Agenda for mm2

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Agenda for mm2

• Context
• Basis vectors
• Basis images
• Different transforms
• KLT/PCA Theory
• PCA Applications
• What to remember

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Block diagram of (visual) coding

• Purpose communication or storage system
• Coder (en)coder decoder codec
• Source encoder removes redundancy
• Channel encoder adds redundancy
• A/D, D/A, en/decryption optional
• Only deal with the source coder

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Source coder block diagram
Coded bit-string

• Transformation new representation of data
• Differential coding, transform coding (MM2)
• Quantization In-reversible process gt lossy
  coding
• Codeword assignment (entropy coding) Info.
  Theory
• Huffman-, run length-, arithmetic-, dictionary
  coding

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General transforms
2D
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Discrete Fourier transform (DFT)
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Discrete Hadamard transforms (DHT)
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Discrete Cosine transform (DCT)

• Compression factor vs. reconstructed image
  quality
• 1) KLT, 2) DCT, 3) DFT,DHT

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Karhunen-Loeve transform (KLT)

• AKA Hotelling transform, Principal component
  analysis (PCA) (which basis vectors/images to
  use)
• Forget images and compression
• Basis vectors adopt to the data
• Powerful tool when reducing the dimensionality
• Striking properties Linear, easy to understand,
• de-correlates the data gt less redundancy
• Key idea Represent the data in a more compact
  manner

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Applications of KLT/PCA

• Dimensionality reduction
• Fit data to known equation
• Align data
• Compression
• Single image
• Multiple images (Static)
• Multiple images (Dynamic)

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Compression (static)
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Compression (static)
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Compression (static)
Original
Eigen-images
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What to remember (1)

• Transforms can be interpreted as a set of basis
  vectors (1D) or basis images (2D) and the related
  coefficients (weighting of basis vectors or basis
  images)
• DCT, DFT, DHT have fixed basis images
• KLT calculates basis images from data gt optimal
• Performance
• 1) KLT
• 2) DCT
• 3) DTF, DHT, others

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What to remember (2)

• Applications of KLT
• Dimensionality reduction
• Fit data to known equation
• Align data
• Compression
• Single image
• Multiple images
• Static
• Dynamic
• The end

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Truncation of coefficients

• Zonal
• Defined from statistics
• Risk of ignoring high values
• Threshold
• Coefficients gt TH are kept
• Normalisation and round off