The Lossless JPEG standard

1. The Lossless JPEG standard • y=(a+b)/2 = 145 • r=145-180=-35 • Category (r) = 6, Magnitude (r) = 100011 • 1’s complement of cat (r) = 011100 • Rep(35)={6,011100} • Let Huff. code(6) = 1110 • Code(-35)=1110011100 MSB=0 fpr numbers < 0 10 bits

2. The JPEG-LS standard • Loco project (http://www.hpl.hp.com/loco/) • Near-lossless encoding • decoder output does not differ from the input by no more than a pre-specified value • JPEG-LS coder • Context modeling – encoding of a pixel depends on the previous pixels • Run-length encoder – for smooth parts of the image • Predictor – like in the lossless JPEG scheme • Error Coder – to reconstruct the difference between the prediction and the signal

3. The JPEG-LS standard • Context Model • two probability models: flat areas and edge-areas • compute d1=d-a, d2=a-c, d3=c-b • quantize d1, d2, d3 to Q1, Q2, Q3 using thresholds T1, T2, T3. For 8-bit images they are 3, 7, 21 • any Q can take up to 9 possible values based on the threshold interval it is in • This produces 93-1=728 combinations for {Q1,Q2,Q3}, or 364 using symmetry

4. The JPEG-LS standard • Run-mode coder • If gradients are close to 0, the encoder gets into a run-mode • So long as |x-b|  , the encoder reads subsequent samples • Then it returns the run-length • If end-of-line is reached, it encodes the last sample • At the pixel x the predictor computes prediction error e=y-x where min(a,b) if c max(a,b) y= max(a,b) if c  min(a,b) a+b-c • Remove any prediction bias • Remap e to e = 2e for positive e and –2e-1 for negative e • Encode e with Golomb-Rice encoding

5. The JPEG-LS standard • The parameter k for Golomb-Rice encoding is obtained by • k = • A[i]: accumulated sum of prediction errors • N[i]: number of prediction residuals seen in context i • Removal of prediction bias • Idea: the prediction error must follow a 2-sided geometric distribution • Computed using A[i] – how? • B[i], sum of errors after correction and C[i], the correction itself are also stored

6. Lempel-Ziv-Welch Compression • Non-prefix encoding scheme • Algorithm • Step 1: Initialize string table with basic characters • Step 2: Initialize prefix […]  empty repeat until no character left • Step 3: Create variable currentStream by reading the next character C from characterstream • Step 4: Check if currentString in the string table • If yes then […]  […] C; go to step 3 • Else add to […] C the string table • Output code for [...] to codestream • […]  next character • Go to step 3

7. Lempel-Ziv-Welch Compression • Take a 4 character alphabet: p q r s • Consider a message “p q p r p q p” • Construct String table • 0:p, 1:q, 2:r, 3:s • Initialize prefix • prefix=[] • currentstring = [] p • This is in table, so prefix =[p] • currentstring =[p] q • Not in table, update table, and output code for p 0  • prefix=[q], code character : 0:p, 1:q, 2:r, 3:s, 4:pq • currentstring =[q]p • Not in table, update table, and output code for q 1  • Prefix=[p], code character : 0:p, 1:q, 2:r, 3:s, 4:pq, 5:qp

8. Representing digital raster images • Issues: • Raw versus compressed • Single-image versus multi- image • Color representation • Singe versus multi-resolution

9. The GIF Format Control block A file generated from the grammar <GIF Data Stream> ::= Header <Logical Screen><Data>* Trailer <Logical Stream> ::= Logical Screen Descriptor [Global Color Table] <Data> ::= <Graphic Block> <Special Purpose Block> <Graphic Block> ::= [Graphic Control Extension] <Graphic Rendering Block> <Graphic Rendering Block> ::= <Table-Based Image> | Plain Text Extension <Table-Based Image> ::= Image Descriptor [Local Color Table] Image Data <Special Purpose Block> ::= Application Extension | Comment Extension Not used for decoding

10. The GIF Format • Structure of a block • Block Size:byte • Data Value: byte • Logical Screen Descriptor • Logical Screen Width • Logical Screen Height • Packed Bits • Global Color Table Flag • Color Resolution: number of bits per primary color - 1 • Sort Flag • Size of Global Color Table • Background Color Index • Pixel Aspect Ratio

11. The GIF Format • Image Descriptor • Image Separator • Image Left Position • Image Top Position • Image Width • Image Height • Packed Fields • Local Color Table Flag • Interlace Flag: Interlace patter is 4-pass • Sort Flag • Size of Local Color Table

12. The GIF Format • Table-Based Image Data • LZW Minimum Code Size: same as number of color bits • Compression Steps • Establish Code Size • Perform Compression • Build Series of Bytes • Package bytes into blocks • Image Data in sub-blocks of at most 255 bytes • Graphic Control Extension • Extension Introducer • Graphic Control Labrl • Block Size • Packed Bits • Disposal method, user input flag, transparent color flag • Delay Time • Transparent Color Index

13. Network-Aware Formats • A tradeoff problem • Compression efficiency vs. progressive transmission performance • Network factors • Packet loss • Asynchronous arrival of packets at destination • Progressive Transmission Factors • % of picture visible as a function of time • Same given a certain amount of packet loss

14. Network-Aware Formats • Recent Research in University of Delaware • NETCICATS project (http://www.eecis.udel.edu/~iren/netcicats.html) • Primary idea • Break the picture into maximum transmission unit (MTU) sized chunks that a link layer will carry without the IP layer further fragmenting it • The MTU sized picture fragments (also called application data units) should be “self contained” to the extent possible

15. The GIFNC Proposal • The Screen Descriptor • An ADU could be a color map or data • An ADU has an extra byte that identifies • The image number of an image • A local color map and the image identifier to which it belongs • If an ADU is a color map • The start and end indices of the color map • The image descriptor • The image is always interlaced • L and G flags for the last image and all ADUs of the last image respetively