Image Compression Digital Image processing

CMPT365 Multimedia Systems 1
Media Compression
- Image
Spring 2015
CMPT 365 Multimedia Systems

Facts about JPEG
 JPEG - Joint Photographic Experts Group
 International standard: 1992
 Most popular format
 Other formats (.bmp) use similar techniques
 Lossy image compression
 transform coding using the DCT
 JPEG 2000
 New generation of JPEG – well, never succeeds
 DWT (Discrete Wavelet Transform)

Three Major Observations
 Observation 1:
 Useful image contents change relatively slowly across the
image, i.e., it is unusual for intensity values to vary widely
several times in a small area, for example, within an 8x8
image block.
- much of the information in an image is repeated,
hence “spatial redundancy".
Compression Ratio: 7.7 Compression Ratio: 33.9

Observations
 Observation 2:
 Psychophysical experiments suggest that humans are
much less likely to notice the loss of very high spatial
frequency components than the loss of lower frequency
components.
- the spatial redundancy can be reduced by largely
reducing the high spatial frequency contents.

Observations
 Observation 3:
 Visual acuity (accuracy in distinguishing closely spaced
lines) is much greater for gray (black and white) than for
color.
- chroma subsampling (4:2:0) is used in JPEG.

8x8 DCT Example
Original values of an 8x8 block
(in spatial domain)
Corresponding DCT coefficients
coefficients
(in frequency domain)
(in frequency domain)
DC Component
or u
o
r
v

JPEG Steps
1 Block Preparation
- RGB to YUV (YIQ) planes
2 Transform
- 2D Discrete Cosine Transform (DCT) on 8x8 blocks.
3 Quantization
- Quantized DCT Coefficients (lossy).
4 Encoding of Quantized Coefficients
Zigzag Scan
Differential Pulse Code Modulation (DPCM) on DC component
Run Length Encoding (RLE) on AC Components
Entropy Coding: Huffman or Arithmetic

JPEG Diagram

RGB Input Data
RGB Input Data After Block Preparation
After Block Preparation
JPEG: Block Preparation
Input image: 640 x 480 RGB (24 bits/pixel) transformed to three planes:
Y: (640 x 480, 8-bit/pixel) Luminance (brightness) plane.
U, V: (320 X 240 8-bits/pixel) Chrominance (color) planes.

Block Effect
 Using blocks, however, has the effect of isolating
each block from its neighboring context.
 choppy (“blocky") with high compression ratio
Compression Ratio: 60.1

JPEG: Quantized
DCT Coefficients
Uniform quantization:
Divide by constant N and round result.
In JPEG, each DCT F[u,v] is divided by
a constant q(u,v).
The table of q(u,v) is called quantization table.
q(u,v)
F[u,v]
Rounded
F[u,v]/ Q(u,v)

More about Quantization
 Quantization is the main source for loss
 Q(u, v) of larger values towards lower right corner
• More loss at the higher spatial frequencies
• Supported by Observations 1 and 2.
 Q(u,v) obtained from psychophysical studies
• maximizing the compression ratio while minimizing
perceptual losses

JPEG: Encoding of Quantized
DCT Coefficients
 DC Components (zero frequency)
 DC component of a block is large and varied, but often close
to the DC value of the previous block.
 Encode the difference from previous
• Differential Pulse Code Modulation (DPCM).
 AC components:
 Lots of zeros (or close to zero)
 Run Length Encoding (RLE, or RLC)
• encode as (skip, value) pairs
• Skip: number of zeros, value: next non-zero component
 (0,0) as end-of-block value.

JPEG: Zigzag Scan
Maps an 8x8 block into a 1 x 64 vector
Zigzag pattern group low frequency coefficients in top of vector.

Recall: 2-D DCT Basis Matrices
For 2-point DCT For 4-point DCT

Recall: 2-D DCT Basis Matrices: 8-point DCT

Why ZigZag Scan
 RLC aims to turn the block values into sets
<#-zeros-to-skip , next non-zero value>.
 ZigZag scan is more effective

Runlength Encoding (RLE)
 Further compression: statistical (entropy) coding
A typical 8x8 block of quantized DCT coefficients.
Most of the higher order coefficients have been quantized to 0.
12 34 0 54 0 0 0 0
87 0 0 12 3 0 0 0
16 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
Zig-zag scan: the sequence of DCT coefficients to be transmitted:
12 34 87 16 0 0 54 0 0 0 0 0 0 12 0 0 3 0 0 0 .....
DC coefficient (12) is sent via a separate Huffman table.
Runlength coding remaining coefficients:
34 | 87 | 16 | 0 0 54 | 0 0 0 0 0 0 12 | 0 0 3 | 0 0 0 .....

Entropy Coding
 Huffman/arithmetic coding
 Lossless

JPEG Modes
 Sequential Mode
 default JPEG mode, implicitly assumed in the discussions
so far. Each graylevel image or color image component is
encoded in a single left-to-right, top-to-bottom scan.
 Progressive Mode.
 Hierarchical Mode.
 Lossless Mode

Progressive Mode
 Progressive
 Delivers low quality versions of the image quickly, followed by
higher quality passes.
 Method 1. Spectral selection
- higher AC components provide detail texture information
 Scan 1: Encode DC and first few AC components, e.g., AC1, AC2.
 Scan 2: Encode a few more AC components, e.g., AC3, AC4, AC5.
 ...
 Scan k: Encode the last few ACs, e.g., AC61, AC62, AC63.

Progressive Mode cont’d
 Method 2: Successive approximation:
- Instead of gradually encoding spectral bands, all DCT
coefficients are encoded simultaneously but with their
most significant bits (MSBs) first
 Scan 1: Encode the rst few MSBs, e.g., Bits 7, 6, 5, 4.
 Scan 2: Encode a few more less signicant bits, e.g., Bit 3.
 ...
 Scan m: Encode the least signicant bit (LSB), Bit 0.

Hierarchical Mode
 Encoding
 First, lowest resolution picture (using low-pass filter)
 Then, successively higher resolutions
• additional details (encoding differences)
 Transmission:
 transmitted in multiple passes
 progressively improving quality
 Similar to Progressive JPEG

Lossless Mode
 Using prediction and entropy coding
 Forming a differential prediction:
 A predictor combines the values of up to three
neighboring pixels as the predicted value for the current
pixel
 Seven schemes for combination
 Encoding:
 The encoder compares the prediction with the actual
pixel value at the position `X' and encodes the
difference using entropy coding

7 Predictors

Comparison with Other Lossless

JPEG Bitstream

JPEG 2000
 JPEG 1992
 JPEG 2000
 .jp2 for ISO/IEC 15444-1
 .jpx for extended part-2 specifications (ISO/IEC
15444-2)
 Wavelet transform based
 20% gain in compression

JPEG 2000 vs JPEG
 Original image

JPEG2000 vs JPEG

Further Exploration
 Textbook Chapter 9
 Other sources
 The JPEG Still Image Compression Standard by
Pennebaker and Mitchell
 JPEG2000: Image Compression Fundamentals, Standards,
and Practice by Taubman and Marcellin
 Image and Video Compression Standards: Algorithms and
Architectures, 2nd ed. by Bhaskaren and Konstantinides

Image Compression Digital Image processing

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