1. An Algorithm for Compression of Bilevel Images
Authors: Maire D. Reavy and Charles G. Boncelet
Source: IEEE Transactions on Image Processing, Vol. 10, No. 5, May 2001
Speaker: Guu-In Chen
Date: 2001/9/13

2. INTRODUCTION Algorithm for lossless bilevel image compression: G3:
1980
Run lengthmodified Huffman encoder
Suitable for business documents
Not for halftone images
JBIG (JBIG1):
1993
An arithmetic coder (IBM QM-coder)
& halftone images
Not been implemented commercially
More than 24
patents

3. INTRODUCTION (cont.)
BACIC (Block Arithmetic Coding for Image Compression):
1997
Block arithmetic coder (BAC)
Suitable for business documents
& halftone images
Compression ratio:
Documents:~JBIG, 2.4xG3
halftone images:>JBIG, 6.1xG3

4. Documents

5. Halftone Image
- by Floyd-Steinberg error diffusion
Grayscale Image

6. Halftone Image
- by dispersed-dot ordered dither

7. Halftone Image
- by clustered-dot ordered dither

8. BAC predeterminiate the number of codewords K
K is as large as possible to maximize BAC’s coding efficiency.
calculate the overall p0 (p1=1- p0)
p0 :the probability of a bit equaling zero
build BAC coding tree BAC codebook
raster-scan the image
From the root of BAC coding tree, one bit one node moves forward till a leaf and outputs its number (ie, codeword).
The coding tree is small and constant, the encoder and decoder can each store a copy of this tree.

9. For example: K=16 (0-15 or 0000-1111) p0 =0.8
BAC coding tree:
K0=[p0K] K1=K-K0
[•]:rounded to the nearest integer unless
[p0K]=KK0 =K-1 , K1=1
　or [p0K]=1 K0 =1, K1= K-1 K K1 K0

10. BAC coding tree:
K=16 (0-15), p0 =0.8

11. Bitstream:
Code: or 11
(with the size of image in the header)

12. BACIC BASIC propose an adaptive BAC coding tree:
p0 (p1=1- p0) is no longer constant;
using a three-line or five-line template to estimate p0 (p1);
constructing only that portion of the tree that is needed to generate a codeword.

13. The template used by BACIC
For documents & error diffusion halftone
The essences:
ri counts the previously coded pixels equaling one.
si counts all the previously coded pixels.
For a context, the estamate of p1:
For ordered dither halftone

14. The template used by BACIC (cont.)
For every context:
ri (0)=1.0 ri (n+1) = px *ri (n)
si (0)=2.0 si (n+1) = *si (n)
n : the sequence no. px: the value of the current pixel
0.985: the weight to make the recent pixels have greater influence on the probability estimate of the current pixel than earlier pixels do.
0.006: to correct the overestimate p1 when si (n) reach its upper limit

15. The example for adaptive BAC coding tree
p0={0.80, 0.90, 0.25, 0.90 …….}, K=16
Input stream : …….
Output: 2

16. Decoding:
p0 of the first pixel is 0.80 and K=16. The according index is 2.
16*0.80=13, (13-1)>=2, so go down the lower path from the root of BAC coding tree.
p0 of the second pixel is 0.90, 13*0.90=12, (12-1)>=2, so go down the lower path .
p0 of the third pixel is 0.25, 12*0.25=3, (3-1)>=2, so go down the lower path .
p0 of the forth pixel is 0.90, 3*0.90=2, (2-1)<2, so go down the upper path, and the node is a leaf, so this index 2 decoded to be 0001.

17. Experimental results

18. ordered dither halftone