TRLE An Efficient Data Compression Scheme for Image Composition of Parallel Volume Rendering Systems

Transcription

1 TRLE An Effcent Data Compresson Scheme for Image Composton of Parallel Volume Renderng Systems Chn-Feng Ln, Yeh-Chng Chung, and Don-Ln Yang Department of Informaton Engneerng Feng Cha Unversty, Tachung, Tawan 47, R.O.C. E-mal: {cfln, ychung, Abstract In ths paper, we present an effcent data compresson scheme, the template run-length encodng (TRLE) scheme, for mage composton of parallel volume renderng systems. Gven an mage wth 2n 2n pxels, n the TRLE scheme, the mage s treated as n n blocs and each bloc has 2 2 pxels. Snce a pxel can be a blan or non-blan pxel, there are templates n a bloc. To compress an mage, the TRLE scheme uses the templates to encode blocs row by row. Blocs n the same row are encoded as a TRLE_sequence. By pacng all TRLE_sequences n a pacet, the pacet s the compressed partal mage that can be sent/receved among processors. To evaluate the performance of the TRLE scheme, we compare the proposed scheme wth the BR, the RLE, and the BRLC schemes. Snce a data compresson scheme needs to cooperate wth some data communcaton schemes, n the mplementaton, the bnary-swap (BS), the parallel-ppelned (PP), and the rotate-tlng (RT) data communcaton schemes are used. By combnng the four data compresson schemes wth the three data communcaton schemes, we have twelve mage composton methods. These twelve methods are mplemented on a PC cluster. The data computaton tme and the data communcaton tme are measured. The expermental results show that the TRLE data compresson scheme wth the RT data communcaton scheme outperforms other eleven mage composton methods. Keyword: mage composton, boundng rectangle, run-length encodng, template run-length encodng, parallel volume renderng systems.. Introducton Volume renderng [2] can be used to analyze the shape and volumetrc property of three-dmensonal objects n research areas such as medcal magng and scentfc vsualzng. However, most volume renderng methods that produce effectve vsualzatons are computaton ntensve. It s dffcult for them to acheve nteractve renderng rates for large datasets. In addton, volume datasets are too large to be stored n the memory of a sngle processor. One way to solve the above problems s to parallelze the seral volume renderng methods [2]. A parallel volume renderng system [8], n general, conssts of three stages; the data partton stage, the data render stage, and the mage composton stage. In the data partton stage, the volume dataset s parttoned nto sub-volumes by an effcent data parttonng method and the sub-volumes are dstrbuted to processors. In the data render stage, each processor uses a volume renderng algorthm on the assgned sub-volume to generate a partal mage. In the mage composton stage, the partal mages generated by processors are composted to form a fnal mage []. When the number of processors s large, the mage composton stage becomes a bottlenec of a parallel volume renderng system. Hence, a good mage composton method s very mportant to the performance of a parallel volume renderng system. In general, there are two ways to mprove the performance of mage composton of parallel volume renderng systems []. One s to use an effcent data communcaton scheme to mnmze the data communcaton overheads n sendng and recevng the partal mages of processors. The other s to use an effcent data compresson scheme to reduce the communcaton szes of partal mages. The reasons for usng a data compresson scheme are two-folds. Frst, a partal mage may contan many blan pxels. These blan pxels are useless n mage composton. If we can flter out these blan pxels n some ways, the sze of a partal mage can be reduced, that s, the data transmsson tme among processors can be reduced. Second, f we can flter out blan pxels of a partal mage, the number of over operatons spent on these blan pxels for composton can be elmnated. By reducng the data communcaton sze of a partal mage, the overall mage composton tme can be mproved. In ths paper, we focus on fndng an effcent data compresson scheme for mage composton. The boundng rectangle (BR) and the run-length encodng (RLE) are two well-nown data compresson schemes used n computer graphcs [3]. They are also used n the mage composton of a parallel volume Proceedngs of the Frst Internatonal Symposum on Cyber Worlds (CW 2) /2 $7. 22 IEEE

2 renderng system [9] [3]. Ma et al. [9] used the BR scheme for data compresson. In [9], the BR scheme uses a boundng rectangle to embrace the non-blan pxels of the partal mage of a processor. The mage composton usng the BR scheme conssts of three steps. Assume that processor needs to composte the partal mages of P and. In the frst step, the boundng rectangle to embrace the non-blan pxels of the partal mage of P s formed. P then sends pxels n the boundng rectangle to by a data communcaton scheme n the second step. In the thrd step, uses the over operaton to composte the pxels n the sent boundng rectangle wth the pxels of ts partal mage. An example of the mage composton usng the BR scheme s gven n Fgure. P P (a) Partal mages (b) P sends ts BR to Fgure. An example of the BR scheme If there are many blan pxels n a boundng rectangle of a partal mage, the BR scheme may not have good performance. An example of ths case s gven n Fgure 2. In Fgure 2, the boundng rectangle of P s the whole partal mage of P. P needs to send the whole partal mage to. However, only the blac porton of the trangle contans non-blan pxels. Most of pxels n the boundng rectangle that contans the trangle are blan pxels. In ths case, the BR scheme nether reduces the data communcaton sze for P nor reduces the number of over operatons for. P P (a) Partal mages (b) P sends ts BR to Fgure 2. An example of the worst case of the BR scheme Yang et al. [3] used the RLE scheme for data compresson. In [3], the RLE scheme encodes each scanlne of a partal mage. The mage composton usng the RLE scheme conssts of four steps. Assume that processor needs to composte the partal mages of P and. In the frst step, pxels of the partal mage n P are encoded by usng the RLE scheme and the correspondng RLE codes are formed. P then sends the RLE codes and the correspondng non-blan pxels to by a data communcaton scheme n the second step. In the thrd step, decodes the RLE codes to get the partal mage of P. then uses the over operaton to composte the partal mages of P and n the forth step. An example of the mage composton usng the RLE scheme s gven n Fgure 3. P RLE codes Intermedate mage XX XXXX XXXXXX XXXXXXXX XXXXXXXXXX 2 XXXXXXXXXXXX XXXXXXXXXXXXXX 32 () RLE encodng (2) Send RLE codes (3) RLE decodng (4) compostng Fgure 3. An example of the RLE scheme If the non-blan and blan pxels of the partal mage are nterlaced, the RLE scheme s not effcent snce the RLE codes are too large. An example of ths case s gven n Fgure 4. In Fgure 4, the RLE codes are larger than the values of the non-blan pxels, that s, the data sze of the RLE codes s large than that of the partal mage. The data transmsson overhead s ncreased. P RLE encodng X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X Fgure 4. An example of the worst case of the RLE scheme Yang et al. [3] combned the BR and the RLE schemes, denoted as the BRLC scheme, to reduce the data communcaton szes. The BRLC scheme frst uses the BR scheme to fnd a boundng rectangle wth non-blan pxels of a partal mage. The scheme then apples the RLE scheme to encode the pxels n the boundng rectangle. For many cases, the BRLC scheme performs better than the BR and the RLE schemes. However, the BRLC scheme cannot solve the problems presented n Fgure 4 ether. To overcome the dsadvantages of the BR, the RLE, and the BRLC schemes, we propose an effcent data compresson scheme, the template run-length encodng (TRLE) scheme, for mage composton of a parallel volume renderng system. Gven an mage wth 2n 2n pxels, n the TRLE scheme, the mage conssts of n n blocs and each bloc has 2 2 pxels. Snce each pxel s ether a blan or a non-blan pxel, there are sxteen blan/non-blan pxel combnatons n a bloc. We call these sxteen blan/non-blan pxel combnatons as templates. Wth these templates, the TRLE scheme encodes a partal mage bloc by bloc smlar to the RLE scheme. However, the TRLE scheme can flter out or use small space to encode blocs whose four pxels are blan pxels, that s, the TRLE scheme can encode a partal mage accordng to the shape of non-blan pxels. In the TRLE scheme, the bt operatons, and, or, and xor, are used to encode and decode a partal mage. Hence, the TRLE scheme s easy to be mplemented and the tme Proceedngs of the Frst Internatonal Symposum on Cyber Worlds (CW 2) /2 $7. 22 IEEE

3 spent on encodng and decodng s small compared to the overall mage composton tme. An example of the TRLE scheme s gven n Fgure 5. Snce the TRLE scheme can encode a partal mage accordng to the shape of non-blan pxels, t can solve the problems of the BR, the RLE, and the BRLC schemes effcently. For example, for the mage shown n Fgure 5, the data sze compressed by usng the BR, the RLE, the BRLC, and the TRLE schemes s 64 = 24, = 376, = 376, and 32 + = 528 bytes, respectvely (assume that each pxel requres bytes to store values). The data sze compressed by the TRLE scheme s the smallest among these four data compressed schemes. P TRLE encodng 49 X X X X X X X X 2 49 X X X X X X X X pxel. For a pxel n a bloc, t s ether a blan or a non-blan pxel. There are sxteen blan and non-blan pxel combnatons n a bloc. We defne these blan and non-blan pxel combnatons as templates. To represent these templates, 4-bt bnary codes are used. Gven a 4-bt bnary code b 3 b 2 b b, b 3, b 2, b, and b denote the pxel wth label,, 2, and 3 n a bloc, respectvely. The value of b n a 4-bt bnary code s f the correspondng pxel s a blan pxel. Otherwse, b s. The 4-bt bnary codes of the templates are gven n Fgure 7. In Fgure 7, whte squares represent blan pxels whle blac squares represent non-blan pxels. 2 bloc 3 bnary code b 3 b 2 b b 2 3 label order Fgure 6. The label of pxels n a bloc 3 49 X X X X X X X X 4 49 X X X X X X X X Fgure 5. An example of the TRLE scheme template bnary code template bnary code template bnary code template bnary code To evaluate the performance of the TRLE scheme, we compare the proposed scheme wth the BR, the RLE, and the BRLC schemes. Both theoretcal and expermental analyses are conducted. In theoretcal analyss, we analyze the ranges of data compresson rato of these four schemes. By combnng the four data compresson schemes and three data communcaton schemes (the bnary-swap (BS) [9], the parallel-ppelned (PP) [5], and the rotate-tlng (RT) [7] methods), we have twelve mage composton methods. In the expermental, for each method, the data computaton tme and the data communcaton tme are measured on a PC cluster. The expermental results show that the TRLE data compresson scheme wth the RT data communcaton scheme outperforms other mage composton methods. The rest of the paper s organzed as follows. The TRLE scheme wll be presented n Secton 2. In Secton 3, we analyze the ranges of data compresson rato of the TRLE, the BR, the RLE, and the BRLC schemes. In Secton 4, we analyze these 2 mage composton algorthms n terms of the communcaton tme and the computaton tme. In Secton 5, the expermental results of these 2 mage composton methods on a PC cluster wll be dscussed. 2. The TRLE data compresson scheme Gven an mage wth 2n 2n pxels, n the TRLE scheme, the mage s treated as n n blocs and each bloc has 2 2 pxels. Pxels n a bloc are labeled as shown n Fgure 6. A pxel of an mage s a blan pxel f ts value s less than a threshold. Otherwse, t s a non-blan Fgure 7. The 4-bt bnary codes of templates Gven an mage conssts of n n blocs and each bloc has 2 2 pxels, to compress the mage, the TRLE scheme uses the templates to encode blocs row by row. Blocs n the same row are encoded as a TRLE_sequence (wll be defned later). By pacng all TRLE_sequences n a pacet, the pacet s the compressed mage that can be sent/receved among processors. We have the followng defntons. Defnton : A template_code s an 8-bt long code. In a template_code, the lower four bts represent the bnary code of a template. The upper four bts represent the repetton of the template specfed n the lower four bts. A template_code can represent up to 5 replcaton of a template. An example of a template_code s gven n Fgure 8. In Fgure 8, the template_code s "2A". It means that two consecutve blocs are the same bloc and are encoded by template "". repetton bnary code template_code b 7 b 6 b 5 b 4 b 3 b 2 b b 2A One Byte two blocs Fgure 8. An example of a template_code Proceedngs of the Frst Internatonal Symposum on Cyber Worlds (CW 2) /2 $7. 22 IEEE

4 Defnton 2: A TRLE_code conssts of a template_code and the values of non-blan pxels n a template. The number of bytes to store the values of a pxel depends on the volume data used. For the volume data used n ths paper, each pxel s represented by bytes. An example of TRLE_code s gven n Fgure 9. In Fgure 9, the template_code of the TRLE_code s "2A". It means that two consecutve blocs are the same bloc and are encoded by template "". In template "", pxels wth labels and 2 are non-blan pxels. The frst bytes followed the template_code n the TRLE_code store the values of non-blan pxel P, the next bytes store the values of non-blan pxel P 2 followed by the values of P 3 and P 4. TRLE_pacet contans the four TRLE_seqences. Form the TRLE_seqences shown n Fgure, we can see that the TRLE scheme can encode an mage accordng to the shape of non-blan pxels n the mage. For example, the blan pxels outsde the trangle are fltered out n the TRLE_seqences. For blan pxels nsde the trangle, they are only encoded by template_codes. Therefore, n general, the TRLE scheme can have better compresson rato compared wth the BR, the RLE, and the BRLC schemes. ndex TRLE_code TRLE_code TRLE_code TRLE_code TRLE_code 2 5 P P 2 2A P 3 P 4 P 5 P 6 F P 7 P 8 P 9 P 8 P 2A P 2 P 3 P 4 P 5 TRLE_sequence Row P P 3 P 5 P 7 P 9 P P 2 P 4 end P 2 P 4 P 6 P 8 P P 3 P 5 TRLE_code 2A P P 2 P 3 P 4 P two blocs P 3 Bloc Bloc 2 Bloc 3 Bloc 4 Bloc 5 Bloc 6 Bloc 7 Bloc 8 Bloc 9 Fgure. An example of a TRLE_sequence template_code (one byte) the values of non-blan pxels ( * 4 bytes) P 2 P 4 Fgure 9. An example of a TRLE_code Defnton 3: A TRLE_sequence s an encoded sequence for blocs n the same row of an mage. It conssts of a 2-byte ndex to store the coordnate of the frst bloc that contans non-blan pxels n a row, a set of template_code/trle_code for blocs n the same row, and an end byte "". In the 2-byte ndex, the frst byte and the second byte store the row ndex and the column ndex of the bloc, respectvely. An example of a TRLE_sequence s gven n Fgure. For the TRLE_sequence shown n Fgure, the 2-byte ndex s "2 ". It means that the TRLE_sequence encodes the blocs n the frst row of an mage. The frst bloc that contans non-blan pxels n the frst row s the second bloc. Fve TRLE_codes are followed the 2-byte ndex. They encode the blocs n the frst row accordng to templates. At the end of the TRLE_sequence s an end byte wth value "". It ndcates the end of row. In the example, t s possble that there are blocs followed bloc 8. However, they are blocs whose four pxels are blan pxels and are elmnated from the TRLE scheme. From ths example, we can see that the purpose of the 2-bype ndex and the end byte of a TRLE_sequence s to fnd the boundary of an mage. In a TRLE_sequence, for the 2-byte ndex, the TRLE scheme can handle an mage wth sze up to pxels. For an mage sze over pxels, the TRLE scheme uses a 4-byte ndex (x and y occuped 2-bye each) that can handle an mage wth sze up to blocs. Defnton 4: A TRLE_pacet s a one-dmensonal array to store the set of TRLE_sequence of a partal mage. An example of a TRLE_pacet s gven n Fgure. In Fgure, an mage wth 8 8 pxels that conssts of 4 4 blocs s gven. There are four TRLE_seqences. The Fgure. An example of a TRLE_pacet Accordng to the above defntons, the TRLE scheme can easly encode a partal mage to form a TRLE_pacet or decode a TRLE_pacet to get the correspondng mage. In the TLRE scheme, bt operatons, and, or, and xor are used to encode and decode an mage. The computaton overheads spent on encodng and decodng of an mage are small. 3. Theoretcal analyss of data compresson schemes One of the reasons to use a data compresson scheme n the mage composton stage of a parallel volume renderng system s to reduce the data transmsson tme of partal mages. In the followng, we analyze the BR, the RLE, the BRLC and the TRLE data compresson schemes n terms of the data compresson rato. Based on the data compresson rato of a data compresson scheme, we derve the best and the worst case bounds of a data compresson scheme. A summary of the notatons used n ths secton s gven below. A pxel of a partal mage s represented by bytes n our analyss. PA The number of pxels n a partal mage. PA nb The number of non-blan pxels of a partal mage. PA BR The number of pxels n a boundng rectangle of Proceedngs of the Frst Internatonal Symposum on Cyber Worlds (CW 2) /2 $7. 22 IEEE

5 the BR scheme. CODE RLE The encodng code sze of the RLE scheme. CODE BRLC The encodng code sze of the BRLC scheme. CODE TRLE The encodng code sze of the TRLE scheme. The compresson rato of a partal mage of method M s defned as The total data sze per bytes CR( M ) =. The total compressed data sze per bytes Due to paper lmtaton, a summary of the ranges of data compresson rato for these four data compresson schemes s gven n Table. The range comparson of the data compresson rato of the four data compresson schemes are shown n Fgure 2. In Fgure 2, the range of the BR scheme covers those of other three schemes. It ndcates that the compresson raton s heavly nfluenced by the shape of an mage. The range of the BRLC scheme also covers that of the RLE scheme. It also ndcates that the BRLC scheme s more senstve to the shape of an mage than the RLE scheme. The range of the TRLE scheme overlaps those of the RLE and the BRLC schemes. However, the average compresson rato of the TRLE scheme s better than those of the RLE and the BRLC schemes. Table. The ranges of data compresson rato of four data compresson schemes Method Ranges BR CR(BR) RLE PA 2 CR(RLE) PA 2 BRLC CR(BRLC) PA TRLE CR(TRLE) PA + PA 2 + PA 3 PA + PA nb 4 PA PA PA PA nb nb PA PA PA PA PA PA nb CR(BR) CR(RLE) CR(BRLC) CR(TRLE) nb Fgure 2. The comparson of the ranges of CR of the four data compresson schemes 4. Analyss of mage composton methods wth data compresson schemes To use a data compresson scheme n the mage composton stage of a parallel volume renderng system, t needs to combne wth some data communcaton schemes to send/receve partal mages among processors. The followng s a generc mage composton algorthm wth a data compresson scheme. Algorthm Comm_Compress_Scheme(P, A) { /* P s the number of processors. */ /* A s the ntal mage of each processor. */. for = to communcaton_step do { 2. for each processor P r do parallel { 3. P r sends compress(a) to P ; 4. P r receves compress(a) from ; 5. P r uses the over operaton to composte the receved compress(a) wth ts local mage; 6. } 7. } end_of_comm_compress_scheme In ths secton, we analyze the theoretcal performance of the BS, the PP, and the RT data communcaton schemes wth the BR, the RLE, the BRLC, and the TRLE data compresson schemes. The three data communcaton schemes and the four data compresson schemes have 2 combnatons. A summary of the notatons used n ths secton s gven below. P The number of processors. P The processor wth ran. A The mage sze n pxels. S(M) The number of communcaton steps of method M. N The number of ntal blocs of a partal mage n the RT method. T s The startup tme of a communcaton channel. T c The data transmsson tme per byte. T o The computaton tme of the over operaton per pxel. T comm (M) The total communcaton tme of method M. T comp (M) The total computaton tme of method M. T comm (M, P ) The communcaton tme of P n the th communcaton step of method M. T comp (M, P ) The computaton tme of P n the th communcaton step of method M. Tencode ( M, P ) The data encodng tme of P n the th communcaton step of method M. Tdecode ( M, P ) The data decodng tme of P n the th communcaton step of method M. A ( M, P ) The pxel sze for sent/receved by P n the th communcaton step of method M. A ( M ) The pxel sze of partal mage of P n the th communcaton step of method M., A BR ( M ) The number of pxels of a boundng rectangle of A ( M ). Anb ( M ) The number of non-blan pxels of A ( M ). CODERLE ( M ) The number of the RLE encodng codes of A ( M ). Proceedngs of the Frst Internatonal Symposum on Cyber Worlds (CW 2) /2 $7. 22 IEEE

6 , CODE BRLC codes of A ( M ). CODE TRLE codes of A ( M ). ( M ) The number of the BRLC encodng ( M ) The number of the TRLE encodng T BR The computaton tme for fndng a boundng rectangle. T The computaton tme of encodng a pxel. encode T decode Method BS_BR BS_RLE The computaton tme of decodng a pxel. Table 2. Theoretcal tme of the 2 mage composton methods Tme Tcomm(M)= ( ( ) 8) = Ts + MAX ABR M + P Tcomp(M)= TBR + MAX ( ABR ( M) ) To log = Tcomm(M)= Ts + MAX ( Anb ( M) + CODERLE( M) 2) = P Tcomp(M)= P MAX ( Tencode A ( M ) + Tdecode CODE RLE ( M ) + Anb ( M ) To ) log = Tcomm(M)= Ts + MAX ( Anb ( M ) + CODEBRLC ( M ) 2 + 8) = BS_BRLC Tcomp(M)= TBR + MAX ( Tencode ABR ( M ) + Tdecode CODEBRLC ( M ) + Anb ( M ) Tc ) = Tcomm(M)= Ts + MAX ( Anb ( M) + CODETRLE( M) ) = BS_TRLE Tcomp(M)= MAX Tencode A ( M ) + Tdecode CODETRLE ( M ) + Anb ( M ) To,, PP_BR PP_RLE = ( ) Tcomm(M)= Ts + MAX ( ABR( M) + 8) = Tcomp(M)= TBR + MAX ( ABR ( M) ) To = Tcomm(M)= Ts + MAX ( Anb ( M) + CODERLE( M) 2) = Tcomp(M)= MAX ( Tencode A ( M ) + Tdecode CODE ( M ) + Anb ( M ) To ),, RLE = Tcomm(M)= Ts + MAX ( Anb ( M) + CODEBRLC ( M) 2 + 8) = PP_BRLC Tcomp(M)= TBR + MAX( Tencode ABR ( M) + Tdecode CODEBRLC ( M) + Anb ( M) Tc ) = Tcomm(M)= Ts + MAX ( Anb ( M ) + CODETRLE( M )) = PP_TRLE Tcomp(M)= MAX ( Tencode A ( M) + Tdecode CODETRLE ( M) + Anb ( M) To ) RT_BR RT_RLE = N Tcomm(M)= log N T s + MAX ( ABR( M) + 8) N = N Tcomp(M)= T BR + MAX ( ABR ( M) ) To N = N Tcomm(M)= log NT s + MAXA ( nb ( M) + CODERLE( M) 2) N = N Tcomp(M)= MAX ( T encode A ( M ) + T decode CODE RLE ( M ) + A nb ( M ) T o ) N = N Tcomm(M)= logn T s + MAX ( Anb ( M) + CODEBRLC ( M ) 2+ 8) Tc N = RT_BRLC N Tcomp(M)= T BR + MAX( Tencode ABR ( M) + Tdecode CODEBRLC ( M) + Anb ( M) Tc ) N = N Tcomm(M)= log N T s + MAX ( Anb ( M ) + CODETRLE( M )) N = RT_TRLE N Tcomp(M)= MAX ( T encode A ( M ) + T decode CODE TRLE ( M ) + A nb ( M ) T o ) N = To analyze the theoretcal performance of the mage composton methods, n the cost model, a synchronous communcaton mode s used. In ths model, all processors start ther computaton after each processor completes ts communcaton. In real stuaton, an asynchronous communcaton mode can be appled as well. However, t s dffcult to analyze the theoretcal performance f an asynchronous communcaton mode s used. Accordng to above notatons, the cost model of an mage composton method M s defned as S( M) T total (M) = max{ Tcomm ( M, P ) + Tcomp ( M, P )}. () = In our communcaton model, we assume that each processor can communcate wth all other processors n one communcaton step. T comm (M, P ) s defned as T comm (M, P ) = δ Ts + A ( M, P) Tp, (2) where δ s the number of processors that P sends data to n the th communcaton step. In our computaton model, we assume that the partal mage n each processor s frst encoded by method M. Each pxel of a compressed bloc then receved from another processor s decoded and composted usng the over operaton. Therefore, T (M) s defned as comp (, ) (, ) (, ) comp encode dncode (, ) o T M P = T M P + T M P + A M P T (3) Accordng to Equatons (2) and (3), we can see that A ( M, P ) affects the performance of the mage composton methods. A good data compresson scheme can reduce the value of A ( M, P ) and s mportant to an mage composton method. Due to paper lmtaton, the data communcaton tme and the data computaton tme of the 2 mage composton methods are shown n Table Expermental results To evaluate the performance of the TRLE scheme, we compare the TRLE scheme wth the BR, the RLE, and the BRLC schemes on a PC cluster. The PC cluster s located at Parallel and Dstrbuted Processng Laboratory of Feng Cha Unversty n Tawan. Each node n the PC cluster uses an INTEL Pentum III CPU wth a cloc rate of 8 MHz. There are 32 CPUs n ths PC cluster, and each node has 52KB frst-level data cache and 256MB of memory space. Each node s fully connected by Myrnet, and the networ bandwdth of the PC cluster s 65 MB/sec. A parallel volume renderng system conssts of three man stages: the data partton stage, the volume render stage, and the mage composton stage. To mplement the data compresson schemes, n the data partton stage, we use the effcent -D and 2-D parttonng schemes [6] to dstrbute a volume dataset to processors. In the data render stage, each processor uses the shear-warp factorzaton [4] volume renderng method to generate a partal mage. In the mage composton stage, the twelve mage composton methods are used to composte partal mages. In the PC cluster, we use C and MPICH_GM [] message passng lbrares to mplement the data compresson schemes. Proceedngs of the Frst Internatonal Symposum on Cyber Worlds (CW 2) /2 $7. 22 IEEE

7 Three volume dataset are used to evaluate the performance of these data compresson schemes. The frst test sample s a "bran" dataset, whch generated from the MR scan of a human bran, and the dmensons of the dataset s The second test sample s an "Engne_low" dataset, whch s the CT scan of an engne bloc and the dmensons of the dataset s The thrd s an "Engne_hgh" dataset, whch s the CT scan of an engne bloc. The densty of each voxels s larger than 8, and the dmensons of the dataset s Fgure 3 shows the fnal mages of the test samples. Each mage s grayscale color and contans pxels. (a)bran (b) Engne_low (c) Engne_hgh Fgure 3. Test samples for the data compresson schemes P = (a) The BS scheme P = P = (b) The PP scheme Tcomm(BS_BR) Tcomp(BS_BR) Tcomm(BS_RLE) Tcomp(BS_RLE) Tcomm(BS_BRLC) Tcomp(BS_BRLC) Tcomm(BS_TRLE) Tcomp(BS_TRLE) Ttotal(BS_BR) Ttotal(BS_RLE) Ttotal(BS_BRLC) Ttotal(BS_TRLE) Tcomm(PP_BR) Tcomp(PP_BR) Tcomm(PP_RLE) Tcomp(PP_RLE) Tcomm(PP_BRLC) Tcomp(PP_BRLC) Tcomm(PP_TRLE) Tcomp(PP_TRLE) Ttotal(PP_BR) Ttotal(PP_RLE) Ttotal(PP_BRLC) Ttotal(PP_TRLE) Tcomm(RT_BR) Tcomp(RT_BR) Tcomm(RT_RLE) Tcomp(RT_RLE) Tcomm(RT_BRC) Tcomp(RT_BRC) Tcomm(RT_TRLE) Tcomp(RT_TRLE) Ttotal(BT_BR) Ttotal(RT_RLE) Ttotal(RT_BRLC) Ttotal(RT_TRLE) (c) The RT scheme Fgure 4. The mage composton tme for "Bran" Fgure 4 shows the data communcaton tme and the data computaton tme of the 2 mage composton methods for test sample "Engne_low" dataset on a PC cluster, respectvely. From Fgure 4, we have the followng observatons.. The RT scheme wth the TRLE scheme has the best performance of the 2 mage composton methods for dfferent numbers of processors P = (a) The BS scheme 4 2 P = P = (b) The PP scheme Tcomm(BS_BR) Tcomp(BS_BR) Tcomm(BS_RLE) Tcomp(BS_RLE) Tcomm(BS_BRLC) Tcomp(BS_BRLC) Tcomm(BS_TRLE) Tcomp(BS_TRLE) Ttotal(BS_BR) Ttotal(BS_RLE) Ttotal(BS_BRLC) Ttotal(BS_TRLE) Tcomm(PP_BR) Tcomp(PP_BR) Tcomm(PP_RLE) Tcomp(PP_RLE) Tcomm(PP_BRLC) Tcomp(PP_BRLC) Tcomm(PP_TRLE) Tcomp(PP_TRLE) Ttotal(PP_BR) Ttotal(PP_RLE) Ttotal(PP_BRLC) Ttotal(PP_TRLE) Tcomm(RT_BR) Tcomp(RT_BR) Tcomm(RT_RLE) Tcomp(RT_RLE) Tcomm(RT_BRC) Tcomp(RT_BRC) Tcomm(RT_TRLE) Tcomp(RT_TRLE) Ttotal(BT_BR) Ttotal(RT_RLE) Ttotal(RT_BRLC) Ttotal(RT_TRLE) (c) The RT scheme Fgure 5. The mage composton tme for "Engne_low" P = (a) The BS scheme Tcomm(BS_BR) Tcomp(BS_BR) Tcomm(BS_RLE) Tcomp(BS_RLE) Tcomm(BS_BRLC) Tcomp(BS_BRLC) Tcomm(BS_TRLE) Tcomp(BS_TRLE) Ttotal(BS_BR) Ttotal(BS_RLE) Ttotal(BS_BRLC) Ttotal(BS_TRLE) Tcomm(PP_BR) Tcomp(PP_BR) 8 Tcomm(PP_RLE) Tcomp(PP_RLE) 6 Tcomm(PP_BRLC) Tcomp(PP_BRLC) 4 Tcomm(PP_TRLE) Tcomp(PP_TRLE) 2 Ttotal(PP_BR) Ttotal(PP_RLE) Ttotal(PP_BRLC) P = Ttotal(PP_TRLE) 7 6 (b) The PP scheme P = Tcomm(RT_BR) Tcomp(RT_BR) Tcomm(RT_RLE) Tcomp(RT_RLE) Tcomm(RT_BRC) Tcomp(RT_BRC) Tcomm(RT_TRLE) Tcomp(RT_TRLE) Ttotal(BT_BR) Ttotal(RT_RLE) Ttotal(RT_BRLC) Ttotal(RT_TRLE) (c) The RT scheme Fgure. The mage composton tme for "Engne_hgh" 2. The BS, the PP, and the RT schemes wth the TRLE scheme have better performance than those wth the BR, the RLE, and the BRLC schemes. 3. When the number of processor ncreases, the mage composton tme of any data communcaton scheme wth the TRLE scheme s slghtly ncreased or decreased compared to other data compresson schemes, that s, the tme s n a horzontal lne. Fgures 5 and show the data communcaton tme and the data computaton tme of the 2 mage composton schemes for test samples "Engne_low" and Proceedngs of the Frst Internatonal Symposum on Cyber Worlds (CW 2) /2 $7. 22 IEEE

8 "Engne_hgh" dataset on a PC cluster, respectvely. From Fgures 5 and, we have smlar observatons as those of Fgure Conclusons In ths paper, we have proposed an effcent data compresson scheme, the template run-length encodng (TRLE) scheme, for mage composton of parallel volume renderng systems. To evaluate the performance of the TRLE scheme, we compare the proposed scheme wth the BR, the RLE, and the BRLC schemes. Both theoretcal and expermental analyses are conducted. For the theoretcal analyss, we compare the ranges of the compresson rato of these four data compresson schemes. For the expermental analyss, the BR, the RLE, the BRLC, and the TRLE data compresson schemes have mplemented wth the bnary-swap (BS), the parallel-ppelned (PP), and the rotate-tlng (RT) data communcaton schemes. The data computaton tme and the data communcaton tme are measured on a PC cluster. From the expermental results, we have the followng remars. Remar : The RT scheme wth the TRLE scheme has the best performance of the 2 mage composton methods for dfferent numbers of processors. Remar 2: The BS, the PP, and the RT schemes wth the TRLE scheme have better performance than those wth the BR, the RLE, and the BRLC schemes. Remar 3: When the number of processor ncreases, the mage composton tme of any data communcaton scheme wth the TRLE scheme s almost the same. 7. Acnowledgement Ths wor was partally supported by the Natonal Scence Councl of Republc of Chna under contract NSC9-223-E References Usng Compresson-Based Image Compostng," Proceedngs of the second Eurographcs Worshop on Parallel Graphcs and Vsualzaton, 998. [2] R.A. Drebn, L. Carpenter, and P. Hanrahan, "Volume Renderng," Computer Graphcs (In Proceedngs of SIGGRAPH'88), vol. 22, no. 4, Atlanta, 988, pp [3] J.D. Foley, A. van Dam, S.K. Fener and J.F. Hughes, Computer Graphcs: Prncples and Practce Second Edton n C, Mass.: Addson-Wesley, 99. [4] P. Lacroute, "Analyss of a Parallel Volume Renderng System Based on the Shear-Warp Factorzaton," IEEE Transactons on Vsualzaton and Computer Graphcs, vol. 2, no. 3, 996, pp [5] T.Y. Lee, "Image Composton Schemes for Soft-Last Polygon Renderng on 2D Mesh Multcomputers," IEEE Transactons on Vsualzaton and Computer Graphcs, vol. 2, no. 3, Sep. 996, pp [6] C.F. Ln, Y.C. Chung, and D.L. Yang, "Parallel Shear-Warp Factorzaton Volume Renderng Usng Effcent -D and 2-D Parttonng Schemes on Dstrbuted Memory Multcomputers," The Journal of Supercomputng, vol. 22, no. 3, Jul. 22, pp [7] C.F. Ln, D.L. Yang, and Y.C. Chung, "A Rotate-Tlng Image Composton Scheme for Parallel Volume Renderng on Dstrbuted Memory Multcomputers," Proceedngs of IEEE Internatonal Parallel and Dstrbuted Processng Symposums (CD-ROM), San Francsco, USA, Apr. 2. [8] K.L. Ma, J.S. Panter, C.D. Hansen, and M.F. Krogh, "A Data Dstrbuted, Parallel Algorthm for Ray-Traced Volume Renderng," Proceedngs of 993 Parallel Renderng Symposum (PRS 93), San Jose, Oct. 993, pp [9] K.L. Ma, J.S. Panter, C.D. Hansen, and M.F. Krogh, "Parallel Volume Renderng Usng Bnary-Swap Composton," IEEE Computer Graphcs and Applcatons, vol. 4, no. 4, Jul. 994, pp [] MPI Forum, MPI: A Message-Passng Interface Standard, May 994. [] T. Porter and T. Duff, "Composton Dgtal Images," Computer Graphcs (In Proceedngs of SIGGRAPH'84), vol. 8, Jul. 984, pp [2] J.P. Sngh, A. Gupta, and M. Levoy, "Parallel Vsualzaton Algorthms: Performance and Archtectural Implcatons," Computer, vol. 27, no. 7, Jul. 994, pp [3] D.L. Yang, J.C. Yu, and Y.C. Chung, "Effcent Compostng Schemes for the Sort-Last-Sparse Parallel Volume Renderng System on Dstrbuted Memory Multcomputers," The Journal of Supercomputng, vol. 8, no. 2, Feb. 2, pp [] J. Ahrens and J. Panter, "Effcent Soft-Last Renderng Proceedngs of the Frst Internatonal Symposum on Cyber Worlds (CW 2) /2 $7. 22 IEEE