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# vector - VectorQuantization CAP5015 Fall2005 VoronoiRegion...

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Vector Quantization CAP5015 Fall 2005

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Voronoi Region Blocks:  A sequence of audio. A block of image pixels. Formally:  vector   example: (0.2, 0.3, 0.5, 0.1) A vector quantizer maps  k-dimensional  vectors in the vector  space  R k  into a finite set of vectors  Y =  { y i i  = 1, 2, . ..,  N }.  Each  vector  y i  is  called a code vector  or a  codeword . and the set of all  the codewords is called a  codebook .  Associated with each  codeword,  y i , is a nearest neighbor region called  Voronoi  region,  and it is defined by:  The set of Voronoi regions partition the entire space  R k  .
Codewords in 2-dimensional space.  Input vectors are marked with an  x, codewords are marked with red circles, and the Voronoi regions are  separated with boundary lines.  Two Dimensional Voronoi Diagram

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The Schematic of a Vector  Quantizer
Compression Formula Amount of compression: Codebook size is  K , input vector of dimension  L In order to inform the decoder of which code vector is  selected, we need to use             bits.  E.g. need 8 bits to represent 256 code vectors. Rate: each code vector contains the reconstruction value of  source output samples, the number of  bits per sample   would be:              . Sample: a scalar value in vector. K

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vector - VectorQuantization CAP5015 Fall2005 VoronoiRegion...

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