A Hybrid Vector Quantization Combining a Tree Structure and a Voronoi Diagram

Pseudocode 1

Input: a set of projected codewords 𝐶^′

Output: a tree-structure based codebook

Tree construction procedure:

(1)   root = new node // obtain the root of the tree structure

(2)  ConstructTree(root, 𝐶^′) // apply the recursive function to construct the tree

(3)  return root

Function ConstructTree(node, W)

(4)  According to the set of input codewords, W, apply the LBG algorithm to

    estimate two centroids, 𝑛𝑜𝑑𝑒.𝑐𝑒𝑛𝑡𝑟𝑜𝑖𝑑_𝐿 and 𝑛𝑜𝑑𝑒.𝑐𝑒𝑛𝑡𝑟𝑜𝑖𝑑_𝑅

(5)  Let 𝑠_𝐿=𝜙 and 𝑠_𝑅=𝜙

(6)  Each 𝑤∈𝑊 is assigned to 𝑠_𝐿 or 𝑠_𝑅 depending on whether w is closer to

    𝑛𝑜𝑑𝑒.𝑐𝑒𝑛𝑡𝑟𝑜𝑖𝑑_𝐿 or 𝑛𝑜𝑑𝑒.𝑐𝑒𝑛𝑡𝑟𝑜𝑖𝑑_𝑅

(7)  If the number of 𝑠_𝐿 is greater than a predefined threshold 𝛿 then {

(8)   𝑛𝑜𝑑𝑒.𝑠𝑜𝑛_𝐿 = new node

(9)   ConstructTree(𝑛𝑜𝑑𝑒.𝑠𝑜𝑛_𝐿, 𝑠_𝐿)

(10)  }

(11)  Else {

(12)     𝑛𝑜𝑑𝑒.𝑠𝑜𝑛_𝐿=𝜙

(13)     Find a codeword 𝑐∈𝐶^′ such that 𝑐−𝑛𝑜𝑑𝑒.𝑐𝑒𝑛𝑡𝑟𝑜𝑖𝑑_𝐿 is minimum

(14)     𝑛𝑜𝑑𝑒.𝐼𝑛𝑖𝑡𝑖𝑎𝑙𝐶𝑜𝑑𝑒𝑤𝑜𝑟𝑑_𝐿=𝑐

(15)  }

(16)  If the number of 𝑠_𝑅 is greater than a predefined threshold 𝛿, then {

(17)     𝑛𝑜𝑑𝑒.𝑠𝑜𝑛_𝑅 = new node

(18)     ConstructTree(𝑛𝑜𝑑𝑒.𝑠𝑜𝑛_𝑅, 𝑠_𝑅)

(19)  }

(20)  Else {

(21)     𝑛𝑜𝑑𝑒.𝑠𝑜𝑛_𝑅=𝜙

(22)     Find a codeword 𝑐∈𝐶^′ such that 𝑐−𝑛𝑜𝑑𝑒.𝑐𝑒𝑛𝑡𝑟𝑜𝑖𝑑_𝑅 is minimum

(23)     𝑛𝑜𝑑𝑒.𝐼𝑛𝑖𝑡𝑖𝑎𝑙𝐶𝑜𝑑𝑒𝑤𝑜𝑟𝑑_𝑅=𝑐

(24)  }