DCT

1
DCT

• By Naghmeh Karimi
• The material in this class presentation have been
  collected from different published works of other
  authors and are presented here for educational
  purposes only.
• Under supervision of
• Dr. Fakhraie
• University of Tehran

2
Outline

• Introduction
• JPEG coding
• DCT technique

3
Introduction
4
JPEG Coding

• Lossy
• Lossless

5
Lossless Compression
Source image data
Compressed image data
Predictor
Entropy Coder
Entropy_Table Specifications
6
Lossy Compression

• Baseline sequential mode compression
• Progressive mode
• Hierarchical mode

7
Baseline Sequential mode

• An image is partitioned into some 8 by 8
  non-overlapping pixel blocks from left to right
  and top to bottom.
• Each block is coded individually.

8
Progressive mode

• Start with a low quality image and successively
  improve.
• Spectral selection Send DC component and first
  few AC coefficients first, then gradually some
  more ACs.
• 2. Successive approximation send DCT
  coefficients MSB (most significant bit) to LSB
  (least significant bit).

9
Hierarchical mode

• Down-sample by factors of 2 in each dimension,
  e.g., reduce 640 x 480 to 320 x 240
• 2. Code smaller image using another JPEG mode
  (Progressive, Sequential, or Lossless)
• 3. Decode and up-sample encoded image
• 4. Encode difference between the up-sampled and
  the original using Progressive,Sequential, or
  Lossless.

10
Hierarchical mode

• An image is coded as a sequence of layers in a
  pyramid.
• Except for the top level of pyramid, for each
  luminance and color component at the lower
  levels, the difference between the source
  components and the reference reconstructed image
  is coded.

11
Baseline JPEG Encoder(block diagram)
AC
Zigzag
VLC
Compressed image data
Q
Zero shift
DCT
VLC
Diff
DC
image
12
Color Transformation

• The human visual systems is most sensitive to
  changes in luminance and less to changes in
  chrominance.
• RGB must be converted to the other color systems
  .

13
YUV system

• Y 0.299R 0.587G 0.114B
• U B - Y
• V R - Y

14
Zero Shift

• After transformation Y, U and V are in the range
  of 0,255
• Zero shift changes this range to -128,127

15
DCT

• The strength of transform coding in achieving
  data compression is that the image energy of the
  most natural scenes is mainly concentrated in the
  low frequency region and hence into a few
  transform coefficients.

16
Quantization

• Quantization allows us to reduce the accuracy
  with witch the DCT coefficients are represented
  when converting the DCT to an integer
  representation.
• It tends to make many coefficients zero,
  specially those for high spatial frequencies.
• Two standard table are available for quantization.

17
Zigzag Scan

• The zigzag pattern used in the JPEG algorithms
  orders the basis functions from low to high
  spatial frequencies .
• It facilitate entropy coding by encountering the
  most likely non-zero coefficient first.

18
Run Length Coding

• For the JPEG standard, a symbol is structured in
  2 parts
• Symbol1 (VLC)
• Symbol2 binary representation of
  amplitude

19
Coding DC Coefficients

• The differential rules are categorized based on
  the magnitude range called CAT.
• The CAT is Variable Length Coded.

20
Coding AC Coefficients

• For each non-zero AC coefficient in zigzag Scan
  symbol1 is described as a 2dimentional event of (
  Run, Cat ).
• Cat category for the amplitude of a non-zero
  coefficient.
• Run the number of zeros preceding this non-zero
  coefficient.

21
Coding AC Coefficients(Cont.)

• If Run is greater than 15 then (Run, Cat) must be
  broken to some (15,0) followed by a (Cat1, Run1).
• Example
• (34,5) (15,0),(15,0),(2,5)
• The end of the block is represented by (0,0)

22
Improving DCT Efficiency

• Using LUTs .
• Using FDCT Algorithms.
• Using Pipeline structures.

23
Example
A
5 ? (3,3) ?111111110101101
24
2-DCT
25
First_Technique

• 8-point DCT and IDCT
• DCT
• Input 8 bit
• Output10 bit
• IDCT
• Input 10 bit
• Output8 bit

26
8-point IDCT
27
8-point IDCT(Cont.)
28
Rotator
29
Rotator

• Another Architecture with 3 adder and 3
  multiplier is possible.

30
8-point DCT
31
Rotator
32
Implementation Results
33
Second_Technique
34
1-D IDCT Equation Coefficients
Original Coefficients
Simplified Coefficients
35
Second_Technique
36
Total_Implementation
37
Wave-Forms
38
Results
39
Third_Technique(Pipeline)
40
Pipeline stages
41
Pipeline Structure

• Each 1-D DCT stage 8 clk cycle
• 1-D DCT architecture latency 48 clk cycle
• The transpose buffer latency 64 clk cycle
• Total160 clk cycle

42
Fourth_Technique
43
FDCT (cosine-factors)
44
Data flow graph for 8 point FDCT
45
Schematic of 2-D DCT
46
Schematic of transposition memory
47
Architecture and Operation of2-D DCT Circuit
Reset
Dout
Din
Clk
48
Timing Diagram for External In/Out Port
(A) Serial to Parallel conversion for
input (B)1-D DCT operation (C) Parallel to
Serial conversion for output
49
Functionality of internally generated control
signals
50
Row 1-D DCT Operation
Timing Diagram of Row 1-D DCT
51
Column 1-D DCT Operation
Timing Diagram between Row and Column 1-D DCT
52
Column 1-D DCT Operation (Cont.)
Timing Diagram of the last part of Column 1-D DCT
53
Fast_Multiplier
a
0
0
8a
2a
0
Multiplier
CSA
CSA
S
C
S
C
CSA
C
S
C
CSA
4
Sum
FF
4
Carry
54
Verilog-result(4-bit precision)
55
Matlab-result
56

• Thank you!

List of References 1. 2. 3.