COL783: Digital Image Processingpkalra/col783/session-17.pdf · 2021. 4. 22. · Image Compression...
Transcript of COL783: Digital Image Processingpkalra/col783/session-17.pdf · 2021. 4. 22. · Image Compression...
COL783: Digital Image ProcessingPremKalra
[email protected]://www.cse.iitd.ac.in/~pkalra/col783
DepartmentofComputerScienceandEngineering
IndianInsEtuteofTechnologyDelhi
RecapSome definitions
• Compression ratio • Fidelity criteria
Data Redundancy • Coding • Interpixel • Psychovisual
Compression techniques • Loss-less and Lossy • Symmetric and Asymmetric
Variable length coding • Huffman Coding • Information theoretic analysis
Entropy
Digital Image Processing http://www.cse.iitd.ac.in/~pkalra/col783
ImageCompressionKraft’s inequality
Digital Image Processing http://www.cse.iitd.ac.in/~pkalra/col783
ImageCompressionLower Bound
Shannon’sCodingTheorem
Digital Image Processing http://www.cse.iitd.ac.in/~pkalra/col783
ImageCompressionLower Bound
Digital Image Processing http://www.cse.iitd.ac.in/~pkalra/col783
ImageCompression
Variants of Huffman Coding • Higher order estimate of entropy • Truncated Huffman Coding • Dynamic or Adaptive Huffman Coding
Efficiency of Huffman Coding
H(z)/L(z)
Digital Image Processing http://www.cse.iitd.ac.in/~pkalra/col783
ImageCompressionArithmetic Coding BasicIdea:a) LikeHuffmancodingrequirespriorknowledgeofprobabiliEesb) UnlikeHuffmancoding,whichassignsvariablelengthcodestosymbolsarithmeEc
codingassignscodestoavariablegroupofsymbolsi.e.themessage.c) Thereisnoone-to-onecorrespondencebetweenthesymbolandits
correspondingcodeword.d) Thecodeworditselfdefinesarealnumberwithinthehalf-openinterval[0,1)and
asmoresymbolsareadded,theintervalisdividedintosmallerandsmallersubintervals,basedontheprobabiliEesoftheaddedsymbols.
Digital Image Processing http://www.cse.iitd.ac.in/~pkalra/col783
ImageCompressionArithmetic Coding
Endofmessageorlengthofmessageisknown.Source:DigitalImageProcessing,GonzalezandWoods.Digital Image Processing http://www.cse.iitd.ac.in/~pkalra/col783
ImageCompressionArithmetic Coding
Finalcode068
Source:DigitalImageProcessing,GonzalezandWoods.Digital Image Processing http://www.cse.iitd.ac.in/~pkalra/col783
ImageCompressionArithmetic Decoding Followsencodingprocedure
Code068maybeconvertedtotherealnumber0.068,whichfallsinthefirstsub-interval[0,0.2)thereforefirstsymbolisa1,andsoon.
Digital Image Processing http://www.cse.iitd.ac.in/~pkalra/col783
ImageCompressionDictionary based methods
• CompressingmulEplestringscanbemoreefficientthancompressingsinglesymbolsonly(e.g.Huffmanencoding).
• StringsofsymbolsareaddedtoadicEonary.Lateroccurrencesarereferenced.
• StaEcdicEonary:EntriesarepredefinedandconstantaccordingtotheapplicaEonofthetext
• AdapEvedicEonary:Entriesaretakenfromthetextitselfandcreatedon-the-fly
Digital Image Processing http://www.cse.iitd.ac.in/~pkalra/col783
ImageCompressionDictionary based methods: LZ77 ByLempelandZivin1977aboutlosslesscompressionwithanadapEvedicEonary.• Runsthroughthetextinaslidingwindow• Twobuffersareused-search(history)bufferandalookaheadbuffer.• ThesearchbufferisusedasdicEonary• Sizesofthesebuffersareparametersofthedesign
Source:h4p://jens.jm-s.de/comp/LZ77-JensMueller.pdfDigital Image Processing http://www.cse.iitd.ac.in/~pkalra/col783
ImageCompressionDictionary based methods: LZ77
Look-ahead
Search
Source:h4p://jens.jm-s.de/comp/LZ77-JensMueller.pdf
Digital Image Processing http://www.cse.iitd.ac.in/~pkalra/col783
ImageCompressionDictionary based methods: LZ77
Decoding
Source:h4p://jens.jm-s.de/comp/LZ77-JensMueller.pdf
Digital Image Processing http://www.cse.iitd.ac.in/~pkalra/col783
ImageCompressionDictionary based methods: LZW ExtendedbyWelch(Lempel,ZivandWelch)
Thiscodingschemehasbeenadoptedinavarietyofimagingfileformats,suchasthegraphicinterchangeformat(GIF),taggedimagefileformat(TIFF)andtheportabledocumentformat(PDF).
Digital Image Processing http://www.cse.iitd.ac.in/~pkalra/col783
ImageCompressionDictionary based methods: LZW ExtendedbyWelch(Lempel,ZivandWelch)• UnlikeHuffmancodingandarithmeEccoding,thiscodingschemedoes
notrequireaprioriknowledgeoftheprobabiliEesofthesourcesymbols.
• Thecodingisbasedona“dicEonary”or“codebook”containingthesourcesymbolstobeencoded.ThecodingstartswithaniniEaldicEonary,whichisenlargedwiththearrivalofnewsymbolsequences.
• ThereisnoneedtotransmitthedicEonaryfromtheencodertothedecoder.ThedecoderbuildsanidenEcaldicEonaryduringthedecodingprocess
Digital Image Processing http://www.cse.iitd.ac.in/~pkalra/col783
ImageCompressionDictionary based methods: LZW ExtendedbyWelch(Lempel,ZivandWelch)Example: 32 32 34 32 34 32 32 33 32 32 32 34
ConsideradicEonaryofsize256locaEons(numbered0to255)thatcontainsentriescorrespondingtoeachpixelintensityvalueintherange0-255.
Source:h4ps://nptel.ac.in/courses/117/105/117105083/#Digital Image Processing http://www.cse.iitd.ac.in/~pkalra/col783
ImageCompressionDictionary based methods: LZW ExtendedbyWelch(Lempel,ZivandWelch)
Source:h4ps://nptel.ac.in/courses/117/105/117105083/#Digital Image Processing http://www.cse.iitd.ac.in/~pkalra/col783
ImageCompressionRun Length Coding Run: a string of the same symbol Example
input: AAABBCCCCCCCCCAA output: A3B2C9A2
compression ratio = 16/8 = 2
Digital Image Processing http://www.cse.iitd.ac.in/~pkalra/col783
ImageCompressionPredictive Coding Basic premise: Current pixel is similar to the previous pixel (coherence)
Differential Coding
d(x,y) = I(x,y) – I(x-1,y)
d(x,y) prediction error which is to be encoded.
Digital Image Processing http://www.cse.iitd.ac.in/~pkalra/col783
ImageCompression
Compression
Predictive Coding
Source:DigitalImageProcessing,GonzalezandWoods.Digital Image Processing http://www.cse.iitd.ac.in/~pkalra/col783
ImageCompressionPredictive Coding Decompression
Source:DigitalImageProcessing,GonzalezandWoods.Digital Image Processing http://www.cse.iitd.ac.in/~pkalra/col783
ImageCompressionPredictive Coding
Digital Image Processing http://www.cse.iitd.ac.in/~pkalra/col783