An Algorithm for Compression of Bilevel Images

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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
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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)
• Suitable for business documents
• halftone images
• Not been implemented commercially

More than 24 patents
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INTRODUCTION (cont.)

• BACIC (Block Arithmetic Coding for Image
  Compression)
• 1997
• Block arithmetic coder (BAC)
• Suitable for business documents
• halftone images
• Compression ratio
• DocumentsJBIG, 2.4xG3
• halftone imagesgtJBIG, 6.1xG3

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Documents
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Halftone Image - by Floyd-Steinberg error
diffusion
Grayscale Image
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Halftone Image - by dispersed-dot ordered dither
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Halftone Image - by clustered-dot ordered dither
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BAC

• predeterminiate the number of codewords K
• K is as large as possible to maximize BACs
  coding efficiency.
• calculate the overall p0 (p11- 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.

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For example K16 (0-15 or 0000-1111)
p0 0.8
BAC coding tree K0p0K K1K-K0 rounded to
the nearest integer unless p0KK?K0 K-1 ,
K11 or p0K1 ?K0 1, K1 K-1
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BAC coding tree K16 (0-15), p0 0.8
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Bitstream 11 0011 101 00011 010 Code 15
9 14 7 10 or 11 (with the size of
image in the header)
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BACIC

• BASIC propose an adaptive BAC coding tree
• p0 (p11- 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.

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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
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The template used by BACIC (cont.)

• For every context
• ri (0)1.0 ri (n1) px 0.985 ri (n)
• si (0)2.0 si (n1) 1.0 0.985 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

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The example for adaptive BAC coding tree
p00.80, 0.90, 0.25, 0.90 ., K16 Input
stream 0 0 0 1. Output 2
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• Decoding
• p0 of the first pixel is 0.80 and K16. The
  according index is 2.
• 160.8013, (13-1)gt2, so go down the lower path
  from the root of BAC coding tree.
• p0 of the second pixel is 0.90, 130.9012,
  (12-1)gt2, so go down the lower path .
• p0 of the third pixel is 0.25, 120.253,
  (3-1)gt2, so go down the lower path .
• p0 of the forth pixel is 0.90, 30.902, (2-1)lt2,
  so go down the upper path, and the node is a
  leaf, so this index 2 decoded to be 0001.

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Experimental results
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ordered dither halftone