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 & C b C r ) 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 YC b C r Y is Luminance (Brightness). C b C r is the Chrominance. Sampling: RGB Y CbCb CrCr + (Down Sampling)

6. RGB to YC b C r First the image is divided into 8x8 blocks. RGB YY YY CbCb CrCr + 8 8 8 8 8 8 88 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 s xy DCT 8 88 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 (Q Y & Q CbCr ). 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). 012...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 & C b C r )  2 tables for AC Components (Y & C b C r )

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. YC b C r to RGB

15. JPEG Decoding (cont’d) Inverse DCT: YC b C r to RGB: