Vector Quantization（学习Free Mind知识整理）

阅读http://blog.pluskid.org/?p=57文章中的一些知识整理：

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矢量量化（Vector Quantization）其实也就是逼近，VQ 是将一个向量空间中的点用其中的一个有限子集来进行编码的过程。Vector Quantization------------>http://www.data-compression.com/vq.html#lbg

因为在很多各种能用的聚类方法都可以用，下面是Free Mind的python实现：

from scipy.cluster.vq import kmeans, vqfrom numpy import array, reshape, zerosfrom mltk import image vqclst = [2, 10, 100, 256] data = image.read('example.jpg')(height, width, channel) = data.shape data = reshape(data, (height*width, channel))for k in vqclst:    print 'Generating vq-%d...' % k    (centroids, distor) = kmeans(data, k)    (code, distor) = vq(data, centroids)    print 'distor: %.6f' % distor.sum()    im_vq = centroids[code, :]    image.write('result-%d.jpg' % k, reshape(im_vq,        (height, width, channel)))

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Vector Quantization也介绍了LBG算法，LBG-VQ算法是一个迭代算法，它交替地调整P和C（两个优化准则Nearest NeighborCondition 最近邻条件： 和Centroid Condition质心条件： ），使失真度不断地趋向于它的局部最小值（有点EM的思想哦）。最小的C（码书Codebook）和P（空间划分）。

  LBG Design Algorithm

1. Given . Fixed to be a ``small'' number.
2. Let andCalculate
3. Splitting: For , setSet .
4. Iteration: Let . Set the iteration index.
   1. For , find the minimum value ofover all . Let be the index which achieves the minimum. Set
   2. For , update the codevector
   3. Set .
   4. Calculate
   5. If , go back to Step (i).
   6. Set . For, setas the final codevectors.
5. Repeat Steps 3 and 4 until the desired number of codevectors is obtained.

LBG-VQ的matlab实现：

LBG：

function [codebook index] = LBG_training(ImgPxl, Nc, Vector_Len, er, x, y)   Training_idx = (x*y)/Vector_Len ;   Training_set = reshape(ImgPxl(:), Training_idx, Vector_Len) ;   codebook = zeros(Nc, Vector_Len) ;   for i = 1 : Nc     % 此为最原始设计之初使化 Codebook 算法，但因效果太差     % 更换为下面那一种先做一些平均的动作后取得之算法。     %mean(Training_set((i-1)*Training_idx/Nc+1:i*Training_idx/Nc,:))     %     Child_num = Training_idx/Nc ;     codebook(i,:) = mean(         Training_set(            ((i-1)*Child_num+1)+Child_num/4:i*Child_num-Child_num/4,:         )     ) ; % 因为这一行太长，所以断行成这样..  =.=b   end   % 给予一个初始的平均改善临界值 ( > 0 就行了.. )   thd = 10 ;   % 给予一个极大的上一代 MSE   er_o = 1000000000000000 ;   % 设定初始代数   tol = 0 ;   % 最多 training 代数   mtol = 1000 ;   indxe = zeros(Training_idx,1) ;   ver_d = zeros(Training_idx,1) ;   % Training 初始化   for i = 1 : Training_idx     tmp = Training_set(i,:) ;     er_ds = sum(              ((tmp(ones(size(codebook,1),1),:)-codebook).^2).’             )/Vector_Len ;     [ver_d(i) index(i)] = min(er_ds) ;   end   while( er < thd && tol < mtol)     for i = 1 : Nc       codeset = find(index == i) ;       if ~isempty(codeset)         codebook(i,:) = mean([Training_set(codeset,:) ;codebook(i,:)]) ;       else         % 更新法则，非常精简及没有特别的理论版。          if i == 1           codebook(i,:) = mean(codebook([2 3],:)) ;         elseif i == Nc           codebook(i,:) = mean(codebook([Nc-1 Nc-2],:)) ;         else           codebook(i,:) = mean(codebook([i+1 i-1],:)) ;         end       end     end     while (1)       %以新的 Codebook 针对每一笔 block ，进行选择 Code 的动作       for i = 1 : Training_idx         tmp = Training_set(i,:) ;         % 计算这一代的误差         er_ds = sum(             ((tmp(ones(size(codebook,1),1),:)-codebook).^2).’                 )/Vector_Len ;         [ver_d(i) index(i)] = min(er_ds) ;       end       if (~(er_o == mean(ver_d)))          break ;       else         for i = 2 : Nc-1           codebook(i,:) = mean(codebook([i-1 i i+1],:)) ;         end           end     end     thd = abs((er_o – mean(ver_d.^2))/er_o) ;     er_o = mean(ver_d.^2) ;     tol = tol + 1 ;   end   tol   thd 

VQ:

function EzVQ(ImgFile, Nc, Vector_Len, er, x, y)     ImgPxl = double(imread(ImgFile)) ;     [codebook index] = LBG_training(ImgPxl, Nc, Vector_Len, er, x, y) ;     VQImg = ones((x*y)/Vector_Len, Vector_Len) ;     % 利用 codebook 来进行译码     VQImg = codebook(index,:) ;     VQImg = reshape(VQImg(:), x, y) ;     MSE = mse(ImgPxl – VQImg)     figure(gcf()+1) ;     imshow(uint8(ImgPxl)) ;     title(‘Source Image’) ;     figure(gcf()+1) ;     imshow(uint8(VQImg)) ;     title(‘VQ Image’) ; 

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原文：

http://www.data-compression.com/vq.shtml