Why Compress

1
Why Compress?

• To reduce the volume of data to be transmitted
  (text, fax, images)
• To reduce the bandwidth required for transmission
  and to reduce storage requirements (speech,
  audio, video)

2
Compression

• How is compression possible?
• Redundancy in digital audio, image, and video
  data
• Properties of human perception
• Digital audio is a series of sample values image
  is a rectangular array of pixel values video is
  a sequence of images played out at a certain rate
• Neighboring sample values are correlated

3
Redundancy

• Adjacent audio samples are similar (predictive
  encoding) samples corresponding to silence
  (silence removal)
• In digital image, neighboring samples on a
  scanning line are normally similar (spatial
  redundancy)
• In digital video, in addition to spatial
  redundancy, neighboring images in a video
  sequence may be similar (temporal redundancy)

4
Human Perception Factors

• Compressed version of digital audio, image, video
  need not represent the original information
  exactly
• Perception sensitivities are different for
  different signal patterns
• Human eye is less sensitive to the higher spatial
  frequency components than the lower frequencies
  (transform coding)

5
Classification

• Lossless compression
• lossless compression for legal and medical
  documents, computer programs
• exploit only data redundancy
• Lossy compression
• digital audio, image, video where some errors or
  loss can be tolerated
• exploit both data redundancy and human perception
  properties
• Constant bit rate versus variable bit rate coding

6
Entropy

• Amount of information I in a symbol of occurring
  probability p I log2(1/p)
• Symbols that occur rarely convey a large amount
  of information
• Average information per symbol is called entropy
  H
• H pix log2(1/pi) bits per codeword
• Average number of bits per codeword Nipi
  where Ni is the number of bits for the symbol
  generated by the encoding algorithm

7
Huffman Coding

• Assigns fewer bits to symbols that appear more
  often and more bits to the symbols that appear
  less often
• Efficient when occurrence probabilities vary
  widely
• Huffman codebook from the set of symbols and
  their occurring probabilities
• Two properties
• generate compact codes
• prefix property

8
Run-length Coding

• Repeated occurrence of the same character is
  called a run
• Number of repetition is called the length of the
  run
• Run of any length is represented by three
  characters
• eeeeeee7tnnnnnnnn
• _at_e7t_at_n8

9
Lempel-Ziv-Welch (LZW) Coding

• Works by building a dictionary of phrases from
  the input stream
• A token or an index is used to identify each
  distinct phrase
• Number of entries in the dictionary determines
  the number of bits required for the index -- a
  dictionary with 25,000 words requires 15 bits to
  encode the index

10
Arithmetic Coding

• String of characters with occurrence
  probabilities make up a message
• A complete message may be fragmented into
  multiple smaller strings
• A codeword corresponding to each string is found
  separately

11
Summary

• Statistical encoding exploits the fact that not
  all symbols in the source information occur with
  equal probability
• Variable length codewords are used with the
  shortest ones used to encode symbols that occur
  most frequently
• Static coding -- text type is pre-defined and
  codewords are derived once and used for all
  subsequent transfers
• Dynamic coding -- type of text may vary from one
  transfer to another and same set of codewords are
  generated at the transmitter and the receiver as
  the transfer takes place

12
Image and Video Compression

• Two dimensional array of pixel values
• Spatial redundancy and temporal redundancy
• Human eye is less sensitive to chrominance signal
  than to luminance signal (U and V can be coarsely
  coded)
• Human eye is less sensitive to the higher spatial
  frequency components
• Human eye is less sensitive to quantizing
  distortion at high luminance levels

13
JPEG Encoder

• International standards body -- Joint
  Photographic Experts Group
• JPEG encoder schematic
• Image/block preparation
• DCT computation
• Quantization
• Entropy coding -- vectoring, differential
  encoding, run-length encoding, Huffman encoding
• Frame building

14
Image/block Preparation

• Source image as 2-D matrix of pixel values
• R, G, B format requires three matrices, one each
  for R, G, B quantized values
• In Y, U, V representation, the U and V matrices
  can be half as small as the Y matrix
• Source image matrix is divided into blocks of 8X8
  submatrices
• Smaller block size helps DCT computation and
  individual blocks are sequentially fed to the DCT
  which transforms each block separately

15
DCT Computation

• Each pixel value in the 2-D matrix is quantized
  using 8 bits which produces a value in the range
  of 0 to 255 for the intensity/luminance values
  and the range of -128 to 127 for the
  chrominance values. All values are shifted to the
  range of -128 to 127 before computing DCT
• All 64 values in the input matrix contribute to
  each entry in the transformed matrix
• The value in the location F0,0 of the
  transformed matrix is called the DC coefficient
  and is the average of all 64 values in the matrix
• The other 63 values are called the AC
  coefficients and have a frequency coefficient
  associated with them
• Spatial frequency coefficients increase as we
  move from left to right (horizontally) or from
  top to bottom (vertically). Low spatial
  frequencies are clustered in the left top corner.

16
Quantization

• The human eye responds to the DC coefficient and
  the lower spatial frequency coefficients
• If the magnitude of a higher frequency
  coefficient is below a certain threshold, the eye
  will not detect it
• Set the frequency coefficients in the transformed
  matrix whose amplitudes are less than a defined
  threshold to zero (these coefficients cannot be
  recovered during decoding)
• During quantization, the size of the DC and AC
  coefficients are reduced
• A division operation is performed using the
  predefined threshold value as the divisor

17
Quantization Table

• Threshold values vary for each of the 64 DCT
  coefficients and are held in a 2-D matrix
• Trade off between the level of compression
  required and the information loss that is
  acceptable
• JPEG standard includes two default quantization
  tables -- one for the luminance coefficients and
  the other for use with the two sets of
  chrominance coefficients. Customized tables may
  be used

18
Entropy Coding

• Vectoring -- 2-D matrix of quantized DCT
  coefficients are represented in the form of a
  single-dimensional vector
• After quantization, most of the high frequency
  coefficients(lower right corner) are zero.
• To exploit the number of zeros, a zig-zag scan of
  the matrix is used
• Zig-zag scan allows all the DC coefficients and
  lower frequency AC coefficients to be scanned
  first
• DC are encoded using differential encoding and AC
  coefficients are encoded using run-length
  encoding. Huffman coding is used to encode both
  after that.

19
Differential Encoding

• DC coefficient is the largest in the transformed
  matrix.
• DC coefficient varies slowly from one block to
  the next.
• Only the difference in value of the DC
  coefficients is encoded. Number of bits required
  to encode is reduced.
• The difference values are encoded in the form
  (SSS, value) where SSS field indicates the number
  of bits needed to encode the value and the value
  field indicates the binary form.

20
Run-length Encoding

• 63 values of the AC coefficients
• Long strings of zeros because of the zig-zag scan
• Each AC coefficient encoded as a pair of values
  -- (skip, value), skip indicates the number of
  zeros in the run and value is the next non-zero
  coefficient

21
Huffman Encoding

• Long strings of binary digits replaced by shorter
  codewords
• Prefix property of the huffman codewords enable
  decoding the encoded bitstream unambiguously

22
Frame Building

• Encapsulates the information relating to an
  encoded image

23
Video Compression

• Video as a sequence of pictures (or frames)
• JPEG algorithm applied to each frame -- moving
  JPEG (MJPEG). Exploits only spatial redundancy.
• High correlation between successive frames. Only
  small portion of each frame is involved with any
  motion that is taking place.
• A combination of actual frame contents and
  predicted frame contents are used.
• Motion estimation and motion compensation

24
Frame/Picture Types

• Interframe and intraframe coding. High
  compression ratios can be achieved by using both.
  Random access requirement of image retrieval is
  satisfied by pure intraframe coding.
• I-frames are coded without reference to other
  frames. Serve as reference pictures for
  predictive-coded frames.
• P-frames are coded using motion compensated
  prediction from a past I-frame or P-frame.
• B-frames are bidirectionally predictive-coded.
  Highest degree of compression, but require both
  past and future reference pictures for motion
  compensation.
• D-frames are DC-coded. Of the DCT coefficients
  only the DC coefficients are present. Used in
  interactive applications like VoD for rewind and
  fast-forward operations.

25
Picture Sequence

• I B B P B B P B B I (display order)
• Bitstream order -- I P B B P B B P B B I
• Prediction span, Group of Pictures (GOP)

26
MPEG-video Encoding

• Input frames are preprocessed (color space
  conversion and spatial resolution adjustment).
• Frame types are decided for each frame/picture
• Each picture is divided into macroblocks of 16 X
  16 pixels.
• Macroblocks are intracoded for I frames and
  predictive coded or intracoded for P and B frames
• Macroblocks are divided into six blocks of 8 X 8
  pixels (4 luminance and 2 chrominance) and DCT is
  applied to each block and transform coefficients
  are quantized and zig-zag scanned and
  variable-length coded.