1. JPEG

2. What is JPEG?
JPEG is sophisticated lossy/lossless compression method for color or greyscale still images. It works best on contineous tone images where adjacent pixels have similar colors. One advantage of JPEG is the use of many parameters, allowing the use to adjust the amount of data lost over a wide variety range.

3. Main Goals of JPEG
High Compression Ratio in such cases where images quality is judged as very good to excellent.
The use of many parameters allowing user to experiment and achieve the desired level of compression.
Obtaining good results any kind of continuous tone images.
Sophisticated but not too complex compression method, allowing software and hardware implementation on many platform.
Saveral modes of operations.

4. Modes of JPEG
Sequential Mode: each image component is compressed in a single left to right, top to bottom scan.
Progressive Mode: the images is compressed in multiple blocks to be viewed from coarse to final detail.
Lossless Mode: important for cases where the user decides no pixel should be lost.
Hierarchical Mode: the image is compressed at multiple resolution allowing lower resolution blocks to be viewed without first having to decompressed the following higher-resolution blocks.

5. Basic JPEG Compression
JPEG compression involves the following:
Colour Space Transform and subsampling (YIQ)
DCT (Discrete Cosine Transformation)
Quantization
Zigzag Scan
DPCM on DC component
RLE on AC Components
Entropy Coding — Huffman or Arithmetic

6. JPEG Encoding

7. Colour Space Transform and sub-sampling (YIQ)
The images values are transformed from RGB to luminance/chrominance color space.
The eye is sensitive to small changes in luminance but not in chrominance. So chrominance values can be used to compress the data.
This step is optional but important since the remainder of the algorithm works on each color component saperately.
Without transforming the color space, none of the three color components will tolerate the much loss leading to worse compression.

8. DCT (Discrete Cosine Transformation)
The DCT is applied to each data unit to create an 8x8 map of frequency component.
They represent the average pixel value and successive higher frequency changes within the group.
This prepares the images data for the crucial step of losing information.

9. Quantization
Each of the 64 frequency component in a data unit is divided by a separate number called its quantization coefficient (QC) and then rounded to an integer.
This is the step where the information is lost.
Large QCs cause more loss. So high frequency components typically have larger QCs.

10. Quantization Why do we need to quantise: To throw out bits from DCT.
Example: = 45 (6 bits).
Truncate to 4 bits: 1011 = 11.
Truncate to 3 bits: 101 = 5.
Quantization error is the main source of Lossy Compression.
• DCT itself is not Lossy
• How we throw away bits in Quantization Step is Lossy

11. Quantization Methods Uniform quantization
Divide by constant N and round result (N = 4 or 8 in examples on previous page).
• Non powers-of-two gives fine control
(e.g., N = 6 loses 2.5 bits)

12. Quantization Tables
In JPEG, each F[u,v] is divided by a constant q(u,v).
Table of q(u,v) is called quantization table.
Eye is most sensitive to low frequencies (upper left corner), less sensitive to high frequencies (lower right corner)
JPEG Standard defines 2 default quantization tables, one for luminance (below), one for chrominance. E.g Table below

13. Quantization Table

14. Zig-zag Scan What is the purpose of the Zig-zag Scan:
• To group low frequency coefficients in top of vector.
• Maps 8 x 8 to a 1 x 64 vector

15. Differential Pulse Code Modulation (DPCM) on DC Component
Another encoding method is employed
• DPCM on the DC component at least.
• Why is this strategy adopted:
DC component is large and varies, but often close to previous value (like lossless JPEG).
Encode the difference from previous 8x8 blocks – DPCM

16. Run Length Encode (RLE) on AC Components
Yet another simple compression technique is applied to the AC component:
1x64 vector has lots of zeros in it
Encode as (skip, value) pairs, where skip is the number of zeros and value is the next non-zero component.
• Send (0,0) as end-of-block sentinel value.

17. Huffman (Entropy) Coding
DC and AC components finally need to be represented by a
smaller number of bits (Arithmetic coding also supported in place of Huffman coding):
(Variant of) Huffman coding: Each DPCM-coded DC coefficient is represented by a pair of symbols : (Size, Amplitude) where Size indicates number of bits needed to represent coefficient and Amplitude contains actual bits.
• Size only Huffman coded in JPEG:
Size does not change too much, generally smaller Sizes occur frequently (= low entropy so is suitable for coding,
Amplitude can change widely so coding no real benefit