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

The JPEG-LS standard Loco project ( Loco project 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

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 =728 combinations for {Q1,Q2,Q3}, or 364 using symmetry cad bX

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

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

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

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

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

The GIF Format A file generated from the grammar ::= Header * Trailer ::= Logical Screen Descriptor [Global Color Table] ::= ::= [Graphic Control Extension] ::= | Plain Text Extension ::= Image Descriptor [Local Color Table] Image Data ::= Application Extension | Comment Extension Control block Not used for decoding

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

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

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

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

Network-Aware Formats Recent Research in University of Delaware NETCICATS project ( 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

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