Data Compression - cs.ryerson.ca

Data Compression - cs.ryerson.ca

Data Compression I 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Storage Space Uncompressed graphics, audio and video use considerable space. Too much space even for today's CD and DVD technologies. The most popular compression methods are JPEG (images), MPEG (sound/video) and proprietary techniques from Microsoft and Apple.

6. Data Compression I - Copyright Denis Hamelin - Ryerson University Coding Requirements Images have higher storage requirements than text and video even more. Let's have a comparison for a 640x480 window. Text: 2 bytes for each 8x8 pixel character. 640x480/8x8=4800 characters per page. 4800X2bytes=9600 or 9.4KByte per page. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Coding Requirements

Vector images: A typical 640x480 image has 500 lines approximately. Each line has 2 coordinates (x,y) each and an 8-bit attribute field. x requires 10 bits (log2(640)) and y requires 9 bits (log2(480)). We need 46 bits per line (9+10+9+10+8). The storage required is 500x46/8=2875 or 2.8KByte per image. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Coding Requirements Bitmap images: Individual pixels of a

bitmap can be coded using 256 different colours, requiring 1 Byte per pixel. 640x480x1Byte=307200 or 300KBytes per image. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Coding Requirements Sound: Uncompressed speech of telephone quality is sampled at 8kHz and quantized using 8 bits per sample, yielding a data stream of 64 Kbits/sec. Storage required will be (64Kbps/8)x(1sec/ 1024) = 8KByte for a 1 second sound.

6. Data Compression I - Copyright Denis Hamelin - Ryerson University Coding Requirements Sound: Uncompressed stereo audio signal of CD quality is sampled at 44.1kHz and quantized using 16 bits per sample, yielding a data stream of 176,400 bytes/sec. Storage required will be 172KByte for a 1 second sound. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Coding Requirements

Video: 25 full frames per second. Luminance and chrominance of each pixel are coded using a total of 3 bytes. Data rate is 640x480x25x3bytes=23,040,000 bytes/sec. Storage required will be 21.98MByte for 1 second of video. (Multiply by 5 for HDTV!) 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Compression Requirements

The complexity of the technique should be minimal. The time to decompress should be minimal (<150ms). Fast forward and fast rewind should be available. Random access to individual frames should be possible in less than half a second. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Compression Requirements

Decompression should be possible without interpreting all preceding data. The technique should be independent of the frame size. Synchronization must be possible. Should be economical. Should be portable. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University

Compression Requirements Support for various audio and video rates. Synchronization of audio-video streams (lip synchronization). Compression in software implies cheaper, slower and low quality solution. Compression in hardware implies expensive, faster and high quality solution. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University

Types of Compression Entropy Coding: Lossless compression. Data prior to encoding is identical to data after encoding. Source Coding: Takes into account the semantics of the information. Plays with frequencies and colours: Lossy compression. Hybrid Coding: Most known techniques use a combination of the two kinds of coding. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Steps of Compression

This is the typical sequence of operations performed in the compression of still images and video and audio data streams. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Preparation (images) Analog-to-digital conversion of the original. Generation of the appropriate digital

representation. Image division into 8X8 blocks for example. Fix the number of bits per pixel. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Processing (images) Transformation from time to frequency domain, like Discrete Cosine Transform (DCT).

The DCT helps separate the image into parts (or spectral sub-bands) of differing importance (with respect to the image's visual quality). Why store individual pixel information for what is obviously the exact same shade of gray? Motion vector computation for digital video. Lossless process. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Quantization

Mapping real numbers to integers (reduction in precision). Quantization techniques generally compress by compressing a range of values to a single quantum value. By reducing the number of discrete symbols in a given stream, the stream becomes more compressible. Lossy process. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Entropy Coding

Starts with a sequential data stream of individual bits and bytes. Different techniques are used to perform a final, lossless compression. For example, frequently occurring long sequences of zeros can be compressed by specifying the number of occurrences followed by the zero itself. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Types of Compression

Symmetric Compression: Same time needed for decoding and encoding phases. Used for dialog mode applications Asymmetric Compression: Compression process is performed once and enough time is available, hence compression can take longer. Decompression is performed frequently and must be done fast. Used for retrieval mode applications. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Iterative Processes Processing and quantization steps can be repeated iteratively, such as in the case of Adaptive Differential Pulse Code Modulation (ADPCM). There can either be

feedback (like delta modulation) or multiple techniques can be applied to the data one after the other (like interframe and intraframe coding in MPEG). 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Basic Compression Techniques Hybrid compression techniques are composed of several other techniques. Simplest techniques are based on interpolation that uses the properties of the human eye or ear.

6. Data Compression I - Copyright Denis Hamelin - Ryerson University Run-Length Encoding Content dependent coding. Replaces the sequence of same consecutive bytes with the number of occurrences. The number of occurrences is indicated by a special flag - !. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University RLE Algorithm

If the same byte occurred at least 4 times then count the number of occurrences. Write compressed data in the following format: number of occurrences!the counted byte. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University RLE Algorithm Example: Uncompressed sequence ABCCCCCCCCCDEFFFFGGG

Compressed sequence - AB9!CDE4!FGGG (from 20 to 13 bytes) 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Zero Suppression Used to encode long binary bit strings containing mostly zeros. Each k-bit symbol tells how many 0s occurred between

consecutive 1s. Ex: 0000000 - 7 zeros to be encoded. 111 (3 bit symbol) Ex: 000100000001101 (using 3 bit symbol) 011 111 000 001 (3-7-0-1 zeros between 1s) 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Text Compression

Patterns that occur frequently can be substituted by single bytes. Like begin, end, if Algorithm: Use an ESC byte to indicate that an encoded pattern will follow. The next byte is an index reference to one of 256 words (patterns). Can be applied to still images, audio, video. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Diatomic Coding

Determined frequently occurring pairs of bytes. Analysis of the English language yielded frequently used pairs: re in th he... Replace these pairs by single bytes that do not occur anywhere in the text (like 'X'). Reduction of more than 10% is possible. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Statistical Coding

Fixed length coding Use equal number of bits to represent each symbol. A message of N symbols requires L >= log2(N) bits per symbol. Good encoding for symbols with equal probability of occurrence. Not efficient if probability of each symbol is not equal. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Statistical Coding Variable length encoding

Frequently occurring characters represented with shorter strings than seldom occurring characters. Statistical encoding is dependent on the frequency of occurrence of a character or a sequence of data bytes. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Huffman Coding

Characters are stored with their probabilities. Number of bits of the coded characters differs. Shortest code is assigned to most frequently occurring character. To determine Huffman code, we construct a binary tree. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Huffman Coding 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Huffman Coding

Leaves are characters to be encoded. Nodes contain occurrence probabilities of the characters belonging to the subtree. 0 and 1 are assigned to the branches of the tree arbitrarily - therefore different Huffman codes are possible for the same data. Huffman table is generated. Huffman tables must be transmitted with compressed data. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University

Arithmetic Coding Method for lossless data compression. Normally, a string of characters such as the words "hello there" is represented using a fixed number of bits per character, as in the ASCII code. Like Huffman coding, arithmetic coding is a form of variable-length entropy encoding that converts a string into another representation that represents frequently used characters using fewer bits and infrequently used characters using more bits, with the goal of using fewer bits in total. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Arithmetic Coding

As opposed to other entropy encoding techniques that separate the input message into its component symbols and replace each symbol with a code word, arithmetic coding encodes the entire message into a single number, a fraction n where (0.0 n < 1.0). 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Differential Encoding

Consider sequences of symbols S1, S2, S3 etc. where values are not zeros but do not vary very much. We calculate difference from previous value : S1, S2-S1, S3-S2 etc. Differential Coding is lossy. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Differential Encoding For still images: Calculate difference between nearby pixels or pixel groups.

Edges characterized by large values, areas with similar luminance and chrominance are characterized by small values. Zeros can be compressed by run-length encoding and nearby pixels with large values can be encoded as differences. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Differential Encoding For videos: In a newscast or video phone, the background

does not change often, hence we can use runlength encoding to compress the background. In movies, the background changes - use motion compensation. Compare blocks of 8X8 or 16x16 in subsequent pictures. Find areas that are similar, but shifted to the left or right. Encode motion using a motion vector. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University

Differential Encoding (Sound) Differential Pulse Code Modulation (DPCM). When we use PCM, we get a sequence of PCM coded samples. Represent first PCM sample as a whole and all the following samples as differences from the previous one. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University

Differential Encoding (Sound) 6. Data Compression I - Copyright Denis Hamelin - Ryerson University JPEG JPEG implementation is independent of image size and applicable to any image and pixel aspect ratio. Image content may be of any complexity. JPEG achieves very good compression ratio and good quality image.

6. Data Compression I - Copyright Denis Hamelin - Ryerson University JPEG From the processing complexity of a software solution point of view: JPEG should run on as many available platforms as possible. Sequential decoding (line-by-line) and progressive decoding (refinement of the whole image) should be possible. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University JPEG Modes

Lossy Sequential DCT (Discrete Cosine Transform) based mode: Baseline process that must be supported by every JPEG implementation. Lossless mode: Low compression ratio allows perfect reconstruction of original image. Hierarchical mode: Accommodates images of different resolutions. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Steps of JPEG Compression

Image preparation, Picture processing, Quantization and Entropy coding. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Picture Preparation First the compression algorithm cuts up the image in separate blocks of 88 pixels. The compression algorithm is calculated for each separate block, which explains why these blocks or groups of blocks become visible when too much compression is applied.

6. Data Compression I - Copyright Denis Hamelin - Ryerson University Picture Preparation Each image consists of components or planes. There is at least one plane and a maximum of 255. The planes can be assigned to RGB colours or YIQ or YUV signals. YUV and YIQ are preferred because luminance is more important than chrominance for human vision. Each plane is an array of X*Y pixels. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Picture Preparation

A grey scale image has one plane, a RGB colour image three planes with the same resolution. (Y1=Y2=Y3 and X1=X2=X3) A JPEG image using YUV or YIQ has Y1=4*Y2=4*Y3 and X1=4*X2=4*X3 (4:1:1). The 4:2:2 ratio is now the most popular ratio. Each pixel is represented by a certain number of bits. All pixels of all components must have the same number of bits (2-12 bits). 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Picture Preparation The 4:4:4 ratio

6. Data Compression I - Copyright Denis Hamelin - Ryerson University Picture Preparation The 4:2:2 ratio X1=2X2=2X3 Y1=Y2=Y3 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Picture Preparation (DCT)

Xmax = max(Xi) Ymax = max(Yi) Xi = Xmax * Hi / Hmax Yi = Ymax * Vi / Vmax Hi and Vi are integers between 1 and 4. The color values are changed by coefficients that are relative to the average of the entire matrix that is being analyzed. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University

DCT-Based Mode Coefficient values are then shifted to central values (-128 to 127). Formula is applied 64 times per unit. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University DCT-Based Mode Forward Discrete Cosine Transform. x and y range from 0 to 7 (8x8 pixels).

64 Svu per unit. S00 is the base color (DC), the rest are called AC. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University DCT-Based Mode Inverse Discrete Cosine Transform. Used to decompress the image.

Theoretically lossless but because precision is limited, DCT is lossy. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University DCT-Based Mode The image to the right shows combination of horizontal and vertical frequencies for an 8 x 8 (N1 = N2 = 8) two-dimensional DCT. Each step from left to right and top to bottom is an increase in frequency by 1/2 cycle. For example, moving right one from the top-left square yields a half-cycle increase in the horizontal frequency (goes from white to black). Another move to the right yields two half-cycles (white to black to white). A move down yields two half-cycles horizontally and a half-cycle vertically. The

source data (8x8) is transformed to a linear combination of these 64 frequency squares. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Quantization Lossy process. JPEG application provides a table with 64 entries (one per DCT coefficient). Specific frequencies are given more

importance than others. Sqvu = round (Svu/Qvu) where Qvu are the table entries. Rvu = Sqvu x Qvu to dequantize. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Quantization Effect of quantization: Original quantization Coarser quantization JPEG quality settings (normal, fine, very fine...) are all about quantization.

6. Data Compression I - Copyright Denis Hamelin - Ryerson University Entropy Encoding After image processing we have quantized the DC and AC coefficients. Initial step of entropy encoding is to map the 8x8 plane into a 64-element vector. . . .

"Zig zag scan" 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Entropy Encoding Treat quantized DC coefficients separately from AC coefficients. coefficients are treated separately from AC QuantizedDCDCcoefficient is large and varied, but often close to previous value. coefficients. Use

difference encoding. The DC coefficients determine the basic colour of the data unit. DC coefficients are large and varied, but often close to previous value. Diff_i = DC_i - DC_(i-1) ; Difference DC0 encoding is used. DC1 DC2 i> 0 DC0

Diff1 Diff2 DC3 DC4 DC5 Diff3 Diff4 Diff5 DC6 DC7

DC8 Diff6 Diff7 Diff8 6. Data Compression I - Copyright Denis Hamelin - Ryerson University Entropy Encoding AC Coefficient Processing DCT processing of AC coefficients follow a zig-zag sequence which DCT processing of AC coefficients: means that the coefficients with lower frequencies are encoded first, Implies that we can get a sequence of similar data bytes, hence followed by higher frequencies.

canimplies apply entropy This that weencoding. can get a sequence of similar data bytes, hence can apply entropy encoding. JPEG standard specifies Huffman or Arithmetic encoding, in The JPEG standard specifies Huffman or Arithmetic encoding. In baseline mode only Huffman Coding is used. baseline mode only Huffman Coding is used. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University

Entropy Encoding Algorithm Run-length coding is then applied on AC components of zero values (1x64 has many zeros) and encode them as as pairs (skip, values) . Huffman Coding is once more applied on DC and AC coefficients. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University JPEG Compression Algorithm Summary 6. Data Compression I - Copyright Denis Hamelin - Ryerson University

JPEG Comments Applications do not have to include both an encoder and decoder if the compression and decompression process agree on a common table. The encoded data stream has a fixed interchange format: encoded image data, chosen parameters, tables of the coding process. In

regular mode, the interchange format includes all of the information necessary for decoding without any previous knowledge of the coding process. 6. Data Compression I - Copyright Denis Hamelin - Ryerson University JPEG Interchange Format Frame Start-of-Image Tables, etc. Tables, etc. header header

block End-of-Image ... Scan segment block Scan Restart ... segment

Restart block 6. Data Compression I - Copyright Denis Hamelin - Ryerson University MPE G Encode: (a) motion vector - difference in spatial location of macro-blocks (b) Small difference in content of the macro-blocks Difference Reference image (previous image)

Huffman Code 01001100 Motion vector 6. Data Compression I - Copyright Denis Hamelin - Ryerson University MPEG Video Data Stream Seq Seq SC Video Param

GOP SC PSC Seq Seq Bitstream Param Time Code Type SSC Addr

QT, misc GOP Param Buffer Param Vert Pos Type Encode Param QScale

Motion Vector QScale Seq ... GOP ... Pict Pict ...

Slice Slice ... MB CBP GOP b0 MB ...

b5 Sequence Layer GOP (Group of Pictures) Layer Picture Layer Slice Layer Macro-block Layer Block Layer 6. Data Compression I - Copyright Denis Hamelin - Ryerson University MPEG Audio Data Stream

6. Data Compression I - Copyright Denis Hamelin - Ryerson University End of lesson 6. Data Compression I - Copyright Denis Hamelin - Ryerson University

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