Data Compression 3

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Data Compression (3)

• Hai Tao

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JPEG Compression

• JPEG is the image compression standard developed
  by the Joint Photographic Experts Group
• JPEG was designed for natural image compression
• It convert the original image into YIQ space and
  compress each channel as a separate gray image
• The compression ratio and the quality of the
  decoded images is controlled by quality factor
  (1-100)
• Quality factor gt 35 - no big difference
• Quality factor lt 10 significant difference

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Quality factor

Quality factor 20
Original
Quality factor 75
Quality factor 5
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JPEG Compression Algorithm Overview

• An input image is divided into 8x8 blocks. Each
  block is encoded based on DCT transform
• DCT coefficients are quantized according to a
  quatization matrix
• Entropy coding is used to encode positions and
  the magnitudes of the coefficients

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Color space conversion

• Human visual system has less resolution in color
  than in intensity. As a result, the original
  color images are converted into intensity and
  color channels. One such transformation is
  RGB-gtYIQ

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JPEG 8x8 DCT Transformation

• After DCT compression, only a few DCT
  coefficients have large values in each 8x8 block
• These coefficients are floating-point numbers

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Quantization of the DCT Coefficients

• Each coefficients are converted into an integer
  number using quatization
• The choices of quatization steps
• Large quantization step - Large rounding errors,
  smaller quantized values
• Small quatization step Small rounding errors,
  large quantized coefficients
• The same quatization step for all coefficients ?
  Human visual system is more sensitive to
  relative low frequency changes in images, which
  implies that for high frequency coefficients,
  larger quantization steps can be used without
  causing noticeable image distortion
• What does all this means ?

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JPEG Quantization Matrix

• The low frequency coefficients (upper-left
  corner) have smaller quantization steps,
  therefore more accurately encoded

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JPEG Quantization Using the Quantization Matrix
After quantization
Before quantization
After reconstruction
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Encoding

• We need to compress the quantized coefficients
• Lossless methods are used to
• Encode the position of non-zero coefficients
• Encode the magnitudes of these coefficients

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Encoding

• Zig-Zag encoding of coefficient positions
• Non-zero coefficients and the number of 0s in
  front of them are encoded along the zig-zag path

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Example

• The following quantized coefficient matrix is
  represented as
• (30,0), (-7,1), (-12, 0), (-8, 0), (-1, 0),
  (1,1),(6,0),(-5,0),(-7,0),(-3,0),
• (1,1), (-1,3),(-3,1),(-4,0), (-1,0), (4,0),
  (3,0),(-3,11),(1,0), (-1,0),(end)
• These pairs are encoded using a entropy coding
  method

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JPEG bit stream

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JPEG Bitstream

• Terminology
• Frame image
• Block 8x8 image block
• Segment a group of blocks
• Frame header
• Sample precision (width, height) of image
  number of components unique ID (for each
  component) horizontal/vertical sampling factors
  (for each component) quantization table to use
  (for each component)

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JPEG Bitstream

• Scan header
• Number of components in scan component ID (for
  each component) Huffman table for each component
  (for each component)
• Misc. (can occur between headers)
• Quantization tables Huffman Tables Arithmetic
  Coding Tables Comments Application Data

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Various JPEG modes

• Baseline/Sequential
• Lossless mode
• Progressive mode
• Display low quality image first, and then
  transmit and display more details
• Method 1 Send DC components first, then a few
  low frequency components, and then more
  components
• Method 2 Send significant bits first, then more
  less significant bits

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Decoding

• Decoding is the inverse process of the encoding
• Recover the quantized coefficient matrix
• Recover the coefficient matrix
• IDCT
• JPEG is lossy because of the quatization process

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Evaluation

• To evaluate an image compression algorithm, there
  are two criteria
• Subjective - The visual quality vs. bit rate
  (subjective)
• Objective - The rate distortion curve (Peak SNR
  vs. bit rate)

The difference image when the quality factor is 3
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Evaluation

• The rate distortion curve