On the processing of compressed and encrypted signals and imagery, with applications in efficient, secure computation

376 Pages·1996·13.6 MB·English

by  Schmalz, Mark Steven

ONTHEPROCESSINGOFCOMPRESSEDANDENCRYPTED
SIGNALSANDIMAGERY,WITHAPPLICATIONS
INEFFICIENT,SECURECOMPUTATION
By
MARK STEVENSCHMALZ
ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL
OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT
OFTHEREQUIREMENTSFORTHEDEGREEOF
DOCTOROFPHILOSOPHY
UNIVERSITYOFFLORIDA
1996
Copyright©1996byMarkS.Schmalz
ACKNOWLEDGMENTS
Manythanksaregiventomyfamily,fortheirlovingsupportandencouragement,and
toDrs. Ritter,Wilson,Laine,Rajasekaran,andHarrisfortheiradvisementofthiswork
andassociatedpublicationefforts.SpecialgratitudegoestoGerhardRitter,forhispatient
adviceandencouragmentinthedevelopmentofunifyingtheory.
iii
TABLEOFCONTENTS
page
ACKNOWLEDGMENTS iii
LISTOFFIGURES vi
LISTOFTABLES viii
ABSTRACT ix
1. INTRODUCTION 1
1.1. StudyOverview 2
1.2. PreviousWork 4
1.3. TechnicalApproach 31
1.4. NovelClaims 32
1.5. ImplementationalAdvantagesandDisadvantages 33
2. REVIEWOFNOTATION 35
2.1. OverviewoftheImageAlgebra(lA)Subset 35
2.2. StudyNotation 46
3. FUNDAMENTALTHEORY 49
3.1. MathematicalConcepts 49
3.2. ImageCompression,Encryption,andCompressiveComputation 56
3.3. TaxonomyofImageTransformations 73
3.4. Class-SpecificDerivationalTechniques 79
4. COMPRESSIVEPROCESSING—COMPUTATIONALCOMPLEXITYAND
DATASECURITY 117
4.1. ComplexityofImageAlgebraOperations 118
4.2. ComplexityofCompressiveComputation 124
4.3. FeasibilityofCompressiveComputation 134
4.4. DataSecurity 141
4.5. FeasibilityofEncryptiveComputation 158
5. COMPUTATIONALERRORANDINFORMATIONLOSS 164
5.1. TheoryofErrorPropagationinDiscreteSystems 164
5.2. ErrorPropagationinDiscreteImageAlgebraOperations 173
5.3. TheoryofError-TolerantComputation 180
5.4. FeasibilityofError-TolerantComputation 182
5.5. InformationTheoryandError-TolerantComputation 187
iv
6. CLASS1TRANSFORMATIONS 198
6.1. SubstitutionalCipliers 198
6.2. TranspositionalCiphers 208
6.3. LinearTransforms 211
7. CLASS2TRANSFORMATIONS 223
7.1. GeneralizedClass2Transform 223
7.2. PixelValueCompressionviaBitSlicing 228
8. CLASS3TRANSFORMATIONS 236
8.1. AffineTransformation 236
8.2. SpatialTransformationbyPixelSelection 247
8.3. TranspositionalCiphers 253
9. CLASS4TRANSFORMATIONS 259
9.1. BlockEncoding 259
9.2. SparseMatrixProcessing 261
9.3. TransformCoding 265
9.4. JPEG 268
9.5. BlockTruncationCodingandVPIC 276
9.6. VectorQuantization 291
10. APPLICATIONSOFCOMPRESSIVEIMAGEPROCESSING 302
10.1. CompressiveSmoothing 302
10.2. CompressiveEdgeDetection 310
10.3. VPICMorphologicalOperations 323
10.4. High-LevelCompressiveComputations 326
11. APPLICATIONSINPARALLELCOMPUTING 334
11.1. EffectofDomainCompressionRatio 334
11.2. EffectofRangeCompressionRatio 338
11.3. SimplificationofOperations 339
11.4. PartitioningEfficiency 341
12. CONCLUSIONS 346
12.1. Conclusions 346
12.2. OpenIssuesandFutureWork 350
REFERENCES 356
BIOGRAPHICALSKETCH 362
V
LIST OF FIGURES
1. Commutativitydiagramforprocessingcompressedorencryptedimagerywith
unaryoperations 59
2. (a)ExamplesourceimageathatistransformedbyTtoyield(b)imagea^. Note
reversalofthemiddle4x4-pixelneighborhoodonly 82
3. Exampleofblockfragmentationinpointwisecompressiveoperationsover
non-identicallytesselateddomains: (a)representationofthey-thblockina(solid
line)andb(dottedline),(b)resultantblockdecimationrequiredtoprocessthe
compressedimagesCc=acO' suchthatcorrespondingsub-blocksare
amenabletopointwisecombination 113
4. eCnocmomduitnagtitvraintsyfodrimasgrTaimaonfdamuclotmipprleessainvaelocgoumepsutQa[tioofniamlasgyesotpeemrawtiitohnmQultiple 136
5. Commutativitydiagramofacompressivecomputationalsystemwithmultiple
einmcaogdeinogpertartainosnfoOrjms>wTjhe,rieGCZ^=,2ailadndmu0lti=pl2eanaloguesOj,i>j^Z,/,ofthej-th 137
6. Information-theoreticmodelofcommunication 187
7. Information-theoreticmodelofcommunication 187
8. ArrangementofnoiselevelsinasignalawithentropyH(a)thatpartiallyoccupies
achannelofbandwidthBhavingKnoisebits 195
9. Localaveragingofanoisy,two-dimensional,8-bitimagetransformedbyT(x)=
(x-)-128)mod256:(a-b)sourceimageandtemplateaandt;(c-d)transformed
imageandtemplatea^ands;(e)transformedresultbe;(f)image-domainresultb
=T-i(bc) 206
10. Dualofpointwisemultiplicationovertherangespaceofthepointwiselinear
transformT(x)=cx-|-d 214
11. Recoveryofsourceimageafromimagesumofcontrast-stretchedimagery:(a-b)
sourceimagesaandb,(c-d)linearcontrast-stretchedimagesa^=T(a)andbe=
T(b),(e)Cc=acandb^,(f)recoveryofafrom usinga=T"^(cc-T(b)). . . 215
12. Pixelindexingandoverlapschemeforinformationlossanalysisofanaffine
transform(a)indexingschemeand(b)exampleofpixeloverlap 238
vi
13. LocalaveragingofarotatedBooleanbarchartusingarotatedtemplate: (a-b)
sourceimageaandtemplatet;(c-d)rotatedimageac=T(a)andtemplates
formedbyapplyingTtotheweightmatrixoft,thenrestrictingtothe3x3-pixel
Mooreconfiguration;(e)rotatedlocally-averagedimageac@s;(f)derotated
imager'(ac@s) 251
14. Errorimagesoflocalaveragingusingrotatedandunrotatedtemplates: (a-b)
errorimagese(Equation307)andf(Equation308),takenfromthecentral
(uncropped)portionofdomain(a);(c-d)histogramsoferrorimageseandf. . . 252
15. ErrorandefficiencymeasuresassociatedwithJPEGadditionovernaturalscenes
having3bits/pixelerror 275
16. VCoQdepbooinotkwigsreowadtdhitainodn:er(rao)rianspuatfaunncdtioountpouftccooddeebobookoksizseizaesndMMaentdhoNd,s(1b)-3infoprut
andoutputerrorse,and6„ 300
17. Blockconfigurationforcompressivelocalaveraging,showingblockneighborhoods
(dashedboxes)onXreturnedbyc,r,andj 304
18. ExampleofcompressivesmoothingatCRa=16:1:(a)sourceimage,(b)locally
averagedimageusingunitaryvonNeumanntemplate,(c)compressedarrayof
blockmeansoverwhichprocessingactuallyoccurs,(d)decompressedresultof
compressivesmoothing 307
19. ExampleofVPICcodingofverylow-resolutionBooleanimagery:(a)sourceimage,
(b)VPICrepresentationofa),whereM,xdenotesameanblockofmeanx. . . 318
20. ExampleofVPICcodingofverylow-resolutionBooleanimagery: (a)
boundary-detectionofFigure19a),(d)VPICedgedetectionofFigure19a). . . 319
21. ErroranalysisoftheedgedetectorinFigure20b,intermsoferroneoussource
pixelsperencodingblock 320
22. GreyleveledgedetectionwithVPIC:(a)sourceimage,(b)Sobeledgedetection,
(c)4X4-pixelVPICedgedetectionusingthecodebooksimilartothatgivenin
Example10.2.2.3,(d)noiseandrepresentationalerrorasafunctionofVPIC
blocksize(kxkpixels)forunderwaterandland-basedimagery 321
23. TargetcharacterizationusingVPICcodebookexemplarswithindicesin{1,2,3}:
(a)VPICcodebook,(b)sourceimagewithunitarily-valuedtargetregion,(c)
compressedrepresentation,where1'denotesexemplar1rotatedby90degrees.. 328
24. ExampleofVPIC-basedtargetrecognition: (a)sourceimage,(b)
BTC-compressedimageoveraportionofwhichthetargetrecognitionalgorithm
(Equation410)computes,(c)decompressedtargetlocationimage 330
25. ConversionofaSIMD-parallelmeshtopipelinedcomputationusingcompressive
processing: (a)inputandcomputeovercompressedimage1,(b)input
compressedimage2andcomputeoverimage1,(c)inputcompressedimage3
andcomputeoverimages1and2,(d)inputcompressedimage4,computeover
compressedimages1-3,andoutputcompressedimage1 337
vii
LIST OFTABLES
1. CostsinvolvedinSIMD-parallelcomputationofa2-pixelimage-template
convolutionversusa5-pixelLUToperationoverVPIC-formatimagery. . 339
2. ProcessorcyclesincurredbySIMD-parallelcomputationofa2-pixelimage-
templateconvolutionversusa5-pixelLUToperationoverVPIC-format
imagery 340
VIU
AbstractofDissertationPresentedtotheGraduateSchool
oftheUniversityofFloridainPartialFulfillmentofthe
RequirementsfortheDegreeofDoctorofPhilosophy
ONTHEPROCESSINGOFCOMPRESSEDANDENCRYPTED
SIGNALSANDIMAGERY,WITHAPPLICATIONSIN
EFFICIENT,SECURECOMPUTATION
By
MarkStevenSchmalz
August1996
Chairman: GerhardX. Ritter
MajorDepartment: ComputerandInformationScienceandEngineering
In thisdissertation,wedeveloptheoryand analysespertinent to theprocessingof
compressedorencryptedimagery,calledcompressiveprocessingorencryptiveprocessing.
Encryptiveprocessing, whichisalong-standinggoalofcomputer science, exploits the
processingofsecure(encrypted)operandstoyieldasecurecomputation. Unfortunately,
developmenthasbeenhindered byanobscureunderstandingofmathematicalconcepts
fundamentaltotheencryptionprocess.Similarly,theprocessingofcompressedimagerycan
yieldcomputationalefficienciesasaresultoffewerinputdata.However,suchspeedupsare
notuniformacrosscommonly-usedimagecompressionformatsandmaynotexistforcertain
operationsovertherangespacesofgiventransforms. Additionally, theformulationof
compressivetransformscanbequiteinvolved,whichintuitivelysuggeststhatthederivation
ofcompressivecomputationaloperationsisdifficultinclosedform.
Wefirstdiscusstheorythatisbasictoanunderstandingofcompressiveandencryptive
processing.Usingimagealgebra,arigorousset-theoreticandfunctionalmappingnotation,
ix
wederivenovelalgorithmsforimplementingselectedpointwisearithmetic,neighborhood-
anddomain-specificoperationsontransformeddata. Ouralgorithmsarebothfeasible
,
and portabletonumerous computers, sinceimagealgebrahas been implementedon a
varietyofserialandparallelprocessors,includingtheConnectionMachine,MasParSIMD
processor,ERIM'sCytocomputer,AlliantTech'sPREP,Inmos'Transputerarchitecture,
andtheMartin-MariettaGAPP-IVprocessoruponwhichthePALarchitectureisbased.
Subsequentimplementationaldiscussionemphasizesthefeasibilityofsequentialand
parallelcompressivecomputation. Weshowthatcompressiveprocessingmethodologies
canbemappedtoavarietyofwell-knownarchitectures,especiallySIMDarrayprocessors.
Analysesfocusupontimecomplexity,cost,anderrorduetoinformationloss.Forexample,
weshowthatcompressiveprocessingcanreducetheprocessorcountinparallelarchitectures
withoutcompromisingthecomputationalspeedupobtainedthroughparallelism.Afurther
advantageofselectedcompressivetransformsistheirabilitytofacilitatethemappingof
costlyalgorithmssuchasedgedetectionandcomponentlabellingtocompressiveoperations
implementedintermsoflookuptables. SuchtechniquesrequireonlyI/Ooperationsand
canbestoredinlocalmemoryincertainSIMD-parallelprocessors.