1 The Embedded Block Coding with Optimized Truncation (EBCOT) in JPEG2000

2 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

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

4 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

5 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

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

7 EBCOT Layered Formation

8 The Concept of EBCOT 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

9 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

10 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。

11 The Bit Plan Coding Primitives

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

13 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.

14 Stripe Oriented Scanning Pattern Followed Within Each Coding Pass

15 Zero Coding

16 Run Length Coding Specifically, each of the following conditions must hold: 1) Four consecutive samples must all be insignificant. 2) The samples must have insignificant neighbors. 3) The samples must reside within the same sub-block

17 Example for RLC

18 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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20 Magnitude Refinement Coding

21 Three Coding Pass The JPEG2000 standard three passes Significance Propagation Pass Magnitude Refinement Pass Cleanup Pass

22 Significance Propagation Pass The first 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.

23 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 pass. These samples are processed with the MR primitive.

24 Cleanup Pass Here we code the least significant bit, of all samples not considered in the previous three 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.

25 Cleanup Pass Algorithm(cont.)

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

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

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33 Example 1 For JPEG2000 Encoder(Only Cleanup Pass)

34 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

35 Example 2 For JPEG2000- Two Bit Plane

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

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

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

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

40 Example 2 For JPEG2000 – Bit Plane 2 Magnitude Refinement Pass

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