An Improved HVQ Algorithm for Compression and Rendering of Space Environment Volume Data with Multi-correlated Variables.pdf

VolintBA(Chin.J.SpaceSci.空间科学学报0254-6124/2023/43(4)-0780-060 Lili,CAI Yanxia,WANG Rui,ZOU Yenan,SHI Liqin.An Improved HVQ Algorithm for Compression and Rendering of Space Environmeume Data with Multi-correlated Variables.Chinese Journal of Space Science,2023,43(4):780-785.D0I:10.11728/cjss2023.04.2022-0020An Improved HVQ Algorithm for Compression andRendering of Space Environment Volume Datawith Multi-correlated Variables*1,2BAO Lilil,2CAI YanxiaWANG Ruil2.31,2SHI Liqin,1,2,3ZoU Yenan1(State Key Laboratory of Space Weather,National Space Science Center,Chinese Academy of Sciences,Beijing 100190)2(Key Laboratory of Science and Technology on Environmental Space Situation Awareness,Chinese Academy of Sciences,Beijing 100190)3(University of Chinese Academyof Sciences,Beijing 100049)Abstract Volume visualization can not only illustrate overall distribution but also inner structure and it is animportant approach for space environment research.Space environment simulation can produce several correlatedvariables at the same time.However,existing compressed volume rendering methods only consider reducing theredundant information in a single volume of a specific variable,not dealing with the redundant information amongthese variables.For space environment volume data with multi-correlated variables,based on the HVQ-1d methodwe propose a further improved HVQ method by compositing variable-specific levels to reduce the redundant infor-mation among these variables.The volume data associated with each variable is divided into disjoint blocks of size4 initially.The blocks are represented as two levels,a mean level and a detail level.The variable-specific meanlevels and detail levels are combined respectively to form a larger global mean level and a larger global detail level.To both global levels,a splitting based on a principal component analysis is applied to compute initial codebooks.Then,LBG algorithm is conducted for codebook refinement and quantization.We further take advantage of pro-gressive rendering based on GPU for real-time interactive visualization.Our method has been tested along withHVQ and HVQ-1d on high-energy proton flux volume data,including 5,10,30 and 50 MeV integratedproton flux.The results of our experiments prove that the method proposed in this paper pays the least cost of qual-ity at compression,achieves a higher decompression and rendering speed compared with HVQ and provides satis-ficed fidelity while ensuring interactive rendering speed.Key words Compressed volume rendering,Multi-correlated variables,Space environment,Vector quantization,GPU programmingClassifiedindexP3530IntroductionVolume visualization can not only illustrate overall dis-tribution but also inner structure and it is an importantapproach for space environment researchl-3.By meansof programmability in graphics hardware,real-time in-*Supported by the Key Research Program of the Chinese Academy of Sciences(ZDRE-KT-2021-3)Received May 11,2022.Revised December 1,2022E-mail:CThe Author(s)2023.This is an open access article under the CC-BY 4.0 License(https:/creativecommons.org/licenses/by/4.0)781BAO Lili et al.:An Improved HVQ Alggorithm for Compression and Rendering of.teractive large-scale volume rendering can be rea-lizedl1-4.With the development of space environmentexplorations5 and physical models,scientists can simu-late many space environment situations in detail,eachsimulation producing several variables,hundreds of timesteps and millions of voxels.Because of the limitedmemory capacity,it is difficult to render such large vol-ume data on GPU directly.Vector Quantization(VQ)l,as a Compressed Volume Rendering(CVR)methodl7),can reduce the volume data set to a significantly smallersize and support decompressing at rendering time.Be-cause of the simple,localized and uniform decoding,VQhas been widely applied in many domaisl.8.ierar-chical Vector Quantization(HVQ)is one of the mostcommon VQ methods and can achieve high reconstruc-tion quality,however at the cost of a low compressionratel29-1,Therefore,Hierarchical ector QuantizationWith 1 Detail Level(HVQ-1 d)is proposed to raise thecompression rate while maintaining good fidelity basedon the variation characteristics of space environment.However,these methods just reduce the redundant infor-mation in each volume of each variable.Most space en-vironment simulations can generate several correlatedvariables,such as particle flux values of different chan-nels,density values of different atmospheric compo-nents,etc.There must be massive similar variations orredundant information among these variables.Based onthese,a further improved HVQ algorithm,HierarchicalVector Quantization based on multi-correlated variables(HVQ-mv),is described in this paper.This paper is organized into five sections.In thefollowing section,related works are reviewed.In Sec-tion 2,our improved HVQ algorithm is described.InSection 3,the experiments are introduced,and the re-sults and comparisons are presented.In the last section,aconclusion has been drawn for our paper.1Related WorksVQ technology has been introduced in CVR by Ningand Hesselinkl6.8 Firstly,the entire volume is dividedinto disjoint blocks of nxmxk.Then by vector quantiza-tion,a codebook is generated and these blocks are re-placed by indices in this codebook.This method can ob-tain a high compression rate,however,at the cost of badreconstructionquality.1.1HVQHVQ was proposed by Schneider and Westerman to im-prove the reconstruction quality of vQ29-1.specifical-ly,the volume data set is partitioned into separate blocksof size 43 initially.Then by down-sampling and differ-ence calculation,each block is decomposed into a three-level representation,one mean level and two detail lev-els.An appropriate mapping and an associated code-book are produced for each detail level,by vector quan-tization.During quantization,by applying simple thresh-olding to each detail level,many difference vectors canbe mapped to zero vector directly.In this way,the num-ber of codewords used to present significant non-zerovectors can be maximized and further improve the fideli-ty.HVQ can obtain high reconstruction quality,howev-er,sacrificing compression rate.1.2HVQ-1 dConsidering the significantly positive correlation be-tween space environment variations in the same direc-tion at two different scales,Bao et al.l had theoretical-ly and experimentally proved the low utilization rate ofcodeword combinations and it is unnecessary to use twodetail levels when HVQ is applied to space environmentdomain.Then Bao et al.l proposed HVQ-1 d whichcombines two detail levels in HVQ.By HVQ-1 d,eachblock of size 43 which is partitioned from the entire vol-ume is decomposed to a mean value and a 64-compo-nent difference vector and presented as two levels,amean level and a detail level.An appropriate vectorquantizer is chosen and applied to the detail level,andeach difference vector is replaced by the index in thecodebook.Compared with HVQ,HVQ-1 d can achievea higher compression rate and faster decoding speedwithout sacrificing fidelity.Above methods only consider reducing the redun-dant information in a single volume of a specific vari-able.However,most space environment simulations pro-duce multi-correlated variables at the same time.Thereare similar distribution patterns and variation character-istics among these variables.Therefore,this paper pro-poses HVQ-mv,which not only reduces the redundantinformation in a single volume of a variable,but alsodeals with the redundant information among these corre-latedvariables.7822023,43(4)Chin.J.SpaceSci.空间科学学报2Hierarchical Vector QuantizationBased on Multi-correlated Variables2.1Basic Idea and FrameworkBased on HVQ-1 d,our method further incorporates thecompression among multi-correlated variables for spaceenvironment volume data.The framework of HVQ-mvis illustrated in Figure 1.Starting with space environ-ment volume data and each voxel containing n correlat-ed variable samples,the data associated with each vari-able is divided into disjoint blocks of size 43 initially.For each block,the difference between the mean valueand original data samples is stored in a 64-componentdetail vector.The blocks are represented as two levels,amean level and a detail level.The variable-specific meanvalues and detail vectors associated with n blocks at thesame position are composited and stored in an n-compo-nent mean vector and a 64xn-component detail vector.In this way,variable-specific mean levels and detail lev-els are combined respectively to form a larger globalmean level and a larger global detail level.By means ofVQ,appropriate mappings and codebooks containing n-and 64xn-component codewords are generated for bothglobal levels.LBG algorithmu2l,as one of the mostcommon vector quantization algorithms,is conductedfor codebook refinement and quantization.A splittingbased on a principal component analysis(PCA-split)isapplied to compute initial codebooks for LBG.2.2CompressionFor a volume data set of size nxIxJxK(n variables,thevolume of size IxJxK),assume that each sample isstored in B Byte,the indices into each codebook need1 byte respectively,the length of each codebook is C,and each component in each codeword holds 1 Byte.The compression rate of HVQ-mv can be computed bynXIxJxKxBRcompresion=2IJK/43+Cn64+Cn(1)With the same codebook length,the compressionrate of our method is significantly higher than that ofHVQ and HVQ-1 d(for the compression rate of HVQand HVQ-1 d refer to Referecnce 1,10).Bits per voxeland can be computed by(2IJK/43+Cn64+Cn)8Rbits/oxel=IxJxK(2)2.3Decompression and RenderingThe decompression is coupled with rendering on GPU.To reconstruct a sample for a specific variable,firstly getthe indices of the block that contains the sample.Thenlook up the codebooks to obtain corresponding code-words according to the indices,and get the mean valueand difference value with reference to the storage orderof variables and relative positions in the block.Finally,add the mean value and difference value,and get the re-constructed value.Our method can support progressiverenderingl-7.Fr real-time interactive olume visualiadetaildetailhierarchicalvariable16363decompositionnmeanmeandetaildetailhierarchicalvariable163631decompositionmeanmeandetaildetailhierarchicalvariable01163630decompositionmeanmeanblocks of size 43combinationcombinationdetaildetailVQindices.ofthe0630630163630163063detail levelmeanmeanVQ indices.ofthemean levelFig.1Framework of HVQ-mvBAOLilietal.:AnImporovedHQAlggorithm for Compression and Rendering of.783tion,during the interaction,we only use mean values toreconstruct an approximation for quick browsing,andwhen the interaction stops,we can fully reconstruct toreveal more details.3Results and ComparisonSolar Proton Events(SPE)13 caused by solar activitiesare threats to space missions,because they can lead tothe enhancement of high-energy radiation,furthermoreaffecting the condition of spacecraft and the safety of as-tronauts.Therefore,in the process of space missions,de-cision-makers need to comprehend the distribution ofhigh-energy proton flux.Proton radiation simulation cangenerate several proton flux variables associated withdifferent channels and these variables are positively cor-related.Thus,we test our method along with HVQ andHVQ-1 d on high-energy proton flux data.All experiments in this paper are compiled and rununder Windows 10 on a 1.80 GHz Intel CoreTM i7-8550U CPU with 20.0GB main memory and anNVIDIA Quadro P500.The high-energy proton flux inthe radiation belt at 00:00 UTC,1 March 2022 is pro-duced by AP8 model to test these methods and abbrevi-ated as Proton Radiation Belt(PRB).The size of PRB is4x200200100,4 variables(5 MeV,10 MeV,30 MeV and 50 MeV integrated proton flux)and thevolume of size 200 x200100.The samples are scaledto 0 255 by normalization and each one is stored in1 byte.3.1CompressionResults and ComparisonAs is common in compression,bits per voxel are used tomeasure the rate and Peak Signal-to-Noise Ratio(PSNR)to measure the distortion.The larger PSNR,the less dis-tortion and the higher the reconstruction quality.the rateis varied by adjusting the sizes of codebooks.These re-sults are shown in Figure 2.The rate-distortion curve with HVQ-mv achievesan increase over HVQ-1 d.As we expect,HVQ-mv hasan obvious quality advantage compared with HVQ-1 d,because it can reduce the redundancy information causedby the significant positive correlation among these vari-ables.Correlation coefficients between 10 and 5,30,50 MeV flux are 0.92,0.88,and 0.78 respectively.Both HVQ-mv and HVQ-1 d significantly outperformHVQ,because HVQ-mv and HVQ-1 d extra considerthe spatial variation characteristics of the space environ-mentl.For each curve,as the bits for each voxel in-crease,the reconstruction quality increases.When PSNRreaches 40.0 dB,the MSE is around 6.5.This paper fur-ther compares the reconstruction quality of HVQ,HVQ-1 d and HVQ-mv at rates 0.89,0.88 and 0.78.The asso-ciated points are labeled as triangles in Figure 2,andFigure 3 to 6 illustrate the renderings of the correspond-ing compressed volumes.As in Figure 2 and Figure 3 to 6,although the bitsper voxel rate of HVQ-mv is lower than that of HVQand that of HVQ-1 d,HVQ-mv achieves the best qualityin all variables.Thus HVQ-mv pays the least cost ofquality at compression.HVQ-1 d also still outperformsHVQ.The corresponding compression time is 6.27,21.77 and 341.91 s for HVQ,HVQ-1 d and HVQ-mv re-spectively.The compression of HVQ-mv is the slowest,but that is acceptable since the compression is per-formed once ffliel.45HVQHVQ-1d HVQ-mV4035300.250.500.751.001.251.50Rate/(bit:voxelrl)Fig.2 Rate-distortion curves for all variables of PRB withHVQ,HVQ-1 d and HVQ-mv(Triangles label the points ofHVQ,HVQ-1 d and HVQ-mv at rates 0.89,0.88 and 0.78)Original data(a)HVQ(b)HVQ-1d(c)HVQ-mv(d)10-1105Proton flux/(cm-2.sl.srl)Fig.3Compression quality comparison of rendering5 MeV flux of PRB using HVQ,HVQ-1 d and HVQ-mv7842023,43(4)Chin.J.SpaceSci.空间科学学报Original data(a)HVQ(b)HVQ-1d(c)HVQ-mv(d)10-1105Proton flux/(cm-2.s-l.sr-l)Fig.4Compression quality comparison of rendering10 MeV flux of PRB using HVQ,HVQ-1 d and HVQ-mvOriginal data(a)HVQ(b)HVQ-1d(c)HVQ-mV(d)10-1105Proton flux/(cm-.s-l.sr-l)Fig.5 Compression quality comparison of rendering30 MeV flux of PRB using HVQ,HVQ-1 d and HVQ-mv3.2DecompressionandRenderingResultsandComparisonRendering is applied directly from the compressed vol-umes based on GPU.All our examples are rendered us-ing nearest neighbour interpolation,because linear inter-polation within the codebook is not possible.Renderingresults are referred to Figure 3 to 6.Frame rate is used tomeasure the rendering efficiency and the results areshown in Figure 7.Compared with HVQ,both HVQ-mv and HVQ-1 dachieve higher frame rates due to fewer levels of repre-sentation and less dependent texture reads.The decom-pression and rendering speed of HVQ-mv is slightlylower than that of HVQ-1 d.Because