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The Embedded Block Coding with Optimized Truncation in JPEG2000 蘇文鈺 Prepared By 黃文彬 成大資訊

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JPEG2000 Codec (a) encoder (b) decoder Source Image Data Forward Wavelet Transform Quantization Coefficient bit modeling Compressed Image Data Arithmetic encoding Compressed Image Data Coefficient bit modeling De- Quantization Inverse Wavelet Transform Reconstructed Image Data Arithmetic decoding

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… … 67 … … 203 Original Image Level 2 Wavelet Image DWT Pixel RepresentationWavelet Coefficients … … … … … 4 …… … 0 Wavelet Image DWT Quantization... Wavelet Compression … … … … … 0 …… … 0

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A Zero-tree Rough Image Header Sequence of Zero-trees Zero-tree Encoding File Structure Rough Image SPIHT Algorithm For Wavelet Compression

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The JPEG2000 Encoder The part of EBCOT T1 Embedded Block Coding Operates on block samples T2 Coding of block contributions To each quality layer Operates on block summary info Embedded block bit-streams Block of sub-band samples Full-featured bit-stream

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Quantization The quantization operation is defined by the step size parameter,,through Here, denotes the samples of sub-band, while denotes their quantization indices. The step size for each sub-band is specified in terms of an exponent,, and a mantissa,, where

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From “Sub band” to “code block” to “bit stream”

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EBCOT Layered Formation

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The Concept of EBCOT Sub-Block Significance Coding Bit-Plan Coding Primitives Zero Coding Run Length Coding Sign Coding Magnitude Refinement Coding Fractional Bit-Planes and Scanning Order Significance Propagation Pass Magnitude Refinement Pass Cleanup Pass Layer Formation and Representation Packet Header Coding Packet Body Coding

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Sub-bank and Code Block and sub-block Generally, Code Block size is 64*64 or 32*32 and sub-code block size is 16*16. The scanning order of the sub block to be used. Each code block is coded independently. Code Block Code Sub-Block

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Significant Significance: 當一個係數 bit-plane 的值，第一次由０變為１，則此 時這個係數將變為 Significance 。 Refinement: 當一個係數已經是 Significance ，則這個係數接下來的 bit 皆稱之為 Refinement 。 Sign: 即係數的符號值。

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The Bit Plan Coding Primitives

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Scan coding q = sign Bit plan 1 Bit plan 2 Bit plan 3 Bit plan 4 Bit plan 5 Bit plan

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Four Types of Coding Operation for Bit Plan Coding Zero Coding Used to code new significance. Run Length Coding Reduce the average number of symbols needed to be coded. Sign Coding Used to code the sign right after a coefficient is identified significant. Magnitude Refinement Coding 3 context depending on the significance of its neighbors and whether it is the first time for refinement.

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Stripe Oriented Scanning Pattern Followed Within Each Coding Pass

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Zero Coding The objective here is to code, given that

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Run Length Coding Specifically, each of the following conditions must hold: 1) Four consecutive samples must all be insignificant, i.e., 2) The samples must have insignificant neighbors, i.e., 3) The samples must reside within the same sub-block 4) The horizontal index of the first sample,, must be even.

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Example for RLC

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Sign Coding 當 symbol 由 insignificance 變為 significance ，此時必須將送出該 symbol 的 sign 值，而 sign 值是由垂直及水平鄰近點的 sign 值和 significance 來查表決定 context states 。

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Magnitude Refinement Coding Specifically, is coded with context 0 if, with context 1 if and and with context 2 if

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Three Coding Pass The JPEG2000 standard other three pass Significance Propagation Pass Magnitude Refinement Pass Cleanup Pass

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Significance Propagation Pass The coding pass for each bit plane is the significance pass. This pass is used to convey significance and (as necessary) sign information for samples that have not yet been found to be significant and are predicted to become significant during the processing of the current bit plane.

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Magnitude Refinement Pass During this pass we skip over all samples except those which are already significant, and for which no information has been coded in the previous two passes. These samples are processed with the MR primitive.

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Cleanup Pass Here we code the least significant bit, of all samples not considered in the previous two coding passes, using the SC and RLC primitives as appropriate if a sample is found to be significant in this process, its sign is coded immediately using the SC primitive.

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Cleanup Pass Algorithm(cont.)

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The EBCOT encoding procedures Algorithm for encoder Initialize the MQ encoder Initialize the context states according to each coding table Set For each Initialize all the variable For If Perform Encoder-Pass0 (Significance propagation pass) Perform Encoder-Pass1 (Magnitude refinement pass) Perform Encoder-Pass2 (Cleanup pass)

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A Simple Example For Bit Plan Coding bit plane1 bit plane2 bit plane3 bit plane4 Example : 10 = = = = -0111

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Block diagram of the embedded block coder

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EBCOT Decoder Algorithm for decoder Initialize the context states according to each coding table For each Initialize all the variable For If Perform De-Significance propagation pass Perform De-Magnitude refinement pass Perform De-Cleanup pass

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Redefine JPEG2000 Table Context label in RLC: RLC(0),UNIFORM(18/0x1D)

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Example 1 For JPEG2000 Encoder(Only Cleanup Pass)

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Example 1 For JPEG2000 Decoder (Only Cleanup Pass) 第一個讀入的值為 context label 即 coding 的方式, 查表可知 00 為 Run-length coding. 第二個讀入的值為 symbol 即本身 的二進位值, 此例為 1

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Example 2 For JPEG2000- Two Bit Plane

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Example 2 For JPEG2000 – Bit Plane 1 Cleanup Pass (1)

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Example 2 For JPEG2000 – Bit Plane 1 Cleanup Pass (2)

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Example 2 For JPEG2000 – Bit Plane 2 Significance Pass (1)

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Example 2 For JPEG2000 – Bit Plane 2 Significance Pass (2)

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Example 2 For JPEG2000 – Bit Plane 2 Magnitude Refinement Pass

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Example 2 For JPEG2000 – Bit Plane 2 Cleanup Pass (1)

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Arithmetic Coding - MQ Coder Before talking about MQ coder, we must understand the Arithmetic coding. Because the MQ coder is almost the same as a binary arithmetic coding. Just only one difference between them. Where is the probability of the zero or one from? For binary arithmetic coding, the probability of zero or one is driven by the pre-processing. In other words, before arithmetic coding, the probability of zero or one have been already known, and it’s through the statistic of all data. In MQ coder, the probability of zero or one is by the dynamic decision.

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Arithmetic Coding - MQ Coder In JPEG2000 standard, there is a table for MQ coder. The table provides the new probability of zero or one. The table is shown in the next page. In the beginning, the probability of zero or one is 0.5, and it is the start of table. And the next probability of zero or one depends on the input context that is zero or one. If the input context is zero, the new probability of zero becomes larger in the table. Otherwise, it becomes smaller.

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Arithmetic Coding - MQ Coder

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Arithmetic Coding – Binary Arithmetic Coding Algorithm Initialize,,, For each Set If Propagate carry While Renormalize Set

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Arithmetic Coding – Binary Arithmetic Coding Algorithm Propagate carry Emit-bit(1) If, execute times, emit-bit(0) Set Else Set Renormalize Increment Shift If if, emit-bit(1) else increment Else if emit-bit(0) execute times,emit-bit(1) Set

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Arithmetic Coding - MQ Coder algorithm Initialize, For each and If If (encode an MPS) else(encode an LPS) If If (The symbol was a real MPS) else (The symbol was a real LPS) While renormalization

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Arithmetic Coding - MQ Coder Example We want to encode 1101 and the coding pass is always in context 1 (1) Initial A = 0x8000, C = 0x0000, k = 0, B = 0, ct = 12, Sn = 0 Encode 1 X = 1, Sn = 0, k = 0 P = 5601, A = A – P = 29ff A(29ff) S = 1 – Sn = 1 X = S => C = C + P = 5601 A(29ff) Sn = 1 and k = 1 A = a7fc, C = 15804, ct = 10 While A < 0x8000 A = 2A, C = 2C, ct = ct -1 if ct = 0 Transfer-Byte

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Arithmetic Coding - MQ Coder Example Encode 1 X = 1, Sn = 1, k = 1 P = 3401, A = A – P = 73fb A(73fb) > P(3401) X = S => C = C + P = = 18c05 A(73fb) k = 2 A = e7f6, C = 3180A, ct = 9 Encode 0 X = 0, Sn = 1, k = 2 P = 1801, A = A – P = cff5 A(cff5) > P(1801) X != S => A = 1801 A(1801) Sn = 1 and k = 9 A = c008, C = 18c050, ct = 6

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Arithmetic Coding - MQ Coder Example Encode 1 X = 1, Sn = 1, k = 9 P = 3801, A = A – P = 8807 A(8807) > P(3801) X = S => C = C + P = 18c = 18f851 A(18f851) > 0x8000 and X != Sn => Sn = 1 and k = 9 A = c008, C = 18c050, ct = 6

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Combined EBCOT with MQ Coder Encoder-Pass0 Procedure (significance propagation) Algorithm For each location, j, following the stripe-based scan of above figure if and, MQ-Encode(,) If, Encode-Sign() else

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Combined EBCOT with MQ Coder Encode-Sign Procedure Algorithm Determine and from and using Table 2 If, MQ-Encode(, ) Else MQ-Encode(, )

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Combined EBCOT with MQ Coder Encoder-Pass1 Procedure (magnitude refinement) Algorithm For each location, j, following the stripe-based scan of above Figure Ifand, Find form and using table3 MQ-Encode(, )

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Combined EBCOT with MQ Coder Encoder-Pass2 Procedure (cleanup) Algorithm For each location, j, following the stripe-based scan of above Figure ifand,(entering a full stripe column) (signifies not using run mode) if for all,(enter run mode) while and, if MQ-Encode( ) else(run interruption) MQ-Encode( )

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Combined EBCOT with MQ Coder (cleanup pass cont.) If and, if, (no need to code significance) else MQ-Encode( ) if, Encode-Sign( )

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