Color Names 特征提取并進行PCA降維 （Learning Color Names for Real-World Applications）

之前的一篇部落格裡介紹了CN特征的提取，在實際應用中，很多算法為了提高計算效率，都會将CN特征進行降維，比如

Danelljan M, Shahbaz Khan F, Felsberg M, et al. Adaptive color attributes for real-time visual

tracking[C]//Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. 2014: 1090-1097

即ColorTracking跟蹤算法就采用了PCA降維，将CN特征降為了2維。

這裡就在上一篇的基礎上加上PCA降維的部分：

首先是改動一下im2c.m函數

im2c.m

function out=im2c(im,w2c,color)
% input im should be DOUBLE !
% color=0 is color names out
% color=-1 is colored image with color names out
% color=1-11 is prob of colorname=color out;

% order of color names: black , blue , brown     , grey     , green , orange  ,  pink   , purple  ,  red     , white    , yellow
color_values =     {  [0 0 0] , [0 0 1] , [.5 .4 .25] , [.5 .5 .5] , [0 1 0] , [1 .8 0] , [1 .5 1] , [1 0 1] , [1 0 0] , [1 1 1 ] , [ 1 1 0 ] };

if(nargin<3)
   color=0;
end

RR=im(:,:,1);GG=im(:,:,2);BB=im(:,:,3);

index_im = 1+floor(RR(:)/8)+32*floor(GG(:)/8)+32*32*floor(BB(:)/8);

if(color==0)
   [max1,w2cM]=max(w2c,[],2);  %max第1次元為列，第2次元為行 max1為相應最大值，w2cM為索引
   out=reshape(w2cM(index_im(:)),size(im,1),size(im,2));
end

if(color>0 && color < 12)
   w2cM=w2c(:,color);
   out=reshape(w2cM(index_im(:)),size(im,1),size(im,2));
end

if(color==-1)
   out=im;
   [max1,w2cM]=max(w2c,[],2);  
   out2=reshape(w2cM(index_im(:)),size(im,1),size(im,2));
         
   for jj=1:size(im,1)
        for ii=1:size(im,2) 
          out(jj,ii,:)=color_values{out2(jj,ii)}'*255;
        end
   end
end

% 添加的部分代碼
% color=-2 return probabilities
if(color==-2)
   out=reshape(w2c(index_im,:),size(im,1),size(im,2),size(w2c,2));
end
           

然後是example_color_naming.m函數添加部分代碼

example_color_naming.m

% load the word to color names matrix. The words are a 32x32x32 grid on the sRGB space. 

load('w2c.mat');
dim_final = 3; %降維後的維數

im=double(imread('car.jpg'));       % load test image
sz = size(im);
dim_1 = sz(1)*sz(2);

% compute the color name assignment for all pixels in image im:
cn_feature=im2c(im,w2c,-2);          
cn_reshaped = reshape(cn_feature, [dim_1, size(cn_feature, 3)]);

%下面是使用PCA提取主成分的步驟        
% compute the mean appearance
data_mean = mean(cn_reshaped, 1);

% substract the mean from the appearance to get the data matrix
data_matrix = bsxfun(@minus, cn_reshaped, data_mean);

% calculate the covariance matrix 協方差矩陣
cov_matrix = 1/(dim_1 - 1) * (data_matrix' * data_matrix);
[pca_basis, pca_variances, ~] = svd(cov_matrix); %奇異值分解

% calculate the projection matrix as the first principal
% components and extract their corresponding variances 投影矩陣projection_matrix是第一主成成分
projection_matrix = pca_basis(:, 1:dim_final); %這裡得到了新的投影矩陣
projection_variances = pca_variances(1:dim_final, 1:dim_final);

% projection matrix and variances
old_cov_matrix = projection_matrix * projection_variances * projection_matrix';

[num_pca_in, num_pca_out] = size(projection_matrix);

cn_pca = reshape(cn_reshaped * projection_matrix, [sz(1), sz(2), num_pca_out]);

imshow(cn_pca);
           

這裡是将圖像的CN特征降維成3維，并且顯示出來，結果如圖：