image processing

1. Introduction to JPEG
Alireza Shafaei (79136107)
Fall 2005

2. Bitmap Images
 RGB Color Model (Red, Green & Blue)
 3 bytes of Information for each Pixel:
 1 byte for Red, 1 byte for Green & 1 byte for Blue
 Memory space of a 640 × 480 24-bit RGB
color image:
 640 × 480 = 307,200 pixels
 307,200 × 3 = 921,600 bytes = 900 kilobytes
 Image Compression Methods (like JPEG)

3. What is JPEG?
 “Joint Photographic Expert Group”, A joint effort by
the CCITT and the ISO. (1991)
 An Image Compression Method for continuous-
tone still images, both grayscale and color.
 Facts on Human Visual System used in JPEG:
1. The eye seems to be more sensitive at the luminance of a
colour than at the nuance of that colour. (Y & CbCr)
2. The eye is much more sensitive to lower spatial
frequencies than to higher frequencies

4. JPEG Encoding Steps
 JPEG Baseline Sequential Mode:
1. Color Space Transformation & Sampling
2. DCT
3. Quantization
4. Zig-Zag Scan
5. DPCM & RLE
6. Entropy Coding

5. Color Space Transformation
 RGB to YCbCr
 Y is Luminance (Brightness).
 CbCr is the Chrominance.
 Sampling:
RGB
RGB
Y
Cb Cr
+ (Down Sampling)

6. RGB to YCbCr
 First the image is divided into 8x8 blocks.
RGB RGB
RGB RGB
Y Y
Y Y
Cb
Cr
+
8
8
8 8
8
8
8 8
8
8
8
4 x 64 x 3 byte 4 x 64 x 1 byte 2 x 64 x 1 byte
Y = 0.299 R + 0.587 G + 0.114 B
Cb = - 0.169 R - 0.331 G + 0.500 B
Cr = 0.500 R - 0.419 G - 0.081 B

7. Discrete Cosine Transform (DCT)
DCT
Coefficients
sxy DCT
8
8 8
8

8. DCT (cont’d)
 Why we apply DCT?
 To move from Spatial Domain to Frequency
Domain.
 Why not FFT?
 DCT is like FFT, but can approximate linear
signals well with few [real] coefficients.
 DCT is slow
 1024 multiplications and 896 additions.
 JPEG 2000: Wavelet Transforms.

9. Quantization
 DCT Coefficients are 12 bits per sample.
 Why Quantization?
 To reduce number of bits per sample.
 F'[u, v] = round ( F[u, v] / Q[u, v] )
 Two Quantization Tables are used in JPEG
Header File (QY & QCbCr).
 Quantization error is the main source of the
Lossy Compression.

10. Zig Zag Scan
 8x8 Blocks to a 1x64
Vector.
 Why Zig Zag Scan?
 To sort 8x8 DCT
coefficients based on the
spatial frequencies (low
frequency coefficients in
top of vector).
0 1 2 . . . 63
DC Component
(No Frequency)
Highest Frequency
1x64 Vector:

11. DPCM & RLE
1. DPCM on DC Component
 Differential Pulse Code Modulation.
 DC component is large and varied, but often
close to previous value.
2. RLE on AC Components
 Zero Run Length Encoding.
 1 x 64 vector has lots of zeros in it.
 57,45,0,0,0,0,23,0,-30,-16,0,0,1,0,0,0, 0 , 0 ,0 , only 0,..,0
RLC: (0,57); (0,45); (4,23); (1,-30); (0,-16); (2,1); EOB
EOB = (0,0)

12. Entropy Coding
 Entropy Coding is a form of compression that
relies on developing "code" words in a library
for the input values or "symbols".
 Huffman Coding in JPEG.
 4 Huffman Tables are stored in JPEG Header
File:
 2 tables for DC Component (Y & CbCr)
 2 tables for AC Components (Y & CbCr)

13. JPEG Encoding Diagram

14. JPEG Decoding
 Inverse of Encoding.
 Steps:
1. Decode Huffman Bit Stream
2. Decode DC Component (DPCM) and AC
Components (RLE)
3. Unpack Anti-ZigZag
4. Multiply by Quantization
5. Apply Inverse DCT
6. YCbCr to RGB

15. JPEG Decoding (cont’d)
 Inverse DCT:
 YCbCr to RGB: