled the number of ctive voxels by chnging the trnsfer function width (the rnge of non-trnsprent dt vlues). Strting with % width trnsfer function covering no bins, we incresed the width until ll dt vlues were clssified s non-trnsprent nd ll bins were loded. The top three rows of the figures in the color plte show representtive imges under this scenrio. In Figure 5, we compre the performnce of DTHT ctive sets lone with the performnce of DTHT ctive nd differentil sets, rendering ech dt set with n error bound of λ = 1.% nd trnsfer functions of vrying widths. The performnce is principlly driven by the width of the trnsfer function, nd it is cler tht significnt speed gin in loding the dt cn be chieved with the differentil sets. Totl Rendering Cost (seconds) Totl Rendering Cost (seconds) DTHT direct loding DTHT differentil updting histogrm 1 Trnsfer function width (%) () Isbel - Temperture DTHT direct loding DTHT differentil updting histogrm 1 Trnsfer function width (%) (c) Turbulent Jets Cumultive sum of histogrm (%) Cumultive sum of histogrm (%) Totl Rendering Cost (seconds) Totl Rendering Cost (seconds) DTHT direct loding DTHT differentil updting histogrm 1 Trnsfer function width (%) 1 (b) Isbel - Pressure 1 1 DTHT direct loding DTHT differentil updting histogrm 1 Trnsfer function width (%) Figure 5: λ = 1.% Rendering nd dt loding performnce for DTHT using ctive nd differentil files. The reported times re verged over multiple time steps. We next investigted the performnce of our lgorithm for different isovlue rnges, collecting the sme mesurements Cumultive sum of histogrm (%) Cumultive sum of histogrm (%) s before for constnt width (1%) trnsfer functions with different plcements. The bottom three rows of the figures in the color plte show representtive imges under this scenrio. The results for λ = 1.% nd different dt sets re shown in Figure. Totl Rendering Cost (seconds) Totl Rendering Cost (seconds) DTHT direct loding DTHT differentil updting histogrm 1 Plcement of 1% width trnsfer function () Isbel - Temperture DTHT direct loding DTHT differentil updting histogrm 1 Plcement of 1% width trnsfer function (c) Turbulent Jet Convolved histogrm (%) Convolved histogrm (%) Totl Rendering Cost (seconds) Totl Rendering Cost (seconds) DTHT direct loding DTHT differentil updting histogrm 1 Plcement of 1% width trnsfer function (b) Isbel - Pressure 1 1 DTHT direct loding DTHT differentil updting histogrm 1 Plcement of 1% width trnsfer function Figure : λ = 1.% Performnce for DTHT using ctive nd differentil files, showing lso the rtio of ctive voxels to ll voxels (in yellow). A trnsfer function spnning 1% of the dt rnge ws used with different centre points. Results re verged over severl time steps. To simplify comprison, we clculted the rtio between the differentil DTHT updtes nd direct DTHT updtes for both sets of experiments. Since the gol of this pper ws to improve the loding times, we excluded rendering time from our figures. The gol ws to investigte the cses in which updting the octree using differentil files were fster thn strightforwrd loding of the ctive files. Figure 7 nd Figure show the rtio between the performnce of the two methods, respectively for different width trnsfer function nd constnt width trnsfer function. In third experiment we investigted performnce for fixed time but vrying trnsfer function. Compred to the brute-force method, where ll of the dt is loded, our method tkes dvntge of the rendering prmeters to lod only the voxels prticipting in the finl rendering. Chnging the trnsfer function cused new bins to be dded to or removed from the dt set. The results re shown in Figure 9. Loding time of DTHT methods depends gretly on the mount of ctive voxels. In both experiments, when smll number of voxels re ctive, loding the octree directly from the ctive files is comprtively fster thn using the differentil files. It is minly becuse of the fct tht loding the octree directly from the ctive_voxels files, requires going through the octree only once per ech bin, while in the differentil method, it will be twice per ech bin; once to remove the invlid voxels, using voxels_to_remove files nd then to Convolved histogrm (%) Convolved histogrm (%) c The Eurogrphics Assocition 5.

8 H. Younesy, T. Möller & H. Crr / Differentil Time-Histogrm Tble rtio of direct loding to differentil updting λ=% λ=.3% λ=1.% λ=3.% 15 rtio = 1 histogrm Trnsfer function width (%) () Isbel - Temperture Cumultive sum of histogrm (%) rtio of direct loding to differentil updting λ=% λ=.3% λ=1.% λ=3.% 15 rtio = 1 histogrm Trnsfer function width (%) (b) Isbel - Pressure Cumultive sum of histogrm (%) Time (ms) resizing trnsfer function moving trnsfer function 1 Bins () Isbel - Temperture Time (ms) resizing trnsfer function moving trnsfer function 1 Bins (b) Isbel - Pressure rtio of direct loding to differentil updting λ=% λ=.3% λ=1.% λ=3.% rtio = 1 histogrm 1 Trnsfer function width (%) (c) Turbulent Jet Cumultive sum of histogrm (%) rtio of direct loding to differentil updting λ=% λ=.3% λ=1.% λ=3.% rtio = 1 histogrm 1 Trnsfer function width (%) Cumultive sum of histogrm (%) Time (ms) resizing trnsfer function moving trnsfer function 1 Bins (c) Turbulent Jets Time (ms) resizing trnsfer function moving trnsfer function 1 Bins Figure 7: Rtio between DTHT differentil updting time nd DTHT direct loding time for different error bounds, for different trnsfer function widths. Figure 9: Loding time of incrementl trnsfer function chnges. rtio of direct loding to differentil updting rtio of direct loding to differentil updting λ=% λ=.3% λ=1.% λ=3.% rtio = 1 histogrm 1 Plcement of the 1% width trnsfer function () Isbel - Temperture λ=% λ=.3% λ=1.% λ=3.% rtio = 1 histogrm 1 Plcement of the 1% width trnsfer function (c) Turbulent Jet Convolved histogrm (%) Convolved histogrm (%) rtio of direct loding to differentil updting rtio of direct loding to differentil updting λ=% λ=.3% λ=1.% λ=3.% rtio = 1 histogrm 1 Plcement of the 1% width trnsfer function 1 (b) Isbel - Pressure 1 1 λ=% λ=.3% λ=1.% λ=3.% rtio = 1 histogrm 1 Plcement of the 1% width trnsfer function Figure : Rtio between DTHT differentil updting time nd DTHT direct loding time for different error bounds nd different plcements of trnsfer function of constnt width (1%). dd the new voxels using voxels_to_dd files. Hence, memory ccess time nd octree processing time overcomes the files trnsction time when smll mounts of dt re red from the hrd drive. As the number of ctive voxels increses, more dt need to be loded/updted from the externl storge. Hence, the memory-storge trnsctions become the bottleneck. Since there re reltively few dt in the differentil files, the performnce of updting the octree using the differentil files becomes better thn the direct loding. However, the rtio of this performnce highly depends on the temporl coherence Convolved histogrm (%) Convolved histogrm (%) of the dt set. For exmple since the Turbulent Vortex Flow dt set isn t s temporlly coherent s the other three dt sets, even with 1.% error bound, the differentil updting is slower thn the direct loding nd tht s simply becuse the number of voxels_to_dd + voxels_to_remove is lrger thn the ctul mount of ctive_voxels. Noise in the digrms re minly due to loding the dt through locl re network connection which is fst, but does not lwys provide constnt dt rte. There re lso lrge vritions in some prts of Figure 7 nd Figure. It cn be seen tht the noise is mostly in the prts in which not mny voxels re ctive. This is becuse of the fct tht, s the loding times become smller, they become more error prone to be ffected by slightest ctivities in the hrdwre or the operting system. 7. Conclusion nd future work Efficient explortion nd visuliztion of lrge time-vrying dt sets is still one of the chllenging problems in the re of scientific visuliztion. In this pper we studied the temporl coherence of sequentil times nd histogrm nd sptil distribution of dt in time-vrying dt sets nd proposed new dt structure clled differentil time histogrm tble (DTHT) to tke dvntge of these chrcteristics to efficiently lod nd render time-vrying dt sets. In preprocessing step, we encode the temporl coherence nd histogrm distribution of the dt in the DTHT dt structure. Lter, during the visuliztion step, we use this differentil informtion to ccelerte updting dt by minimizing the mount of dt tht needs to be trnsfered from disk into min memory. To store the dt in externl storge nd to keep the ctive dt in min memory, we use c The Eurogrphics Assocition 5.

9 H. Younesy, T. Möller & H. Crr / Differentil Time-Histogrm Tble n octree dt structure which ccelertes loding nd processing dt by exploiting sptil distribution. The work presented in this pper ws minly focused on nlyzing the sttisticl chrcteristics of lrge dtsets to reducing the dt trnsfer between memory nd externl storge during the visuliztion process. We re plnning to further improve performnce by pplying compression schemes for the dt in lef nodes nd dding multi-level informtion to the sub-levels of the dt structure to enble multiresolution renderings. Currently the rendering time is dominting the overll time to produce n imge. This is due to the fct, tht the rendering lgorithm hs not been optimized t this point. We pln to tke dvntge of the octree dt structure for hierrchicl rendering of our dt in our next implementtion. Imge cching, occlusion culling nd prllel rendering will further drsticlly improve the rendering performnce. Our future work includes pplying proper modifictions to DTHT in order to enble the extrction of isosurfces nd to hndle multi-modl dtsets, investigting methods to chnge the error bounds (λ) during run time bsed on the user control nd the trnsfer funtion nd methods to del with multi-dimensionl trnsfer functions. References [CMM 97] CIGNONI P., MARINO P., MONTANI C., PUPPO E., SCOPIGNO R.: Speeding Up Isosurfce Extrction Using Intervl Trees. IEEE Trnsctions on Visuliztion nd Computer Grphics 3, (1997), [CSS9] CHIANG Y.-J., SILVA C. T., SCHROEDER W. J.: Interctive out-of-core isosurfce extrction. In Proceedings of IEEE Visuliztion 9 (199), pp [CVCK3] CHHUGANI J., VISHWAMANTH S., COHEN J., KUMAR S.: Isoslider: A system for interctive explortion of isosurfces. In Proceedings of Eurogrphics Visuliztion Symposium 3 (3), pp. 59, 3. 3 [Gl91] GALLAGHER R. S.: Spn Filtering: An Optimiztion Scheme For Volume Visuliztion of Lrge Finite Element Models. In Proceedings of Visuliztion 1991 (1991), IEEE, pp [LC7] LORENSEN W. E., CLINE H. E.: Mrching cubes: A high resolution 3d surfce construction lgorithm. ACM SIGGRAPH Computer Grphics 1, (July 197), [LSJ9] LIVNAT Y., SHEN H.-W., JOHNSON C. R.: A Ner Optiml Isosurfce Extrction Algorithm Using the Spn Spce. IEEE Trnsctions on Visuliztion nd Computer Grphics, 1 (199), [MS] MA K.-L., SHEN H.-W.: Compression nd ccelerted rendering of time-vrying volume dt. In Workshop on Computer Grphics nd Virtul Relity, Intl. Computer Symposium (). 3 [OM1] ORCHARD J., MÖLLER T.: Accelerted Spltting Using 3D Adjcency Dt Structure. In Proceedings of Grphics Interfce 1 (1), pp [RHP] REINHARD E., HANSEN C. D., PARKER S.: Interctive ry trcing of time vrying dt. In Proceedings of the Fourth Eurogrphics Workshop on Prllel Grphics nd Visuliztion (), pp [SBS] SOHN B.-S., BAJAJ C., SIDDAVANAHALLI V.: Feture bsed volumetric video compression for interctive plybck. In Proceedings of IEEE Symposium on Volume Visuliztion nd Grphics (), pp [SCM99] SHEN H.-W., CHIANG L.-J., MA K.-L.: A fst volume rendering lgorithm for time-vrying fields using time-spce prtitioning (tsp) tree. In Proceedings of IEEE Visuliztion 99 (1999), pp , 7 [SH99] SUTTON P., HANSEN C. D.: Isosurfce extrction in time-vrying fields using temporl brnch-onneed tree (t-bon). In Proceedings of IEEE Visuliztion 99 (1999), pp , 3 [She9] SHEN H.-W.: Isosurfce extrction in timevrying fields using temporl hirrchicl index tree. In Proceedings of IEEE Visuliztion 9 (199), pp [SJ9] SHEN H.-W., JOHNSON C. R.: Differentil volume rendering: fst volume visuliztion technnique for flow nimtion. In Proceedings of IEEE Visuliztion 9 (199), IEEE Computer Society Press, pp [WG9] WILHELMS J., GELDER A. V.: Octrees for fster isosurfce genertion. ACM Trnsctions on Grphics 11, 3 (July 199), , 3 [WMW] WYVILL G., MCPHEETERS C., WYVILL B.: Dt structure for soft objects. Visul Computer (19), 7 3. [WTTL9] WAN M., TANG L., TANG Z., LI X.: Pcbsed quick lgorithm for rendering semi-trnsprent multi-isosurfces of volumetric dt. In Proceedings of Visuliztion 199 (199), pp c The Eurogrphics Assocition 5.

10 H. Younesy, T. Möller & H. Crr / Differentil Time-Histogrm Tble Figure 1: Rendered Imges with representtive trnsfer functions. Displyed re six rows of ech dt set - (left to right) Isbel temperture, Isbel pressure, Turbulent Jets nd Turbulent Vortex Flow. The top three rows show growing trnsfer functions, nd the bottom three rows show shifting trnsfer functions, corresponding to our experiments in this section. c The Eurogrphics Assocition 5.