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JPEG Image Compression

JPEG stands for Joint Photographic Expert Group

The major steps in JPEG compression involve.

  1. Compressing at the block level (8*8)
  2. Colour space transform and subsampling (RGB->YCbCr)
  3. DCT (Discrete Cosine Transform)
  4. Quantisation
  5. Zigzag scan
  6. DPCM on DC component
  7. RLE(Run Length Encoding) on AC Components
  8. Entropy coding — Huffman or arithmetic

Implementation

Conversion

  • Colour space transform and subsampling
    • CMY for printer
    • YCbCr
      • Y
        • Luminosity Component ( 0-255)
      • Cb
        • Chrominance Blue ( -127 - 128)
      • Cr
        • Chrominance Red ( -127 - 128)
    • YCbCr used for downsampling of color components
Y = a*R + b*G + c*B
Cb = d*R + e*G + f*B
Cr = g*R + h*G + i*B

DCT

  • 8 * 8 bits
  • Center around -127 - 128
  • DCT * DCT CoEff = Centered 8 * 8 bits
  • Quantization table(50% or compression determined) to divide the DCT CoEff table to zero
  • Zigzag serialization
  • Huffman table
  • DCT3 = Inverse DCT
  • Image
    • Stored at 1 bit per pixel (Black and White)
    • 8 Bits per pixel (Grey Scale, Colour Map) or 24 Bits per pixel (True ßColour)
  • Audio
    • Audio signals are continuous analog signals.
    • CD Quality Audio requires 16-bit sampling at 44.1 KHz Even higher audiophile rates
  • Video
    • Raw video can be regarded as being a series of single images.
    • There are typically 25, 30, or 50 frames per second

Huffman Coding

  • Number of Zero preceding, Symbol, Value
  • Marker
    • Two Byte values (FFXX )
    • Determines what is coming next
    • Marker for
      • Quantization Table
      • Huffman Table
      • Huffman coded bitstream
      • Start of Image Marker
        • FFD8 / SOI
        • FFEN / APPN (Application Specific)
          • APP0 JFIF
          • Followed by the value of Data Byte to read (2 Bytes)
        • FFDB / DQT
          • Followed by length (2 Byte)
          • Table Info (1 Byte)
            • First 4 bits - Quantization table 8 bits/ 16 bits
            • Table type - Luminance Table / Chrominance Table
          • Table Values (64 Bytes / 128 Bytes)
          • The chrominance channel is quantized more heavily than the luminance channel.
        • FFCX - Start of frame
          • 13 markers
          • FFC0 - Baseline DCT
          • FFC2 - Progressive DCT
            • Length (2 Byte)
            • Precision (1 Byte) Value 8
            • Height (2 Byte)
            • Width (2 Byte)
            • Channels, Number of Components
              • 1 - Grayscale
              • 3 - YCbCr
              • 4 - CmYk
              • Loop N times
                • Component ID
                • Sampling Factor
                • Quantization Table
        • DRI
          • Define Restart Interval (FFDD)
          • Length (2 Byte) 0004
          • Relative value that is added to DC coefficient
          • 0 - Ac Coefficient in MCU
          • 1-63 - Dc Coefficient in MCU
        • Huffman Table (FFC4)
          • Length (2 Byte)
          • Table Info
            • AC/DC | Table ID
          • [16 bytes] - Number of codes of each length
          • Symbols themselves
          • Codes are what we encounter in Huffman coded bitstream, we calculate those codes. Codes will be of variable length.
          • The symbol will be 8 bits, which is a descriptor of codes.
          • Huffman Symbols
            • 1 Byte
              • 4 bits - how many zeros preceding
              • 4 bits - length of co-efficient. eg. 5 -> 3
            • 160 possible symbols
            • 2 special Symbol
              • F0 - Skip 16 zeros
              • 00 - Rest is zero
          • DC Huffman Table
            • 12 symbols
        • Start of scan - SOS (FFDA)
          • Length
          • Number of color channels/ Components
            • Baseline JPEG
              • equal to the total number of color components
            • Progressive
              • May define one color channel
            • Component ID
            • Huffman Table ID
              • Upper nibble - DC Huffman table ID
              • Lower Nibble - AC Huffman Table ID
          • Start of selection - 0 (Same for baseline jpeg)
          • End of selection - 63 (Same for baseline jpeg)
          • Successive approximation (For baseline both nibble 0)
// Nondifferential Huffman-coding frame
const byte bits SOF0 = (byte bits)0xc0; // baseline dct
const bytebits SOF1 = (bytebits)0xc1; // extended dct
const bytebits SOF2 = (bytebits)0xc2; // progressive dct
const bytebits SOF3 = (bytebits)0xc3; //  Lossless (Sequential)

// Differential Huffman-coding frame
const bytebits SOF5 = (bytebits)0xc5; // Sequential DCT
const bytebits SOF6 = (bytebits)0xc6; // Progressive DCT
const bytebits SOF7 = (bytebits)0xc7; // lossless

// Nondifferential Arithmetic-coding frame
const bytebits SOF9 = (bytebits)0xc9; // extended dct
const bytebits SOF10 = (bytebits)0xca; // progressive dct
const bytebits SOF11 = (bytebits)0xcb; // lossless

// Differential Arithmetic-coding frame
const bytebits SOF13 = (bytebits)0xcd; // sequential dct
const bytebits SOF14 = (bytebits)0xce; // progressive dct
const bytebits SOF15 = (bytebits)0xcf; // lossless

/// Huffman Table
const bytebits DHT = (bytebits)0xc4;

/// Quantization Table
const bytebits DQT = (bytebits)0xdb;

/// Start of Scan
const bytebits SOS = (bytebits)0xda;

/// Define Restart Interval
const bytebits DRI = (bytebits)0xdd;

/// Comment
const bytebits COM = (bytebits)0xfe;

/// Start of Image
const bytebits SOI = (bytebits)0xd8;

/// End of Image
const bytebits EOI = (bytebits)0xd9;

/// Define the Number of Lines
const bytebits DNL = (bytebits)0xdc;

// JFIF identifiers
const bytebits JFIF_J = (bytebits)0x4a;
const bytebits JFIF_F = (bytebits)0x46;
const bytebits JFIF_I = (bytebits)0x49;
const bytebits JFIF_X = (bytebits)0x46;

// Application Reserved Keywords
const bytebits APP0 = (bytebits)0xe0;
const bytebits APP1 = (bytebits)0xe1;
const bytebits APP2 = (bytebits)0xe2;
const bytebits APP3 = (bytebits)0xe3;
const bytebits APP4 = (bytebits)0xe4;
const bytebits APP5 = (bytebits)0xe5;
const bytebits APP6 = (bytebits)0xe6;
const bytebits APP7 = (bytebits)0xe7;
const bytebits APP8 = (bytebits)0xe8;
const bytebits APP9 = (bytebits)0xe9;
const bytebits APP10 = (bytebits)0xea;
const bytebits APP11 = (bytebits)0xeb;
const bytebits APP12 = (bytebits)0xec;
const bytebits APP13 = (bytebits)0xed;
const bytebits APP14 = (bytebits)0xee;
const bytebits APP15 = (bytebits)0xef;

const bytebits RST0 = (bytebits)0xd0;
const bytebits RST1 = (bytebits)0xd1;
const bytebits RST2 = (bytebits)0xd2;
const bytebits RST3 = (bytebits)0xd3;
const bytebits RST4 = (bytebits)0xd4;
const bytebits RST5 = (bytebits)0xd5;
const bytebits RST6 = (bytebits)0xd6;
const bytebits RST7 = (bytebits)0xd7;
  • Baseline jpeg renders line by line while progressive jpeg renders blur then makes it clear.

References