Ch. 3: Image Compression Multimedia Systems
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1 4/24/213 Ch. 3: Image Compression Multimedia Systems Prof. Ben Lee (modified by Prof. Nguyen) Oregon State University School of Electrical Engineering and Computer Science Outline Introduction JPEG Standard YUV or YIQ conversion and subsampling DCT Quantization Zig-Zag ordering and RLE/DPCM RLE on AC Coefficients DPCM on DC Coefficients Variable Length Coding (entropy Coding) JPEG Header Format JPEG Compression Modes Chapter 3: Image Compression 2 1
2 4/24/213 Introduction Image bandwidth requirement: pixels/frame and true colors (3 bytes) 64 x 48 x 3 = KB To transfer over 64-Kbps ISDN channel takes almost 2 minutes (115 sec)! Many different formats JPEG GIF (Graphics Interchange Format) Based on LZW Handles only 8-bit color images (more suitable for graphics or drawing) TIFF (Tagged Image File Format) Can store many different types, e.g., 1-bit, grayscale, 8-bit, 24-bit, etc. PNG (Portable Network Graphics) EXIF (Exchange Image File) Image format for digital cameras Chapter 3: Image Compression 3 Outline Introduction JPEG Standard YUV or YIQ conversion and subsampling DCT Quantization Zig-Zag ordering and RLE/DPCM RLE on AC Coefficients DPCM on DC Coefficients Variable Length Coding (entropy Coding) JPEG Header Format JPEG Compression Modes Chapter 3: Image Compression 4 2
3 4/24/213 JPEG JPEG (Joint Photographic Experts Group) Became a standard in 1992 Takes advantage of the limitations of the human vision system Eye-brain cannot see extremely fine detail It is worse for color Compression ratio 1:1 to 3:1 Typical compression: 1:1 to 2:1 Lossy, but hardly noticeable. Chapter 3: Image Compression 5 JPEG Compression JPEG: 45KB (1:1.4) 476x7x24 467KB JPEG: 11.6KB (1:4) Chapter 3: Image Compression 6 3
4 4/24/213 JPEG Encoding Chapter 3: Image Compression 7 YUV Encoding Recall that human eye less sensitive to variations in color than in brightness. Chrominance Subsampling 1 byte for luminance component, and 4 bits for each chrominance components (4:2:2 coding). Requires only 2/3 of the space (RGB = 24 bits), so better compression! Conversion Chapter 3: Image Compression 8 4
5 4/24/213 Subsampling Example below shows 4:2: subsampling, i.e., every other row and column are ignored. In 4:2:2, only every other column is ignored. When displayed, the size of the pixel is doubled, called pixel doubling. Chapter 3: Image Compression 9 Discrete Cosine Transform Spatial domain Frequency domain. Outputs DCT coefficients (containing spatial frequencies), which relate directly to how much the pixel values change as function of their position in the block. A lot of variations in pixel values Represents an image with a lot of fine detail. Small variations in pixel values Uniform color change and little fine detail. When there is little variations in pixel values, only a few data points are required to represent the image. DCT does not provide any compression. Rearranges the data into a form that allows another coding technique to compress the data more effectively. 5
6 4/24/213 1-Dimensional DCT An image consisting of an array of pixel values, which varies in space, can be represented as the sum of frequency components with frequency range from to N-1: DCT(i) 2 N C(i) N 1 x 1 if i (DC) C(i) 2 1 if i (AC) 2x 1 pixel(x)cos i 2N Typically, changes in intensity is very gradual with very few sharp edges => little or no contribution from higher spatial frequencies. Basis Cosine Functions 1 7 pixel (x) 2 2 x pixel() pixel(1) pixel(2) 7 x 7 x 2x 1 pixel (x)cos( 16 * ) 2x 1 pixel (x)cos( 16 *2 ) DCT() DCT(1) DCT(2) DC pixel(3) pixel(4) pixel(5) pixel(6) pixel(7) 7 x 7 x 7 x 2x 1 pixel (x)cos( 16 *3 ) 2x 1 pixel (x)cos( 16 *4 ) 2x 1 piexl (x)cos( 16 *5 ) DCT(4) DCT(4) DCT(5) DCT(6) DCT(7) AC 7 x 2x 1 pixel (x)cos( 16 *6 ) 7 x 2x 1 pixel (x)cos( 16 *7 ) Chapter 3: Image Compression 12 6
7 4/24/213 Inverse 1-D DCT N 1 2 pixel(x) N C(i) 2x 1 DCT(i)cos i 2N i S() N 1 N 2 N C(i) 2x 1 DCT(i)cos i 2N i DC Component AC Component 1 C(i) 2 if i 1 if i Chapter 3: Image Compression 13 Inverse 1-D DCT Chapter 3: Image Compression 14 7
8 4/24/213 2-D DCT Key component of both JPEG and MPEG. Represented by a weighted sum of 8 8 cosine functions. DCT(i, j) x 1 C(i)C(j) pixel(x, y)cos i cos 2y 1 j 4 x y pixel(x, y) C(i)C(j)DCT(i, j)cos 2x 1 i cos 2y 1 j i j 1 2 C(x) if x 1 if x 2-D DCT Chapter 3: Image Compression 16 8
9 4/24/213 DCT Example (1) Divide the image into 8 8 blocks. Computation grows rapidly as function of N ( N2). Research has shown this size results in minimal lost in terms of fidelity for a variety of images. Pixel values are shifted into the range [-128, 127] with zero in the center. 8-bit pixel values produce 12-bit signed coefficient values. Some errors due to rounding, but minimal. 2-D DCT 9
10 4/24/213 DCT Example (2) 8x8 Image Block DCT (After shifting by -128) DC Coefficient Low Freq High Freq Low Freq High Freq DC coefficient is related to the average of the pixel values in the block pixel(x, y) x y AC coefficient represents a measure of pixel variation. Chapter 3: Image Compression 19 Quantization (1) Attempts to determine what information can be safely discarded without significant loss in visual fidelity. Human eye is less sensitive to chrominance than to luminance. Human eye cannot perceive subtle color changes, i.e., small AC coefficients. Human eye is most sensitive to low-spatial frequencies, i.e., less subtle features of the image. Reduce precision => reduce number of number of bits. Divide DCT coefficients DCT(i, j) by Quantization coefficient Q(i,j) and truncate. DCT(i, j) DCT Q (i, j) Q(i, j) Chapter 3: Image Compression 2 1
11 4/24/213 Quantization (2) Uses Quantization Table derived from extensive empirical measurements: Luminance Chrominance Many high frequency coefficients end up being zeroed => high compression rate! Chapter 3: Image Compression 21 Quantization (3) Quantization Chapter 3: Image Compression 22 11
12 4/24/213 Zig-Zag Scan The length of zero values can be increased by placing low-frequency coefficients before highfrequency coefficients using zig-zag ordering E OB Chapter 3: Image Compression 23 Lossless Compression This is where real compression is done. DC and AC coefficients treated differently DC coefficients determine the basic color (or intensity) of a block. Chapter 3: Image Compression 24 12
13 4/24/213 DC Coefficient Encoding (1) Differential DC coefficient is generated by performing DIFF(x) = DC(x)-DC(x-1), where x and x-1 represent two successive 8 8 blocks. Typically a strong correlation between DC levels of two adjacent 8 8 blocks => a small value! Encoded using symbol-1 and symbol-2: Symbol-1 - Defines # of bits used to encode DIFF(x). Encoded using Variable Length Coding (VLC). Symbol-2 - Represents the amplitude of DIFF(x). Encoded using Variable Length Integer (VLI). Chapter 3: Image Compression 25 DC Coefficient Encoding (2) VLC Coding of Symbol-1 Bit Size(m) Huffman Code Differential DC Coeff. Value 1 1 (-1,1) 2 11 (-3,-2)(2,3) 3 1 (-7-4)(4 7) 4 11 (-15-8)(8 15) 5 11 (-31-16)(16 31) (-63-31)( 63) ( )(64 127) ( )( ) ( )( ) ( )( ) ( )( ) Chapter 3: Image Compression 26 13
14 4/24/213 DC Coefficient Encoding (3) VLC encoding of Symbol-1: e.g., DIFF(x) = 3 => from Huffman table => VLC = 11 VLI encoding of Symbol-2 If DIFF(x), take m LSBs of DIFF(x) e.g., DIFF(x) = 3 = 11 => VLI = 11 If DIFF(x) <, take m LSBs of 2 s-complement of DIFF(x) -1. e.g., DIFF(x) = -3 => TC[DIFF(x)-1] = => VLI =. Chapter 3: Image Compression 27 DC Coefficient Encoding (4) VLI Encoding -3 ( ) (size)(diff(x)) -3 If DIFF(x), take m LSBs of DIFF(x) If DIFF(x) <, take m LSBs of TC[ DIFF(x) -1] VLC Encoding Differential Bit Huffman DC Coeff. Value Size (m) Code (-1,1) 1 1 (-3,-2)(2,3) 2 11 (-7..-4)(4..7) 3 1 ( )(8..15) 4 11 ( )(16..31) 5 11 (-63..-)(..63) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) (11)() Chapter 3: Image Compression 28 14
15 4/24/213 AC Coefficient Encoding (1) Similar to DC coefficient encoding, but uses RLE since AC coefficients tend to have many zeros! Symbol-1 (using VLC) Symbol-2 (using VLI) (run length, size)(amplitude) # of consecutive zeros (4 bits: -15) # of bits used to encode the amplitude Amplitude of the AC coefficient (variable) Chapter 3: Image Compression 29 AC Coefficient Encoding (2) Bit Size (m) AC Coeff. Value 1 (-1,1) 2 (-3,-2)(2,3) 3 (-7..-4)(4..7) 4 ( )(8..15) 5 ( )(16..31) 6 (-63..-)(..63) 7 ( )( ) 8 ( )( ) 9 ( )( ) 1 ( )( ) Chapter 3: Image Compression 3 15
16 4/24/213 AC Coefficient Encoding (3) -3 4 VLI Encoding If AC(x), -3 ( ) take m LSBs of AC(x) If AC(x) <, take m LSBs of TC[ AC(x) -1] (rl, size)(ac(x)) Bit AC Coeff. Value Size (m) -3 (-1,1) 1 (-3,-2)(2,3) 2 2 (7-4)(4 7) 3 (-15-8)(8 15) 4 (-31-16)(16 31) 5 (-63 -)( 63) 6 ( )(64 127) 7 ( )( ) 8 ( )( ) 9 ( )( ) 1 (4, 2) AC Huffman Table ( )() Chapter 3: Image Compression 31 AC Huffman Table A partial listing of the AC Huffman table. (RL, Size) Code Length Code Value (, ) 4 11 (EOB) (1, 1) 4 11 (1, 4) (1, 5) (2, 4) (4, 1) (8, 1) (13, 1) Chapter 3: Image Compression 16
17 4/24/213 Coefficient Encoding Example Original zig-zag sequence (-49,)(,, -12,) (, -16,) (,,,, -1,)(, 9,)(, -1,)(,,,,,,,, -1,)(, -1,)(,,,,,,,,,,,,, 1,)(,,,,,,,,,,,,,,,,,,,,,,,, EOB) Decimal equivalent (6)(-49) (2,4)(-12) (1,5)(-16) (4, 1)(-1) (1,4)(9) (1,1)(-1) (8,1)(-1) (1,1)(-1) (13,1)(1) (,) Assume this is the first DC value from a picture! Encoded sequence (111)(111) ( )(11) ( )(1111) (11111)() ( )(11) (11)() (111111)() (11)() ( )(1) (11) => 14 bits! (compared to = 512 bits) Chapter 3: Image Compression 33 JPEG Compression Example Uncompressed (262 KB) Compressed (5) (22 KB, 12:1) Compressed (1) (6 KB, 43:1) Chapter 3: Image Compression 34 17
18 4/24/213 Outline Introduction JPEG Standard YUV or YIQ conversion and subsampling DCT Quantization Zig-Zag ordering and RLE/DPCM RLE on AC Coefficients DPCM on DC Coefficients Variable Length Coding (entropy Coding) JPEG Header Format JPEG Compression Modes Chapter 3: Image Compression 35 JPEG Header Formats Start of Image SOI xffd8 Compressed Image Data Frame End of Image EOI xffd9 Q Table, etc header Scan... Scan Scan - a pass through the pixels (e.g., red component) Table, etc header Segment Restart Segment Restart... Segment - a group of blocks block block... block Block - 8x8 group of pixels # of components in scan # bits used to digitize each component Pointer to Huffman table Mode (baseline, progressive, hierarchical) Length of header Sample precision W/H of image # of components H/V sampling factor (for each component) Q table to use (for each component) Chapter 3: Image Compression 36 18
19 4/24/213 Outline Introduction JPEG Standard YUV or YIQ conversion and subsampling DCT Quantization Zig-Zag ordering and RLE/DPCM RLE on AC Coefficients DPCM on DC Coefficients Variable Length Coding (entropy Coding) JPEG Header Format JPEG Compression Modes Chapter 3: Image Compression 37 JPEG Compression Modes Lossy Sequential DCT based mode The one we just talked about. Baseline process that must be supported by every JPEG implementation. Expanded Lossy DCT based mode Enhancements to baseline process. Lossless mode Low compression ratio. Allows perfect reconstruction of original image. Hierarchical mode Accommodates images of different resolutions. 19
20 4/24/213 Expanded Lossy DCT based mode Specifies progressive encoding (in addition to baseline sequential mode). Allows arithmetic encoding (as well as Huffman encoding). 5%-1% better than Huffman encoding. But, slightly more complex and protected by a patent. Chapter 3: Image Compression 39 Progressive Mode First display low quality image and then successfully improved. Useful for human interaction over low data rate communication channels (e.g., telephone lines). A buffer is added at the output of the quantizer to store all the coefficients. Progressiveness is achieved in two ways: Spectral selection: Send DC component first, then gradually send more AC coefficients. Successive approximation: Send DCT coefficients MSB to LSB (e.g., 4 MSBs). Or, send quantized DCT coefficients first, next send the difference between the quantized and the non-quantized coefficients with finer quantization step-size. Chapter 3: Image Compression 4 2
21 4/24/213 Progressive Mode Chapter 3: Image Compression 41 Progressive Mode Example Scan 1: DC (Y,Cb,Cr) Scan 2: AC 1-2 (Y) Scan 3: AC 3-5 (Y) Scan 4: AC 1-63 (Cr) Scan 5: AC 1-63 (Cb) Scan 6: AC 6-9 (Y) Scan 7: AC 1-63 (Y) Chapter 3: Image Compression 42 21
22 4/24/213 Lossless Mode Predictive method. DCT not used. Combine three neighboring pixels as the predicted value for the current pixel. Compare this prediction with the actual pixel value at the position. Encodes the difference losslessly. Much lower compression ratio than DCT-based (typically 2:1) C A B X A, B, and/or C X Chapter 3: Image Compression 43 Lossless Mode Predictor Prediction No prediction 1 A 2 B 3 C 4 A + B - C 5 A + (B - C)/2 6 B + (A - C) / 2 7 (A + B) / 2 p p p2 1 1 p First pixel I(, ) will have to use itself Other pixels at the first row always use P1, at the first column always use P2. Chapter 3: Image Compression 44 22
23 4/24/213 Hierarchical Mode Image is encoded at multiple resolutions using a pyramid structure. Good for viewing high resolution image on low resolution display. Method Down-sample by factors of 2 in each dimension, e.g., reduce to 24 Code smaller image using another JPEG mode. Sequential, Progressive, or Lossless. Decode and up-sample encoded image. Encode difference between the up-sampled and the original using Progressive, Sequential, or Lossless. Can be repeated multiple times. Chapter 3: Image Compression 45 Hierarchical Mode Example Compared to the baseline mode. Size: 4% Time to Decompress: 3% Time to Compress: 43% Size: 11% Time to Decompress: 11% Time to Compress: 91% Size: 35% Time to Decompress: 43% Time to Compress: 169% Size: 12% Time to Decompress: 165% Time to Compress: 7% Chapter 3: Image Compression 46 23
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