DTC FLE COPY NCS TB 87-8 NATONAL COMMUNCATONS SYSTEM q. nm TECHNCAL NFORMATON BULLETN 87-8 N NTRANSFORM CODNG AND DFFERENTAL Qz PULSE CODE MODULATON FOR GROUP 4 FACSMLE DTC ELECTE JUL 10]1! l AUGUST 1987 Apprork kr pub~c ntm"q 9o o7 12 051
REPOCU TD U :AYC:"h VA(- 4 TT71E A N ;u U August 1987 Fnal N Transform Codng and Dfferental Pulse Code Modulaton for Group 4 Facsmle 6' AUTH OF S) C-DCA100-83-C-O047 Delta nformaton Systems, nc. -, ". Horsham Busness Center, Bldg. 3 300 Welsh Road Horsham, PA 19044 9 SPO.0NSOR!,,, G MON kt HN. A.ENC NA'E., -.N - - 0 " N- ' T Natonal Communcatons System r c -r_ m 9OR?.,F Offce of Technology & Standards Washngton, DC 20305-2010 NCS TB 87-8 12.a [C;ST B O', 2',, L,'B %.7v }.M / :.. ' h 2b DSTk23BUT'CN CODE Approved for Publc Release; Dstrbuton s unlmted. 13. ABSTRACT S" Ths document compares Transform Codng wth Dfferental Pulse Code Modulaton (DPCM) n order to determne the relatve effectveness of each technque as appled to the compresson of gray scale mages for Group 4 facsmle. At the present tme, the CCTT Recommendatons for Group 4 facsmle permts the transmsson of black-whte magery only. Consequently, any nput page contanng gray scale nformaton, such as a photograph, wll be severely dstorted by basc Group 4 machnes. However, there are plans by the CCTT to add a Gray Scale opton to the Group 4 facsmle standard for transmttng pctoral data... J.1_ -D ff Dffe lal Pulse Code Modulaton (DPCM), --Facsmle, 1 165 Group 4 Transform. Gray Scale Codng,/fj ~LlVCVC.V ~ ~, 17. SECJR;T C.CTc F O F RE PO R T TH P _(2 ''. Unclassfed Unclassfed Unclasgfed L 4, T
m NCS TECHNCAL NFORMATON BULLETN 87-8 TRANSFORM CODNG AND DFFERENTAL PULSE CODE MODULATON FOR GROUP 4 FACSMLE PROJECT OFFCER APPROVED FOR PUBLCATON: DENNS BODSON Senor Electroncs Engneer Offce of NCS Technology and Standards DENNS BODSON Assstant Manager Offce of NCS Technology and Standards FOREWORD Among the responsbltes assgned to the Offce of the Manager, Natonal Communcatons System, s the management of the Federal Telecommuncaton Standards Program. Under ths program, the NCS, wth the assstance of the Federal Telecommuncaton Standards Commttee dentfes, develops, and coordnates proposed Federal Standards whch ether contrbute to the nteroperablty of functonally smlar Federal telecommuncaton systems or to the achevement of a compatble and effcent nterface between computer and telecommuncaton system. n developng and coordnatng these standards, a consderable amount of effort s expended n ntatng and pursung jont standards development efforts wth approprate techncal commttees of the Electroncs ndustres Assocaton, the Amercan Natonal Standards nsttute, the nternatonal Organzaton for Standardzaton, and the nternatonal Telegraph and Telephone Consultatve Commttee of the nternatonal Telecommuncaton Unon. Ths Techncal nformaton Bulletn presents an overvew of an effort whch s contrbutng to the development of compatble Federal, natonal, and nternatonal standards n the area of facsmle. t has been prepared to nform nterested Federal actvtes of the progress of these efforts. Any comments, nputs or statements of requrements whch could assst n the advancement of ths work are welcome and should be addressed to: Offce of the Manager Natonal Communcatons System ATTN: NCS-TS Washngton, DC 20305-2010
COMPUTER SMULATON OF TRANSFORM CODNG FOR GROUP 4 FACSMLE August, 1987 * Fnal Report Submtted to: NATONAL COMMUNCATONS SYSTEM Offce of Technology and Standards Washngton, DC 20305 Contractng Agency: DEFENSE COMMUNCATONS AGENCY Contract Number - DCA100-83-C-0047 Modfcaton/Task Number - P00009/2 DELTA NFORMATON SYSTEMS, NC. Horsham Busness Center, Bldg. 3 300 Welsh Road Horsham PA 19044
1 Table of Contents Secton Page 1.0 ntroducton.... 1-1 1.1 Synopss... 1-. 2 2.0 Techncal Approach..... 2-1 2.1 Transform Codng Technques....... 2-1 2.1.1 Transformaton Technques... 2-3 2.1.2 Sub-block Codng Technques.... 2-6 2.2 Algorthm Descrptons....... 2-10 2.2.1 Dscrete Cosne Transform... 2-11 2.2.2 Condtonal Zonal Codng..... 2-12 2.2.3 Adaptve Zonal Codng..... 2-15 2.2.4 Chen-Smth Codng........ 2-16 2.2.5 mage Dependent Chen-Smth Codng.... 2-20 2.3 Selecton of Test mages......... 2-21 3.0 Results......... 3-1 3.1 Compresson Statstcs....... 3-1 3.2 Output mages..... 3-8 3.3 Algorthm Complexty........ 3-23 3.4 DPCM Comparson.... 3-25 4.0 Conclusons and Recommendatons... 4-1 For 4.1 Conclusons....... 4-1 4.2 Recommendatons for Further Study..... 4-4 d APPENDX A - SOFTWARE DOCUMENTATON L1n REFERENCES > Dstrbuton/ By a Avalablty Codes ~ and/or---, A Dst j Specal
- 1.0 NTRODUCTON 3 Ths document summarzes work performed by Delta nformaton Systems, nc., for the Offce of Technology and Standards of the Natonal Communcatons System, an organzaton of the U. S. Government, headed by Natonal Communcatons System Assstant Manager for the Offce of Technology and Standards, Denns Bodson. Mr. Bodson s responsble for the management of the Federal Telecommuncatons Standards Program, whch develops telecommuncatons standards, the use of whch s mandatory for all Federal agences. The purpose of ths study, performed under Task 2 of Modfcaton Number P00009 of contract number DCA100-83-C-0047, was to compare Transform Codng wth Dfferental Pulse Code Modulaton (DPCM) n order to determne 3 the relatve effectveness of each technque as appled to the compresson of gray scale mages for Group 4 facsmle. At the present tme, the CCTT Recommendatons for Group 4 facsmle permt the transmsson of black-whte magery only. Consequently, any nput page contanng gray scale nformaton, such as a photograph, wll be severely dstorted by basc Group 4 machnes. However, there are plans by the CCTT to add a gray scale opton to the Group 4 facsmle standard for transmttng pctoral data. Both Dfferental Pulse Code Modulaton (DPCM) and transform codng technques have been used wth some success to compress pctoral (gray scale) data. Each of these technques has some attractve characterstcs and some lmtatons. Transform 1-1
codng systems acheve superor performance at hgh compresson, and show less senstvty to pcture data statstcs compared to DPCM systems. On the other hand, DPCM systems acheve better performance at lower compresson and are less complex to mplement, as compared to transform codng systems. Ths report s comprsed of four sectons. Secton 1.0 provdes a bref descrpton of the objectves of the study and contans a synopss that outlnes the results obtaned and conclusons made. Secton 2.0 presents the techncal approach employed n the study and ncludes a dscusson of gray scale compresson technques, detaled descrptons of the transform codng algorthms smulated, and a dscusson of the test mage selecton process. The results of the smulaton study are presented n Secton 3.0, and the conclugons and recommendatons made based on these results are contaned n Secton 4.0. 1.1 Synopss Transform codng algorthms generally consst of two basc steps, the transformaton step and the sub-block codng step. n the transformaton step, the mage s frst dvded nto subblocks of (NxN) pxels each (n ths study N=16); each sub-block s then transformed from a set of gray level values nto a set of coeffcents by applyng to t a lnear transformaton such as the Fourer transform. n ths study, t was determned that the type of transform employed had less of an mpact on mage 1-2
compresson than the sub-block codng technque employed. An analyss of the avalable transforms, based on complexty of mplementaton and overall performance, was performed; the Dscrete Cosne transform (DCT) was selected as the transform to be employed n smulatng four transform codng algorthms, each of whch employs a dfferent sub-block codng technque. Four sub-block codng technques were then selected from among the many avalable algorthms of ths type. The condtonal zonal codng technque compresses an mage by dscardng all but a pre-determned number of coeffcents wthn each sub-block (.e. those n a specfed "zone" of the sub-block) and then further quantzng the retaned coeffcents. The adaptve zonal codng technque s a varaton of the condtonal zonal codng technque; t adds the element of mage dependency n that t determnes the number of coeffcents retaned n each sub-block based on the local mage statstcs. The basc Chen-Smth codng technque s more complex than the two zonal codng technques n that t requres two passes over an mage n order to compress t. n the frst pass, statstcal nformaton s gathered n order to characterze the mage; n the second pass, these statstcs are employed n order to assgn code bts to the coeffcents n each sub-block. The mage dependent Chen-Smth codng technque s a varaton of the basc Chen-Smth codng technque that adds mage dependency to the compresson process. The effect of ths mage dependency s * that more codng bts are assgned to the more actve regons of 1-3
the mage and fewer codng bts are assgned to the less actve regons of the mage. At a gven target compresson, the mage dependency mproves the mage qualty wth mages contanng a sgnfcant amount of actvty and mproves the acheved compresson wth less actve mages. Two DPCM compresson algorthms were smulated n a prevous study performed by Delta nformaton Systems; the frst, condtonal DPCM, employs a three-neghbor gray level value predctor, a non-lnear three-bt quantzer, Huffman entropy codng, and an optonal staggered horzontal subsampler and correspondng nterpolator; the second, adaptve DPCM, employs a three neghbor gray level value predctor, an extended non-lnear fve-bt quantzer, adaptve arthmetc codng, and optonal horzontal and vertcal spatal flters. The mage dependent Chen-Smth codng algorthm produced the best overall mage qualty of the four transform codng algorthms, followed by the basc Chen-Smth, adaptve zonal, and condtonal zonal codng algorthms. The DPCM algorthms * produced mage qualty comparable to the transform codng algorthms at bt rates above 1 bt/pxel, and performed slghtly better than the transform codng algorthms at bt rates as low as 0.63 bts/pxel. However, the DPCM algorthms could not acheve compresson below 0.63 bts/pxel; the transform codng algorthms offer the advantage of selectable compresson, and thus can reach much lower bt rates (0.10 bts/pxel n ths study). 1-4
The DPCM algorthms are much less complex than the transform codng algorthms n terms of mplementaton, and produce very good mage qualty at relatvely low bt rates. DPCM algorthms should be consdered n applcatons where ease of mplementaton, moderate compresson, and good mage qualty are requred. The transform codng algorthms are much more flexble than the DPCM algorthms parametrcally; they can be modfed easly to sut changng performance requrements. Transform * codng algorthms should be consdered n applcatons where the tradeoff between mage qualty and compresson s varable, and ease of mplementaton s not crtcal. * 1-5
2.0 TECHNCAL APPROACH 2.1 Compresson Technques Fgure 2.1 llustrates the wde range of gray scale codng technques whch could be employed n mplementng a gray scale opton for Group 4 facsmle. Two of these technques, dfferental pulse code modulaton (DPCM) and transform codng, were compared n ths study. Smulatons of several DPCM algorthms were performed by Delta nformaton Systems n a prevous study (Ref. 4); the results of those smulatons were used n ths study for comparson purposes. The smulaton effort n ths study was therefore centered on the transform codng algorthms to be dscussed shortly. Transform codng algorthms, generally speakng, operate as two step processes. The frst step nvolves performng lnear transformatons on the orgnal sgnal (separated nto sub-blocks of N x N pxels each), n whch sgnal space s mapped nto transform space. n the second step, the transformed sgnal s compressed by encodng each sub-block through quantzaton. reconstructon operaton nvolves performng an nverse transformaton of each decoded transformed sub-block. The functon of the transformaton operaton s to make the The transformed samples more ndependent than the orgnal samples, so that the subsequent operaton of quantzaton may be done more effcently. S2-1
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The transformaton operaton tself does not provde compresson; rather, t s a re-mappng of the sgnal nto another doman n whch compresson can be acheved more easly. t s for ths reason that the specfc type of transform used wll have less of an mpact on mage qualty and compresson than the effcent selecton of coeffcents to be retaned and the number of bts allocated to them (.e., quantzaton). Therefore, somewhat greater emphass was put on evaluatng subblock codng technques, whch have more of an mpact on mage qualty and data compresson, than the transformaton technques themselves. 2.1.1 Transformaton Technques Transforms that have proven useful nclude the Karhunen- Loeve, Dscrete Fourer, Dscrete Cosne, and Walsh-Hadamard transforms. These transformaton technques were nvestgated n ths study n order to select one partcular transform technque to be used n the smulaton effort. The selecton was based on the overall performance and relatve complexty of each canddate technque. Karhunen-Loeve Transform The Karhunen-Loeve transform (KLT) s consdered to be an optmum transformaton, and for ths reason many other 2-3
transformatons have been compared to t n terms of performance. However, the KLT has certan characterstcs that make t less than deal for mage processng. These nclude the necessty to estmate the covarance matrx before processng n both row and column processng operatons. Also, the actual egenvector determnaton must be carred out to generate the bass matrx. These drawbacks would not be sgnfcant f the effcency of the KLT was much greater those that of other transforms. However, for data havng hgh nter-element correlaton, the performance of other transforms (such as the Dscrete Cosne transform) s vrtually ndstngushable from that of the KLT, and thus does not warrant ts added complexty. Therefore, the KLT was not chosen for nvestgaton n ths study. Dscrete Fourer Transform The Dscrete Fourer transform s one of the few complex transforms used n data codng schemes. There are dsadvantages n usng a complex transform for data codng, the most obvous of whch s the storage and manpulaton of complex numbers. Agan, as n the case of the KLT, ths complexty ssue would not be a factor f the performance of the DFT was sgnfcantly greater than that of other transforms. However, other transforms whch are less complex perform better than the DFT. For ths reason, the DFT was not nvestgated n ths study. 2-4
Dscrete Cosne Transform The dscrete cosne transform (DCT) s one of an extensve famly of snusodal transforms. n ther dscrete form, the bass vectors consst of sampled values of snusodal or cosnusodal functons that, unlke those of the DFT, are real number quanttes. The DCT has been sngled out for specal attenton by workers n the mage processng feld, prncpally because, for conventonal mage data havng reasonably hgh nter-element correlaton, the DCT's performance s vrtually ndstngushable from that of other transforms whch are much more complex to mplement. Because of ts excellent performance and comparatvely smple mplementaton, the Dscrete Cosne Transform was chosen for evaluaton n ths study. Walsh-Hadamard Transform The three transforms mentoned prevously have basc functons whch are ether cosnusodal,.e. the Fourer and Dscrete Cosne, or are a good approxmaton of a snusodal functon, such as the Karhunen-Loeve Transform. The Walsh- Hadamard Transform s an approxmaton of a rectangular orthonormal functon. The actual transform conssts of a matrx of +1 and -1 values, whch elmnates multplcatons from the transform process. The elmnaton of multplcatons s a sgnfcant property, snce the aforementoned transforms requre S2-5
real or complex multplcatons. However, the Walsh-Hadamard transform does not provde the excellent performance that the Dscrete Cosne Transform provdes. Therefore, the Walsh- Hadamard transform was not chosen for evaluaton n ths study. 2.1.2 Sub-Block Codng Technques Perhaps more mportant than choosng a specfc transform method for mage processng s choosng a method for codng the matrx coeffcents after transformaton. Of the many coeffcent codng schemes dscussed n the lterature, four were selected for evaluaton n ths study. The frst s a smple, non-adaptve, condtonal zonal codng technque whch uses a fxed number of bts to encode an mage. The second s an adaptve, one-pass, mage dependent zonal method whch uses as many bts as necessary to code a partcular mage. The thrd and fourth sub-block codng algorthms selected are varatons of an algorthm developed by Chen and Smth (Ref. 1), whch are sgnfcantly more complex than the two zonal methods. The basc Chen-Smth technque s adaptve, as s the adaptve zonal technque; however, two passes over the mage are necessary. n the frst pass, statstcs are gathered and bt maps are produced. n the second pass the mage s actually coded for transmsson. The second varaton of the basc Chen- Smth algorthm adds mage dependency to the codng scheme. of the codng technques evaluated n ths report use a (16x16) All 2-6
Dscrete Cosne transform. The followng paragraphs descrbe the codng technques n more detal. Condtonal Zonal Technque n condtonal zonal codng, all coeffcents n a sub-block that are outsde a specfed zone (usually the upper left hand corner of the sub-block) are dscarded pror to the quantzaton step. The number of coeffcents retaned per sub-block s selected based on the compresson desred; ths number remans constant for all sub-blocks n the mage. After the sgnfcant coeffcents have been extracted from the sub-block, they are normalzed and quantzed to a fxed number of bts through varous arthmetc operatons based on general mage statstcs. At the recever, arthmetc operatons to reverse the normalzaton process are performed to produce reconstructed transform coeffcents (wth quantzaton error) n the specfed zone of the sub-block; all of the coeffcents dscarded n the encodng process are set to zero, and the reconstructed sub-block s ready to be nversely transformed. Ths technque s extremely smple and requres a mnmal amount of overhead as compared to the Chen-Smth technques to be dscussed shortly. The condtonal zonal technque can be thought of as beng on the smple end of the complexty spectrum, whle the Chen-Smth technques are on the complex end. Ths technque was nvestgated n ths study for that reason; that 2-7
s, to compare a smple and a complex coeffcent codng technque n terms of compresson and mage qualty. Adaptve Zonal Technque The adaptve zonal codng technque s a combnaton of threshold codng and condtonal zonal codng. n straght threshold codng, a specfc energy ampltude s selected, and only those transform coeffcents n a sub-block that are above ths threshold value are retaned; the other coeffcents are dscarded. A major dsadvantage to threshold codng s the overhead requred to store nformaton regardng the locaton wthn the sub-block of the coeffcents whch are retaned. Zonal codng, as descrbed above, quantzes only those' coeffcents n a specfed area, or zone; because the postons of the retaned coeffcents are known, the nformaton concernng ther locatons need not be stored. The adaptve zonal technque s a hybrd scheme provdng the benefts of both zonal and threshold codng. Coeffcents n a specfed zone are compared to a selected threshold value n an ordered pattern untl a coeffcent value below the threshold s encountered. When a coeffcent below the selected threshold s encountered, the remanng coeffcents n the specfed zone are dscarded, and the retaned coeffcents are normalzed and quantzed as n the condtonal zonal codng technque. The only addtonal overhead requred by the adaptve zonal codng 2-8
technque s to store the number of coeffcents retaned n each sub-block. The adaptve zonal codng technque acheves superor performance n terms of compresson over the condtonal zonal codng technque by elmnatng some of the trval coeffcents that would be unnecessarly encoded by the condtonal technque. Basc Chen-Smth Technque The basc Chen-Smth codng technque (Ref. 1) s very popular for codng both monochrome and color mages. Ths technque uses Max's method of optmum quantzer desgn (Ref. 3), assumng Gaussan DC and AC coeffcent probablty densty functons. Transform sub-blocks of the orgnal mage are assgned to one of four classes on the bass of sub-block AC energy. The varance of each coeffcent s calculated and used n a bt allocaton technque n order to determne a bt assgnment map for each class. The transform coeffcents are normalzed by ther correspondng varances to acheve unt varance pror to quantzaton. The basc Chen-Smth approach s desgned to acheve a gven compresson no matter what mage s to be compressed. Ths means that, for a gven compresson, the mage qualty of more complex mages s poorer than that of less complex mages. 2-9
mage Dependent Chen-Smth Technque n addton to the standard Chen-Smth technque descrbed above, a varaton of ths technque was evaluated n ths study. Ths varaton adds mage dependency to the technque by 3 analyzng all of the AC energes of sub-blocks n the mage n order to allocate more bts to busy sub-blocks. More bts are allocated per sub-block to mages wth a hgh amount of actvty, and fewer bts per sub-block are allocated to mages wth a low amount of actvty n order to acheve hgher compresson for mages wth low actvty, and better mage qualty for mages wth hgh actvty. 2.2 Algorthm Descrptons The algorthms for the Dscrete Cosne Transform (DCT) and the four sub-block codng technques are descrbed n ths secton. The DCT algorthm whch was used n each of the four sub-block codng technques s descrbed frst, followed by the descrptons of the four sub-block codng technques. software documentaton for all smulaton software s presented n Appendx A. 2-2-1 The
2.2.1 Dscrete Cosne Transform The mplementaton of the Dscrete Cosne Transform algorthm requres the dvson an mage nto e seres of (NxN) sub-blocks of pxels. Each sub-block s transformed by a two dmensonal (NxN) Dscrete Cosne Transform process as follows: (T] = EC].[D].[C] T where [T] s the transformed sub-block, [C] s the DCT bass matrx, and (D] s the nput data sub-block ((C]T s the transpose of the DCT bass matrx). The DCT bass matrx coeffcents were determned from the followng relaton: C.j = Co-1(2/ N).(cos(.(j + 0.5).(r /N))) where Co = 1/12 for = 0, Co = 1 otherwse, and =j=0 to N-. Ths transformaton converts each (NxN) sub-block of pxels nto an (NxN) matrx of transform coeffcents, whch conssts of one DC coeffcent and (NxN - 1) AC coeffcents. The sum of the squares of all of the AC coeffcents n a gven transform matrx s known as the AC energy of that transform matrx, and wll be * referred to as such throughout ths report. The sze of the (NxN) transform chosen for use n the smulatons was (16xl6). The (16x16) transform sze was chosen * prmarly because t has been used frequently n past applcatons n the mage processng feld. t s also a compromse between an (8x8) transform, whch would ncrease overhead due to the greater number of sub-blocks n an mage, and a (32x32) transform, whch would ncrease the complexty of the 2-11
system. Ths (16x16) Dscrete Cosne Transform was used n the four codng technques dscussed below. 2.2.2 Condtonal Zonal Codng The condtonal zonal codng technque encodes transform coeffcents of a partcular zone of each mage sub-block. The sze of the zone used n the algorthm s determned by an nput parameter that desgnates the desred number of coeffcents to be retaned for quantzaton. The number of coeffcents retaned n each sub-block remans constant throughout the encodng of the mage, whch makes ths technque non-adaptve. When smulatons were performed on tranng mages, statstcs were gathered on transform coeffcents over the entre set of tranng mages. These statstcs ncluded the varances of the coeffcents, whch were employed n order to determne the processng order of the coeffcents wthn the selected zone of the sub-block, and the mnmum-maxmum values of the coeffcents, whch were used to normalze and quantze the coeffcents for compresson purposes. The varances were computed assumng an AC coeffcent mean of zero. The coeffcent processng order was determned based on decreasng coeffcent varances. Ths order s much lke the classcal zg-zag technque (Fgure 2.2) wth mnor varatons (Fgure 2.3). The reason for the change n order from the zgzag orderng was that the zg-zag orderng dd not exactly match 2-12
1 3 4 10 11 21 22 36 37 55 56 2 5 9 12 20 23 35 38 54 57 6 8 13 19 24 34 39 53 58 7 14 18 25 33 40 52 59 15 17 26 32 41 51 60 16 27 31 42 50 61 28 30 43 49 62 29 44 48 63 45 47 64 70 46 65 69 66 68 67 Fgure 2.2 - Zgzag Order Technque 1 3 6 10 16 25 35 45 56 2 5 9 14 19 24 34 44 60 4 8 12 20 26 32 43 53 62 7 13 17 28 33 41 52 64 11 18 21 30 39 49 63 15 23 29 36 48 59 70 22 31 38 47 57 68 27 37 42 55 66 40 46 50 61 51 58 67 54 Fgure 2.3 - Orderng Matrx Employed n Zonal Codng 16 13 13 12 10 8 8 5 4 13 13 10 9 9 7 6 5 4 13 10 9 9 8 7 4 5 3 13 10 9 8 8 7 6 4 12 10 9 7 7 7 6 10 8 7 8 7 5 3 10 8 6 7 6 5 10 7 6 5 4 5 6 5 3 5 5 5 7 3 2 Fgure 2.4 - Dvdng Factors Employed n Zonal Codng 2-13
the order of varances of the DCT. Therefore, n order to optmze the quantzaton of coeffcents, ths varaton of the zg-zag technque was mplemented. When a number of coeffcents s specfed for retenton n the zonal technque, the zone s determned by startng wth the DC coeffcent and then proceedng n the order of decreasng varance untl the specfed number of coeffcents s reached. For smulaton purposes, the maxmum number of coeffcents whch * can be kept n ths orderng technque s 70 (t was expermentally determned that all coeffcents beyond the 70 t b were relatvely nsgnfcant.). All coeffcents whch are not quantzed are assumed to be zero at the decoder for nverse transform purposes. The quantzaton technque used s a unform 8-bt quantzer. When statstcs were gathered on the tranng mages, a mnmum-maxmum matrx of coeffcents was produced showng mnmum and maxmum coeffcent values. Once the mnmum and maxmum values were known, dvdng factors were assgned to each coeffcent poston (Fgure 2.4). When a dvson s performed for quantzaton on the coeffcents, the results are placed n 8-bt values for transmsson (7 bts for data and 1 sgn bt). The coeffcent reconstructon s performed by multplyng the 8- bt quantzed value by the dvdng factor for that specfc coeffcent poston. 2-14
2.2.3 Adaptve Zonal Codng The adaptve zonal codng technque employs the same coeffcent orderng and coeffcent quantzaton methods used n the zonal technque. Adaptvty s acheved by proceedng n the order shown n Fgure 2.3 untl a coeffcent s encountered whch s less than a user-specfed AC energy threshold. The orderng system used (by order of varance) s the actual decreasng order of the coeffcents n most cases; however, dependng on the mage data, the actual order may vary from the preset orderng sequence. For ths reason, a look-ahead method was devsed n order to prevent reachng the threshold (whch would termnate the encodng of that sub-block) prematurely f subsequent coeffcents were sgnfcantly greater n magntude than the current coeffcent beng evaluated. When the AC coeffcent threshold s reached, the next two coeffcents n the specfed order are examned. f both of these coeffcents are 50 tmes greater than the AC coeffcent threshold, the processng of the sub-block contnues. Ths type of look-ahead processng was mplemented n order to decrease the probablty of termnatng sub-block encodng before sgnfcant transform coeffcents are encountered. 2-15
2.2.4 Chen-Smth Codng The Chen-Smth codng technque s a two-pass mage codng technque. n the frst pass, transform matrx statstcs are gathered over the entre mage. The statstcs-gatherng process nvolves the storage of the AC energes of all sub-blocks n the mage, and the varances (the sum of the squares of the coeffcents n each poston of the transform matrx over the entre mage) of the transform coeffcents. Once the statstcs are gathered, a map of the mage s produced (Fgure 2.5) usng four sub-block classfcaton levels. The map s produced usng the AC energes of the sub-blocks, assgnng hgh classfcaton levels (4 or 3) to sub-blocks wth hgh AC energes (.e. hgh actvty sub-blocks), and low classfcaton levels (1 or 2) to sub-blocks wth low AC energes (low actvty sub-blocks). The map has (M / 4) entres of each classfcaton level, where M s * equal to the number of sub-blocks n the mage. After the classfcaton map s produced, bt allocaton maps (Fgure 2.6) are generated for each class. The bt allocaton maps are produced usng a bt allocaton functon whch generates each bt map based upon a specfed average amount of bts/coeffcent to be used for quantzaton; a hgher number of average bts are allocated to the hgher classfcaton levels and a lower number of bts to the lower levels. Snce there are an equal number of sub-blocks of each class and each bt allocaton map has a fxed number of average bts, the 2-16
12234443222342111244 32344443132321222444 42444443333321123411 41443343333221233133 42333343331212213433 42224443412111334333 43334423222121233333 44243432121321343333 44234341212311113333 44234312123132213232 44324121231313133312 34421212213233311222 44411212232313212133 44421222121231121123 44323231211222211114 24232212321222111111 31321123233131112211 13221221132211212213 21241431321112311112 22444333412212211112 Fgure 2.5 - Classfcaton map of a (20 x 20) sub-block mage Note: Each value represents (16 x 16) pxel subblock. A 1 specfes a low actvty sub-block; a 4 specfes a hgh actvty sub-block. 42-17
8765433221110000 8654432221110000 8543322111100000 8332110000000000 7665433221110000 6554432221110000 5544332211000000 3322111100000000 6554433221110000 5544433221110000 4433332211100000 2221111100000000 5544433322111000 4443333222110000 3333322211100000 1111111000000000 4443333222111000 3333333222111000 3332222111100000 1111100000000000 3333322222111100 3333222222111100 2222221111100000 1110000000000000 3333322221111100 2222222221111000 2222211111100000 1000000000000000 2223222111111000 2223321111111100 2111211110000000 0000000000000000 2222322111111100 2223432111110000 1112221110000000 0000000000000000 2222221111111000 1212321111101000 1111111100000000 0000000000000000 1111111111100000 1111111111000000 1111111000000000 0000000000000000 1111111111100000 1111111111000000 1110111100000000 0000000000000000 1111111111100000 1111111111000000 1000001000000000 0000000000000000 1111111111000000 1111111111000000 0000001100000000 0000000000000000 1111111111000000 1111111111000000 0000000100000000 0000000000000000 1111111111000000 1111111122100000 1000000011000000 0000000000000000 Class 4 Class 3 Class 2 Class 1 Fgure 2.6 - Bt Allocaton Maps of the Chen-Smth Algorthm 8765555500000000 8765555000000000 8655550000000000 8555550000000000 7765555000000000 7765550000000000 6655550000000000 5555500000000000 6555555000000000 5555550000000000 5555500000000000 5555500000000000 6655550000000000 5555500000000000 5555000000000000 5555000000000000 6655550000000000 5555500000000000 5555000000000000 5550000000000000 6555500000000000 5555500000000000 5550000000000000 5550000000000000 5555500000000000 5555000000000000 5550000000000000 5500000000000000 5555000000000000 5555000000000000 5500000000000000 5500000000000000 5555000000000000 5550000000000000 5500000000000000 5500000000000000 5550000000000000 5550000000000000 5500000000000000 5000000000000000 5500000000000000 5500000000000000 5000000000000000 5000000000000000 5500000000000000 5500000000000000 5000000000000000 5000000000000000 5500000000000000 5500000000000000 5000000000000000 0000000000000000 5500000000000000 5500000000000000 5000000000000000 0000000000000000 5500000000000000 5500000000000000 0000000000000000 0000000000000000 5500000000000000 5500000000000000 0000000000000000 0000000000000000 Class 4 Class 3 Class 2 Class 1 Fgure 2.7 - Varaton of the Bt Allocaton Maps Employed n the Chen-Smth Smulaton 2-18
U compresson to be acheved usng ths technque can be a preset run-tme parameter. For example, f a 1 bt per pxel compresson rato was desred, the number of average bts for classes 1, 2, 3, and 4 would be.67,.83, 1.17, and 1.33, respectvely. n the second pass, the sub-block classfcaton and bt allocaton maps are used to encode the mage for * transmsson. The quantzaton method used n the Chen-Smth technque s the classcal Lloyd-Max quantzaton technque (Refs. 2,3). Ths technque s a non-unform quantzaton scheme whch uses a probablty densty functon (pdf) specfc to the dstrbuton of the data to be quantzed. n the basc Chen-Smth codng technque, the dstrbuton of transform coeffcents s assumed to be Gaussan. Therefore, a Gaussan pdf was used for quantzaton n the smulatons. A varaton of the basc Chen-Smth algorthm nvolvng the * generaton of bt allocaton maps was mplemented for the followng reason. After prelmnary smulatons were performed, statstcs demonstrated that the quantzaton of bts/pxel values below 5 n the bt allocaton maps would have no postve effect on mage qualty, and n some cases would degrade mage qualty. A method was devsed whch would acheve the same number of bts for the bt allocaton map, but would not assgn bts/pxel values of less than 5 to any coeffcent poston. An example of ths method s shown n Fgure 2.7, whch llustrates 2-19
the same bt allocaton maps shown n Fgure 2.6 wth the varaton mplemented. 2.2.5 mage Dependent Chen-Smth Codng The mage dependent Chen-Smth technque s mplemented n the same way as the basc Chen-Smth technque, wth one varaton. The basc Chen-Smth technque s an mage ndependent technque; that s, a preset number of bts s used to encode an mage, wth an equal number of sub-blocks assgned to each class n the classfcaton map, ndependent of mage characterstcs. The mage dependent approach s mplemented at the tme that the mage classfcaton map s produced. The AC energes are examned, and, dependng on ther comparatve values, an approprate number of sub-blocks are assgned each class. For example, f an actve mage s processed, the majorty of class assgnments would be 3's and 4's; f an nactve mage s processed, the majorty of class assgnments would be l's and 2's. Ths varaton of the Chen-Smth technque s dependent on mage characterstcs for class assgnments (and, thus, the m number of total bts for mage encodng) and does not necessarly encode a fxed number of bts ndependent of mage * characterstcs. 2-20
2.3 Selecton of Test Documents The test documents employed n the computer smulaton were selected based on several factors, ncludng mage qualty, avalablty, and feature content. As specfed n the statement of work, three gray scale mages were chosen. These mages are the same three test documents employed n a gray scale study prevously performed by Delta nformaton Systems for the NCS (Ref. 4), n whch Dfferental Pulse Code Modulaton (DPCM) and Bt Plane Codng (BPC) were evaluated. Beyond the advantages these mages provde n terms of mage qualty and avalablty, each mage was selected because t contaned several dstnctve features that would ad n the subjectve evaluaton of the output mages. The EEE face mage was selected because t contans large areas of relatvely smooth tonal range, where artfacts resultng from compresson usually manfest themselves. The aeral photo mage was chosen because t contans low contrast, hgh detal regons sutable for vsual evaluaton of the output mages. The crowd scene mage contans well-defned structures, such as facal characterstcs, whch facltate vsual determnaton of the qualty of reproducton. 2-21
3.0 RESULTS 3.1 Compresson Statstcs The results acheved n the smulatons performed to determne the effects of the parametrc varatons of each of the four transform codng algorthms are summarzed n Tables 3.1 through 3.3. Table 3.1, whch contans the results of the smulatons performed usng the EEE test face mage, ncludes the results of 18 smulaton runs, whereas Tables 3.2 and 3.3 nclude the results for 12 smulaton runs each. The EEE face mage was selected to llustrate the vsual effects of the compresson algorthms; thus, addtonal smulatons were performed wth ths test mage n order to more fully evaluate the effects of the compresson technques on output mage qualty. For each smulaton run, four statstcal measures of performance of the employed algorthm are presented. The frst three, the number of compressed bts (the number of bts output by the quantzaton process), the compresson rato (the number 3 of compressed bts as a functon of the number of bts n the * nput mage), and the compressed number of bts per pxel (the effectve number of bts per pxel requred to transmt the mage), provde a measure wth whch the algorthms can be compared n terms of compresson. The fourth measure, the rootmean-square (RMS) error (a weghted-average dfference between
TABLE 3.1 - COMPRESSON RESULTS ON THE EEE FACE COMPRESSON PXELS LNES ADJUSTABLE COMPRESSED COMPRESSON COMPRESSED RMS MAGE TECHNQUE PER LNE PER MAGE PARAMETERS BTS RATO BTS/PXEL ERROR Condtonal Zonal 1024 1408 1K 5 225280 51.20 0.16 9.01 CK 17 765952 15.06 0.53 5.10 #K 33 1486848 7.76 1.03 3.37 CK 70 3153920 3.66 2.19 2.06 CO 3.00 325032 35.49 0.23 5.52 Adaptve Co 1.50 465648 24.77 0.32 4.42 Zonal 1024 1408 E CO 0.50 849569 13.58 0.59 3.19 Codng E CO 0.04 2345776 4.92 1.63 2.12 E BM 0.08 148915 77.46 0.10 89.6 B M 0.15 299217 38.54 0.21 6.23 Basc F 1024 1408 BM 0.50 777410 14.84 0.54 4.06 Chen-Smth A B 1.00 1475685 7.92 1.02 2.97 C 3f 2.00 3332747 3.46 2.31 1.83 E BM 0.15 202774 56.88 0.14 7.14 Chen-Smth DM 0.30 320570 35.98 0.22 5.78 mage 1024 1408 B 1.00 997840 11.56 0.69 3.32 Dependent BM 1.40 1412863 8.16 0.98 2.72 ~~ _ - 2_ BM 2.50 2585861 4.46 1.79 1.96 * 3-2
1 TABLE 3.2 - COMPRESSON RESULTS ON THE CROWD SCENE CONPRESSON PXELS LNES ADJUSTABLE COMPRESSED COMPRESSON COMPRESSED RNS E NA6E TECHNQUE PER LNE PER BA6E PARAMETERS BTS RATO BTS/PXEL ERROR mk 16 720896 16.00 0.50 3.67 Condtonal Zonal 1024 1408 1K 32 1441792 8.00 1.00 2.56 C Codng E R 1K 65 2928640 3.94 2.03 1.89 0 CO 1.00 737672 15.64 0.51 3.55 Adaptve D Zonal 1024 1408 CO 0.25 1462680 7.89 1.01 2.49 Codng CO 0.05 2626904 4.39 1.82 1.96 S C BM 0.50 768595 15.01 0.53 2.72 E 1024 1408 Chen-Sm th BM 1.00 1485091 7.77 1.03 1.92 N DM 2.00 2982828 3.87 2.07 1.39 E Chen-Svth BN 0.70 867764 13.29 0.60 2.54 mage 1024 1408 " 1.00 1177471 9.90 0.81 2.17 Dependent BM 2.30 2902867 3.97 2.01 1.45 3-3
TABLE3.3- COMPRESSON STATSTCS ON THE AERAL PHOTO COMPRESSON PXELS LNES ADJUSTABLE COMPRESSED COMPRESSON COMPRESSED RMS MAGE TECHNQUE PER LNE PER MAGE PARAMETERS BTS RATO BTSPXEL ERROR C UK 15 675840 17.07 0.47 6.27 Condtonal Zonal 1024 1408 UK 33 1486848 7.76 1.03 3.17 A Codng K 70 3153920 3.66 2.19 2.05 R CO 1.00 1073856 10.74 0.74 5.16 Adaptve Zonal 1024 1408 CO 0.45 1557064 7.41 1.08 3.73 k Codng L CO 0.20 2138528 5.39 1.48 2.80 BN 0.50 747479 15.43 0.51 4.32 P Basc H 1024 1408 BM 1.00 1552633 7.43 1.08 2.58 Chen-Smth T BM 2.00 3334688 3.46 2.31 1.62 0 B" 0.55 719764 16.03 0.50 4.60 ~ ~~~Chen-Su th mage 1024 1408 BM 1.10 1614243 7.14 1.12 2.58 Dependent BM 2.20 2866510 4.02 1.99 1.91 3-4
the gray level value of an orgnal nput pxel and the correspondng pxel n the decoded output mage), provdes a bass upon whch the algorthms can be compared quanttatvely n terms of mage qualty. The RMS error s a quanttatve measure of the mage qualty of the output mage and s calculated as follows: RMS = e, 2 + e2 2 + + en 2 where et s the 8-bt dfference, or error, between the t h pxel n the nput mage and the correspondng th pxel n the decoded output mage, and N s the total number of pxels n the processed mage. The RMS error can also be expressed as a percentage of the dynamc range (20, where n = number of S #K bts/nput pxel) of the gray scale of the mage. Each transform codng algorthm has an adjustable parameter that can be vared n order to select a target compresson; lsted below are the abbrevatons used n Tables 3.1 through 3.3 to dstngush these parameters: Abbrevaton Descrpton Used n the one-pass condtonal zonal algorthm to select the number of coeffcents to be kept n the quantzaton zone of each sub-block. CO Used n the one-pass adaptve zonal algorthm as a cutoff threshold for the elmnaton of nsgnfcant 3-5
BM coeffcents pror to quantzaton. Both the basc and the mage dependent Chen-Smth algorthms assgn bts to each class for quantzaton. BM s used to select the average number of bts per pxel over the four bt map classfcatons. The smulatons performed to evaluate the condtonal zonal codng algorthm were desgned so that the effects of the parametrc varatons were clearly llustrated; the parameter chosen for evaluaton n the condtonal zonal codng smulatons was the number of retaned coeffcents, or zone sze (#K). The * effect of the zone sze parameter on compresson s straghtforward; as t s decreased, the number of compressed bts/pxel s decreased. mage content has no effect on the compresson acheved by the zonal codng technque; the same number of bts s used to encode each sub-block regardless of the statstcs of the sub-block. Smulatons n whch the zone sze was vared were performed n order to determne the parameter's * effect on output mage qualty; the compressons acheved were selected so as to be comparable to the compressons acheved n the DPCM smulatons performed n a prevous study (Ref. 4). The smulatons performed to evaluate the adaptve zonal codng algorthm were desgned so that the effects of the parametrc varatons were clearly llustrated; the parameter chosen for evaluaton n the adaptve zonal codng smulatons was the coeffcent cutoff threshold (CO). The cutoff thresholds S3-6
employed n the smulatons were selected n order to acheve compressons comparable to those acheved for the DPCM and condtonal zonal codng smulatons. Whle the target compressons for the condtonal zonal codng smulatons could be precsely selected wth the zone sze parameter (#K), the target compressons for the adaptve zonal codng smulatons S were more dffcult to select because of the statstcal dependency of the technque. The smulatons performed to evaluate the basc Chen-Smth * codng algorthm were desgned so that the effects of the parametrc varatons were clearly llustrated; the parameter chosen for evaluaton n the basc Chen-Smth codng smulatons was the average number of bts/pxel over the four bt map classfcatons (BM). The average bts/pxel values employed n the basc Chen-Smth smulatons were selected so as to produce compresson results comparable to those of the other codng * technques evaluated n ths study. The smulatons performed to evaluate the mage dependent Chen-Smth codng algorthm were desgned so that the effects of the parametrc varatons were clearly llustrated; the parameter chosen for evaluaton n the mage dependent Chen-Smth codng smulatons was the same as that employed n evaluatng the basc Chen-Smth codng algorthm, namely the average number of bts/pxel over the four bt map classfcatons (BM). The average bts/pxel values employed n the mage dependent Chen- Smth smulatons were selected so as to produce compresson 3-7
results comparable to those of the other codng technques evaluated n ths study; however, the adaptve nature of ths codng technque made t dffcult select target compressons as precsely as was possble wth the basc Chen-Smth codng technque. 3.2 Output mages * Before the mage qualty of the transform codng algorthms can be evaluated, an understandng of the type of dstorton caused by transform codng s requred. The mage dstorton caused by these algorthms manfests tself n "blockng", n whch the edges of the ndvdual sub-blocks become vsually apparent. Transform codng algorthms break the mage nto subblocks and process the mage one sub-block at a tme. Blockng occurs manly n the busy sectons of the mages. A large amount of AC energy exsts n a busy sub-block, meanng that the transform coeffcents of the sub-block contan a large amount of nformaton. Blockng occurs when, through quantzaton, a sgnfcant part of ths nformaton s lost, and the reconstructed sub-block n the output mage s markedly * dssmlar from those sub-blocks surroundng t. Table 3.4 s a lst of the output mages presented n Fgures 3.2 through 3.18; Fgure 3.1 s an llustraton of an photographc reproducton of a wndowed porton of the output orgnal nput mage, the EEE face. Each mage s a 3-8
U TABLE 3.4 - LST OF OUTPUT MAGES FGURE NUMBER MAGE DESCRPTON 3.1 Wndowed porton of Orgnal EEE Face mage 3.2 Condtonal Zonal EEE Face mage at 0.16 bpp 3.3 Condtonal Zonal EEE Face mage at 0.53 bpp 3.4 Condtonal Zonal EEE Face mage at 1.03 bpp 3.5 Adaptve Zonal EEE Face mage at 0.32 bpp 3.6 Adaptve Zonal EEE Face mage at 0.59 bpp 3.7 Adaptve Zonal EEE Face mage at 1.63 bpp 3.8 Basc Chen-Smth EEE Face mage at 0.10 bpp 3.9 Basc Chen-Smth EEE Face mage at 0.54 bpp 3.10 Bpsc Chen-Smth EEE Face mage at 1.02 bpp 3.11 mage Dependent Chen-Smth EEE Face mage at 0.22 bpp 3.12 mage Dependent Chen-Smth EEE Face mage at 0.69 bpp 3.13 mage Dependent Chen-Smth EEE Face mage at 0.98 bpp 3.14 Orgnal Crcular Test mage 3.15 Condtonal Zonal Crcular Test mage 3.16 Adaptve Zonal Crcular Test mage 3.17 Basc Chen-Smth Crcular Test mage 3.18 mage Dependent Chen-Smth Crcular Test mage 3-9
G Fcure 3.1 -Wndowed porton of Orgnal EEE Face maae Fcure 3.2 -Condtonal Zonal EEE Face mage at 0.16 3-10
ue33 CnnlZnlE aeaea.3bp... ue34 CnnlZnl EEFc mg t10 j 3 1
ue35 Aatv oa EEFc mg t03 2 ;M FueAatvoa EE aeaea.912 3 1
ue37 Aatv oa EEFc mg t16 ue38 BscCe-mt EEFc mg t01 3 3 1
Faure 3.10-3.9 - Basc Chen Smth EEE Face ~ Basc Chen-Smth EEE Face maae at 1.02 k22 3-14
. ue31 mc eedn hnsmt EEFc mg t02 j Fgure 3.112 maae Dependent Chen-Smth EEE Face mage at 0.229P 3 1
,++ +. Fgure 3.13 - mage Dependent Chen-Smth EEE Face mage at 0.98 bp2 -- Fgure 3.14 - Orgnal Crcular Teat mage 3-16
Faure 3.15 - Condtonal Zonal Crcular Test mage Faure 3.16 - AdaDtve ~p~j Crcular Test mage 3 3- :1.7
~~re 3.17 - Basc Chen-Smth Crcular Test ~ Fgure 3.18 - mage Deyendent Chen-Smth Crcular Test maae 3-18
mage of one smulaton. The full mage sze was not reproduced photographcally because of the lmtatons of the mage storage and dsplay system used to evaluate the output mages. Note that, as n the earler study (Ref. 4), only the smulatons run on the EEE face mage are represented. The effects of the algorthms were smlar for all three test mages; the EEE face mage was selected as the llustratve example of the output mage qualty of the algorthms n order to facltate drect comparsons wth the results of the DPCM smulatons performed n the earler study. The evaluaton of the mage qualty of each of the four transform codng algorthms, however, * was performed consderng the output mages from the smulatons run on all three test mages. n addton, a crcular test mage, extracted from the EEE test chart from whch the TEEE face mage was obtaned, was compressed wth each transform codng algorthm n order to evaluate the effects of sharp * transtons on the mage qualty produced by the algorthms. The mage qualty produced by the transform codng * algorthms was generally good above 0.5 bts/pxel and far at bt rates as low as 0.16 bts/pxel. Quanttatvely, the hghest RMS error value obtaned n the smulatons employng the EEE face mage was 9.01, obtaned n the condtonal zonal smulaton run n whch 0.16 bts/pxel compresson was acheved. Ths value, measured n gray levels, represents a maxmum error of only 3.5 percent of the dynamc range (256 gray levels) of the mages. The RMS error, whle a good relatve measure of the 3-19
mage qualty produced by the algorthms on a partcular mage, should not be regarded as an absolute measure of mage qualty. The RMS error s only an average measure of mage qualty and does not reflect the fact that the algorthms perform well on mage regons that are relatvely nactve n terms of gray scale actvty and not as well on mage regons that contan a sgnfcant number of gray scale transtons. The condtonal zonal codng algorthm produced mages whch were very good n terms of mage qualty for bt rates above 1 bt/pxel. n Fgure 3.4, only a mnmal amount of blockng can be detected n the hgh detal regons of the mage (e.g. the eyes, the teeth); the overall effect of the blockng s a slght blurrng of the mage. At lower bt rates, the ndscrmnate quantzaton employed by ths codng technque caused sgnfcant dstorton n the output mages. At bt rates on the order of 0.5 bts/pxel, the loss of detal n all areas of the mage s evdent, and the blockng s much more pronounced (see Fgure 3.3). At bts rates below 0.5 bts/pxel, the blockng s severe, and the hgh detal regons of the mage are almost completely degraded (see Fgure 3.2). The adaptve zonal codng algorthm produced mages whch were excellent n terms of mage qualty for bt rates above 1 bt/pxel. The mage n Fgure 3.7 llustrates ths level of mage qualty; no blockng s evdent, and only a slght loss of sharpness s detectable n the hgh detal regons of the mage (e.g. the pupls of the eyes). At lower bt rates, blockng 3-20
begns to occur n mage areas n whch moderate gray level transtons are present. Blockng n these areas s caused by excessve quantzaton; optmzaton of the look-ahead algorthm would mnmze ths dstorton. At bt rates on the order of 0.5 bts/pxel, some blockng s evdent n mage regons contanng moderate detal (e.g. the nose, the lps); the overall sharpness of the mage, however, s only slghtly degraded (see Fgure 3.6). At bt rates below 0.5 bts/pxel, blockng s evdent n areas of moderate to hgh detal, but the overall mage qualty s stll qute good. The basc Chen-Smth codng algorthm produced mages whch were excellent n terms of mage qualty for bt rates above 1 bt/pxel. The mage n Fgure 3.10 llustrates ths level of mage qualty; no blockng s evdent, and only a slght loss of sharpness s detectable n the hgh detal regons of the mage (e.g. the pupls of the eyes). At bt rates on the order of 0.5 bts/pxel, the mage qualty s stll very good; blockng s only slghtly perceptble n the hgh detal regons of the mage, and the overall sharpness of the mage s stll good (see Fgure 3.9). At bt rates below 0.5 bts/pxel, the mage qualty becomes progressvely worse; at 0.1 bts/pxel, the blockng s severe, and the hgh detal regons of the mage are almost completely degraded (see Fgure 3.8). The mage dependent Chen-Smth codng algorthm produced mages whch were excellent n terms of mage qualty for bt rates above 0.5 bts/pxel. Fgure 3.13, n whch the mage was 3-21
H compressed to less than 1 bt/pxel, s vrtually ndstngushable from the uncompressed mage (see Fgure 3.1). At bt rates approachng 0.5 bts/pxel, the mage qualty s stll excellent; as Fgure 3.12 shows, no blockng s evdent, and the overall sharpness of the mage s only slghtly degraded. At bt rates below 0.5 bts/pxel, the mage qualty produced by the mage dependent Chen-Smth algorthm s stll qute good; blockng s evdent around the hgh detal regons of the mage, but the overall mage qualty s stll good (see Fgure 3.11). A crcular test mage, presented n Fgure 3.14, was employed to evaluate the performances of the transform codng algorthms; the black-whte colorng of the crcular test mage provded a good test of the quantzaton functons of the subblock codng algorthms. n comparng Egures 3.15 through 3.18, t s evdent that the mage dependent Chen-Smth codng technque produced the best output mage; the 100's are stll legble n the mage dependent Chen-Smth output mage, but are qute blurred n the output mages of the other compresson technques. Ths s due to the desgn of the mage dependent Chen-Smth algorthm, whch allocates addtonal codng bts to those mage regons whch requre more nformaton to encode them. 3-22
3.3 Algorthm Complexty n Sectons 3.1 and 3.2, the four transform codng algorthms were compared on the bass of compresson and mage qualty. t s also mportant to compare the codng technques on the bass of ther relatve mplementaton complextes. All four algorthms employ the Dscrete Cosne Transform (DCT) n the transformaton step; as such, the dfferences n algorthm complexty occur n the sub-block codng steps of the algorthms. Of the four technques, the condtonal zonal codng algorthm s the least complex. n the transformaton step, the mage s dvded nto sub-blocks, and each sub-block of gray level values s transformed nto a matrx of coeffcents. n the sub-block codng step, the transform coeffcents n a selected zone of the sub-block are normalzed and quantzed to a selected number of bts, and the remanng coeffcents n the sub-block are dscared. Every sub-block wthn an mage s encoded wth the same number of bts, and every mage s encoded wth the same number of bts. The adaptve zonal codng technque s a hybrdzaton of threshold codng and condtonal zonal codng. Threshold codng s a sub-block codng technque n whch each coeffcent n the sub-block s compared to a specfed threshold value n order to determne whether the coeffoent s to be kept or dscarded. One major drawback to threshold codng s the overhead requred to store the locatons wthn the sub-block of each retaned 3-23
coeffcent; adaptve zonal codng elmnates the need for ths overhead by performng the threshold comparson n a specfc order n a pre-determned zone of the sub-block, thus elmnatng the need for the storage of coeffcent locatons. The only overhead requred for adaptve zonal codng s an addtonal byte of nformaton for each sub-block that ndcates the number of coeffcents retaned n that sub-block; other than that, the encodng proceeds exactly as n the condtonal zonal codng technque. The Chen-Smth codng algorthms are relatvely more complex than the zonal codng algorthms; the basc Chen-Smth algorthm processes an mage n two passes. The frst pass over the mage calculates statstcs whch characterze the mage. The statstcs are used to determne the number of bts assgned to each coeffcent of each sub-block of the mage. The AC energes of the sub-blocks are used to produce a sub-block classfcaton map of the mage, n whch each sub-block s assgned to one of four classes, such that there are an equal number of sub-blocks assgned to each class. A bt allocaton map s then produced for each classfcaton, n whch the varances of the transform coeffcents are used to determne the number of bts to be employed to encode the coeffcents. n the second pass, the sub-block classfcaton and bt allocaton maps are employed to * encode the mage. The mage dependent Chen-Smth codng technque s the most complex of the four algorthms smulated. n ths varaton of 3-24
m the basc Chen-Smth algorthm, the AC energes of the sub-blocks are used to assgn classfcatons to the sub-blocks based on mage content rather than on a pre-specfed number of sub-blocks per class. Thus, mages contanng a hgh amount of actvty are compressed wth better output mage qualty, and mages contanng a low amount of actvty acheve better compresson m wthout a sgnfcant loss of output mage qualty. 3.4 DPCM Comparson Two DPCM compresson algorthms were smulated n a study prevously performed by Delta nformaton Systems (Ref. 4). The frst, condtonal DPCM, employs a three-neghbor gray level value predctor, a non-lnear three-bt quantzer, Huffman entropy codng, and an optonal staggered horzontal sub-sampler and correspondng nterpolator. The second, adaptve DPCM, employs a three neghbor gray level predctor, an extended nonlnear fve-bt quantzer, adaptve arthmetc codng, and optonal horzontal and vertcal spatal flters. Quantzaton n DPCM codng refers to the quantzaton of the dfference between the predcted value of the gray level of a pxel and the * actual value. Table 3.5 summarzes the results of the DPCM smulatons whch were performed n a prevous study (Ref. 4); as can be seen, the same test mages employed prevously were used n ths study n order to make the results drectly comparable. 3-25
TABLE 3.5 - DPCH COMPRESSON RESULTS COMPRESSON PXELS LNES ADJUSTABLE COMPRESSED COMPRESSON COMPRESSED RHS KA6E TECHNQUE PER LNE PER MASE PARAMETERS BTS RATO BTS/PXEL ERROR BASE 1890566 6.13 1.30 3.91 Condtonal E 1024 1408 SS 1039426 11.10 0.72 3.96 E DPCN E SS,HS" 912077 12.65 0.63 4.08 F BASE 1975109 5.84 1.37 1.20 A Adaptve C 1024 1408 HSm 1414596 B.15 0.98 2.00 E DPC_ HS, BELL 1444367 7.99 1.00 2.26 C BASE 1994002 5.78 1.39 5.32 R Condtonal 0 1024 1409 SS 1112332 10.37 0.77 4.79 DPCN D SSHSN 968462 11.91 0.67 4.94 S BASE 2406572 4.79 1.67 1.30 C Adaptve E 1024 1408 HSN 1754491 6.57 1.22 2.04 N DPCN E HSNBELL 2296846 5.02 1.59 2.14 A BASE 2144099 5.38 1.49 3.34 E Condtonal R 1024 1408 SS 1251099 9.22 0.97 3.33 DPCN A SSHS" 1131161 10.20 0.78 3.75 L C BASE 2943794 3.92 2.04 1.29 P Adaptve H 1024 1408 HSH 2296903 5.04 1.59 2.36 BPCM 0 HSMDELL 2902523 3.97 2.01 2.47 3-26
Table 3.6 lsts the output mages, presented n Fgures 3.19 through 3.23, assocated wth fve of the DPCM smulatons performed usng the EEE face mage. Because the compresson acheved n the transform codng smulatons was selectable, runs * were performed to closely match the compressons acheved by the DPCM algorthms so that drect mage qualty comparsons could be * performed. The mage qualty produced by both DPCM algorthms was excellent; the hghest RMS error value, obtaned n the baselne condtonal DPCM smulaton run on the crowd scene mage, was 5.32. Ths value, measured n gray levels, represents a maxmum error of only 2 percent of the dynamc range (256 gray levels) of the mages. The two preprocessng steps employed n the DPCM smulatons, horzontal subsamplng and horzontal flterng, had the effect of sgnfcantly ncreasng compresson whle only slghtly degradng the output mage qualty. The condtonal DPCM algorthm wthout preprocessng produced mages whch were excellent n terms of mage qualty; Fgure 3.19 llustrates ths level of qualty. Wth subsamplng (Fgure 3.20), the qualty of the output mages produced by the condtonal DPCM algorthm were stll qute good, wth only a slght blurrng effect evdent n the hgh-detal regons of the mages (e.g. the har and teeth regons of the EEE face mage). When both subsamplng and horzontal flterng were employed n conjuncton wth the condtonal DPCM algorthm, the mage qualty llustrated n Fgure 3.21 was produced at an encoded bt 3-27
TABLE 3.6 - LST OF DPCM OUTPUT MAGES FGURE NUMBER MAGE DESCRPTON 3.19 Condtonal DPCM Encoded EEE Face mage at 1.30 bpp 3.20 Condtonal DPCM Encoded EEE Face mage wth Subsamplng at 0.72 bpp 3.21 Condtonal DPCM Encoded EEE Face mage wth Flterng and Subsamplng at 0.63 bpp 3.22 Adaptve DPCM Encoded EEE mage at 1.37 bpp 3.23 Adaptve DPCM Encoded EEE mage wth Flterng at 0.98 bpp U 3-28
~g~ge 3.19 - Condtonal DPCM Encoded EEE Face ~ at 1.30 ~ U Faure 3.20 - Condtonal DPCM Encoded EEE Face mage wth Sub5amvlng at 0.72 ~pp 3-29
v97a ue32 odtoa PMEcddE aeaewt usmln n leg.3b Fgure 3.21 A odptona DPCM Encoded EEE ae atg 1.37?2 Subam~3n an3 te0at06