A Fast LBG Codebook Training Algorithm for Vector Quantization

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A Fast LBG Codebook Training Algorithm for Vector
Quantization

• Presented by ???

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Motivation

• A fast codebook-training algorithm based on LBG
  algorithm.
• To reduce the computational cost in the codebook
  training processes.

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Outline

• Introduction
• Previous Works
• Proposed Method
• Some Experiments
• Discussions and Conclusions

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Image Compression techniques

• Block truncation coding
• Transform coding
• Hybrid coding
• Vector quantization
• Simple structure and low bit rate

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VQ scheme

• The VQ scheme can be divided into three parts
• Codebook generation
• Encoding procedure
• Decoding procedure

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Codebook Generation

• The most important task for VQ scheme is to
  design a good codebook.
• LBG (Linde-Buzo-Gray) algorithm / Lloyd
  clustering algorithm
• The LBG algorithm is an iterative procedure.

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Euclidean Distance

• The dimensionality of vector k ( wh)
• An input vector x (x1, x2, , xk)
• A codeword yi (yi1, yi2, , yik)
• The Euclidean distance between x and yi

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Codebook Generation
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VQ Codebook Training

• Codebook generation

0 1 . . .
N-1 N
Training Images
Training set
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VQ Codebook Training

• Codebook generation

0 1 . . .
0 1 . . .
254 255
N-1 N
Initial codebook
Training set
Codebook initiation
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VQ Encoding Procedure
Image compression technique
w
h
Image
Index table
Vector Quantization Encoder
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VQ Decoding Procedure
Image compression technique
w
h
Image
Index table
Vector Quantization Decoder
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Codebook search

• To reduce the computational cost for the
  segmentation procedure in the LBG algorithm, many
  fast algorithms for codebook search have been
  developed.
• Partial Distortion Search (PDS)
• Mean-distance-ordered Partial Codebook Search
  (MPS)
• Integral Projection Mean-sorted Partial Search
  (IPMPS)

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Another fast codebook design

• The tree-structured VQ (TSVQ)
• The k-d tree VQ

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Outline

• Introduction
• Previous Works
• Proposed Method
• Some Experiments
• Discussions and Conclusions

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Goal

• To reduce the computation cost in finding the
  closest codeword in the codebook.
• PDS
• MPS
• IPMPS

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Partial distortion search (PDS)

• Closest codeword search
• If the minimal distance of each input vector
  could not be found early, the PDS method can just
  reduce little computation time.

(a0, a1, a2, , a15) input vector
(b0, b1, b3, , b15) codeword
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Mean-distance-ordered Partial Codebook Search
Algorithm (MPS)

• The Squared Euclidean Distance (SED)
• The Squared Mean Distance (SMD)
• The minimal SED codeword is usually in the
  neighborhood of the minimal SMD codeword.

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Mean-distance-ordered Partial Codebook Search
Algorithm (MPS)
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Integral Projection Mean-sorted Partial Search
Algorithm (IPMPS)

• Based on multiple distortion measures with
  different levels of computational complexity.
• Three kinds of integral projections

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Integral Projection Mean-sorted Partial Search
Algorithm (IPMPS)

• Three distortion measures

Test conditions
For each codeword Yi
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Outline

• Introduction
• Previous Works
• Proposed Method
• Some Experiments
• Discussions and Conclusions

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Generalized Integral Projection Model (GIP)

• To reduce the computational cost
• MPS and IPMPS
• IPMPS employs the concept of integral projection
  to reject further codeword in search.

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Generalized Integral Projection Model (GIP)

• Initially, choose one possible projection map of
  the pair (p, q).
• p segments with q pixels in each segment
• For each input vector, compute the projection
  PX(k) of these p segments.
• The distortion measure corresponding to this
  projection map is defined as

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Generalized Integral Projection Model (GIP)

• For each codeword, the following inequality can
  be easily proven true
• The test condition for this projection map can be
  constructed.

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Segment maps
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Fast LBG Algorithm

• Initially, select a set of test conditions by
  repeatedly applying the GIP model with different
  projection maps of the desired pair (p, q).
• Sort the current codebook by the mean values of
  the codewords.
• For each vector, find the corresponding closest
  codeword.

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Fast LBG Algorithm

• Record the index of the closest codeword for each
  training vector.
• Update each codeword
• Overall averaged distortion

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Outline

• Introduction
• Previous Works
• Proposed Method
• Some Experiments
• Discussions and Conclusions

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Experiment Methods 512512 image
LBG PDS MPS
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Experiment Results
the property of the training set
FLBG-1a FLBG-1b
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Outline

• Introduction
• Previous Works
• Proposed Method
• Some Experiments
• Discussions and Conclusions

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Conclusions

• A generalized integral projection model is
  developed to produce the test conditions for the
  speedup of the search process for the VQ codebook
  design.
• To use these test conditions to eliminate the
  need of calculating the squared Euclidean
  distance.
• The property of image
• By choosing proper sets of test conditions for
  different training sets, a great deal of
  computation cost can be reduced.