图像的颜色特征，分块

=====================================================================================================

一种非常简单而有效的颜色特征使由Stricker和Orengo所提出的颜色矩（color moments） [7]。这种方法的数学基础在于图像中任何的颜色分布均可以用它的矩来表示。此外，由于颜色分布信息主要集中在低阶矩中，因此仅采用颜色的一阶矩（mean）、二阶矩（variance）和三阶矩（skewness）就足以表达图像的颜色分布。与颜色直方图相比，该方法的另一个好处在于无需对特征进行向量化。因此，图像的颜色矩一共只需要9个分量（3个颜色分量，每个分量上3个低阶矩），与其他的颜色特征相比是非常简洁的。在实际应用中为避免低次矩较弱的分辨能力，颜色矩常和其它特征结合使用，而且一般在使用其它特征前起到过滤缩小范围（narrow down）的作用。 

三个颜色矩的数学定义：

下面是颜色矩的matlab实现：

function cmVec = colorMom(direc)
% function cmVec = colorMom(direc)
% Input: directory of a JPG image
% Output: a color moment feature vector of the input image. The feature
% vector is extracted from a 5*5 grid and represented by the first 3
% moments for each grid region in Lab color space as a normalized
% 225-dimensional vector.
% Function RGB2Lab (By Mr. Ruzon in Stanford U.) is used in this function.jpgfile = imread(direc);
% jpgfile = imread('shot141_18_NRKF_1.jpg');
if length(size(jpgfile))==2jpgfile1=zeros(size(jpgfile,1),size(jpgfile,2),3);jpgfile1(:,:,1)=jpgfile;jpgfile1(:,:,2)=jpgfile;jpgfile1(:,:,3)=jpgfile;    jpgfile=jpgfile1;direc
end% labfile = RGB2Lab(jpgfile);
[a b c] = size(jpgfile);
% m, n represent sizes of the grid
m = floor(a/5);
n = floor(b/5);
cmVec = zeros(1,225);% 5x5 x9,9个特征
for i=1:5for j = 1:5
%        subimage = labfile((i-1)*m+1:i*m,(j-1)*n+1:j*n,:);subimage = jpgfile((i-1)*m+1:i*m,(j-1)*n+1:j*n,:);
% cal. Mean, ...tmp = (i-1)*5+j-1;
%         I=imshow(subimage,[]);cmVec(tmp*9+1) = mean(mean(subimage(:,:,1)));cmVec(tmp*9+2) = mean(mean(subimage(:,:,2)));cmVec(tmp*9+3) = mean(mean(subimage(:,:,3)));% cal Moment 2 and 3for p = 1:mfor q = 1:n% === Moment2cmVec(tmp*9+4) = cmVec(tmp*9+4) + (subimage(p,q,1)-cmVec(tmp*9+1))^2;cmVec(tmp*9+5) = cmVec(tmp*9+5) + (subimage(p,q,2)-cmVec(tmp*9+2))^2;cmVec(tmp*9+6) = cmVec(tmp*9+6) + (subimage(p,q,3)-cmVec(tmp*9+3))^2;% === Moment3cmVec(tmp*9+7) = cmVec(tmp*9+7) + (subimage(p,q,1)-cmVec(tmp*9+1))^3;cmVec(tmp*9+8) = cmVec(tmp*9+8) + (subimage(p,q,2)-cmVec(tmp*9+2))^3;cmVec(tmp*9+9) = cmVec(tmp*9+9) + (subimage(p,q,3)-cmVec(tmp*9+3))^3;                endendcmVec((tmp*9+4):(tmp*9+9)) = cmVec((tmp*9+4):(tmp*9+9))/(m*n);cmVec(tmp*9+4) = cmVec(tmp*9+4)^(1/2);cmVec(tmp*9+5) = cmVec(tmp*9+5)^(1/2);cmVec(tmp*9+6) = cmVec(tmp*9+6)^(1/2);if cmVec(tmp*9+7) >0cmVec(tmp*9+7) = cmVec(tmp*9+7)^(1/3);elsecmVec(tmp*9+7) = -((-cmVec(tmp*9+7))^(1/3));endif cmVec(tmp*9+8) >0cmVec(tmp*9+8) = cmVec(tmp*9+8)^(1/3);elsecmVec(tmp*9+8) = -((-cmVec(tmp*9+8))^(1/3));endif cmVec(tmp*9+9) >0cmVec(tmp*9+9) = cmVec(tmp*9+9)^(1/3);elsecmVec(tmp*9+9) = -((-cmVec(tmp*9+9))^(1/3));end end
end
% Normalize...
if sqrt(sum(cmVec.^2))~=0cmVec = cmVec / sqrt(sum(cmVec.^2));
end

=====================================================================================================

=====================================================================================================

[FileName,PathName] = uigetfile('*.*','Select the image'); 
Im=imread([PathName FileName]);
imshow(Im)
hold on
L = size(Im);
height=64;
width=64;
max_row = floor(L(1)/height);
max_col = floor(L(2)/width);
seg = cell(max_row,max_col);
%分块
for row = 1:max_row      for col = 1:max_col        seg(row,col)= {Im((row-1)*height+1:row*height,(col-1)*width+1:col*width,:)};  end
end 
for i=1:max_row*max_col
imwrite(seg{i},strcat('m',int2str(i),'.bmp'));  
end
%画出分块的边界
for row = 1:max_row      for col = 1:max_col  rectangle('Position',[160*(col-1),160*(row-1),160,160],...'LineWidth',2,'LineStyle','-','EdgeColor','r');end
end 
hold off

后面贴一个小方法：

A=rand(256,64);
%将A分块
B=mat2cell(A,ones(256/16,1)*16,ones(64/16,1)*16);
%B{i,j}就是所要的分块矩阵
%将分块矩阵合并
C=cell2mat(B)
%C就是合并好的矩阵，即C=A

=====================================================================================================

=====================================================================================================

颜色相关图（color correlogram）是图像颜色分布的另一种表达方式[16]。这种特征不但刻画了某一种颜色的像素数量占整个图像的比例，还反映了不同颜色对之间的空间相关性。实验表明，颜色相关图比颜色直方图和颜色聚合向量具有更高的检索效率，特别是查询空间关系一致的图像。
       一种简化的变种是颜色自动相关图（color auto-correlogram），它仅仅考察具有相同颜色的像素间的空间关系，因此空间复杂度降到O(Nd)。假设图像的记号为I(x,y)，x、y为空间坐标；包含的颜色有C1,C2,C3...Cn.设置两种颜色之间的距离为d.那我们将生成这样的一个直方图：它的bin的个数为n的平方（颜色的组合数目），对于其中的每Bin,Bin的大小为Bin(Ci,Cj) = Σx,y{||I(x,y,Ci)-I(x,y,Cj)|| =d｝。其中，||*||表示像素值为Ci,Cj的两个像素的空间距离，然后统计这样的像素个数。所以，要是设置不同的距d1,d2,d3...dm(共D个).那个Bin的维数为(n*n*D)。进一步，我们只考虑相同颜色之间空间关系，就称为颜色自相关图（colorauto-correlogram）那个Bin的维数为（n*D）。颜色相关图可以看作是一张用颜色对<x, y>索引的表，其中<x, y>的第k个分量表示颜色为c(x)的像素和颜色为c(y)的像素之间的距离小于k的概率。如果考虑到任何颜色之间的相关性，颜色相关图会变得非常复杂和庞大 (空间复杂度为O(N2d))。

       颜色相关图概念来自http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=609412，

                                       http://www.cs.cornell.edu/rdz/Papers/ecdl2/spatial.htm#Huang97

       原文解释：A color correlogram (henceforth correlogram) expresses how thespatial correlation of pairs of colors changes with distance. Informally, a correlogramfor an image is a table indexed by color pairs, where the d-th entry for row (i,j)specifies the probability of finding a pixel of color j at a distancedfrom a pixel of color i in this image. Here d is chosen from a set ofdistance values D (see [Huang] for the formal definition).An autocorrelogram captures spatial correlation between identical colors only.This information is a subset of the correlogram and consists of rows of the form (i,j)only.

颜色自相关图的MATLAB实现：

方法一：

function  output = ColorCorrelogram(rgb,d)  
R = rgb(:,:,1);  
G = rgb(:,:,2);  
B = rgb(:,:,3);  
R_BITS = 2;%bit量化  
G_BITS = 2;  
B_BITS = 2;  
size_color = 2^R_BITS*2^G_BITS*2^B_BITS;%归一化后的颜色种数  
R1=bitshift(R,-(8-R_BITS));  
G1=bitshift(G,-(8-G_BITS));  
B1=bitshift(B,-(8-B_BITS));  
%包含的颜色种数为：4x4x4  
I=R1+G1*2^R_BITS+B1*2^R_BITS*2^B_BITS;%新生图像  
temp = zeros(size_color,1);  
os = offset(d);  
s = size(os);  
for i = 1:s(1)  offset = os(i,:);  glm = GLCMATRIX(I,offset,size_color);  temp = temp+glm;  
end  
hc = zeros(size_color,1);  
for j = 0:size_color-1  hc(j+1) = numel(I(I == j));%Index为j的计数  
end  
output = temp./(hc+eps);  
output = output/(8*d);  
end  
function os = offset(d)  
[r,c] = meshgrid(-d:d,-d:d);  
r = r(:);  
c = c(:);  
os = [r c];  
bad = max(abs(r),abs(c)) ~= d;  
os(bad,:) = [];  
end  
function out = GLCMATRIX(si,offset,nl)  
s = size(si);%图像大小  
[r,c] = meshgrid(1:s(1),1:s(2));%网格化，很明显  
r = r(:);%向量化  
c = c(:);%向量化  
r2 = r+offset(1);%加偏置  
c2 = c+offset(2);%加偏置  
bad = c2<1|c2>s(2)|r2<1|r2>s(1);%筛选出index不在图像内的点  
Index = [r c r2 c2];%原始距离与相对距离的矩阵  
Index(bad,:) = [];%剔除坏点  v1 = si(sub2ind(s,Index(:,1),Index(:,2)));%从索引到数据  
v2 = si(sub2ind(s,Index(:,3),Index(:,4)));  
v1 = v1(:);  
v2 = v2(:);  
Ind  = [v1 v2 ];  
bad = v1~=v2;%这里计算的是颜色自相关图  
Ind(bad,:) = [];  
if isempty(Ind)  oneGLCM2 = zeros(nl);  
else  oneGLCM2 = accumarray(Ind+1,1,[nl,nl]);  
end  
out = [];  
for i = 1:nl  out = [out oneGLCM2(i,i)];  
end  
out = out(:);  
end  

function correlogram_vector=color_auto_correlogram(I,distance_vector)  % This function creates the auto-correlogram vector for an input image of  
% any size. The different distances which is assumed apriori can be user-defined in a vector.  % It implements the algorithm as defined in Huang et al. paper 'Image Indexing using color  
% autocorelogram'  % Input:  
% I=The uint8 matrix representing the color image  
% distance_vector= The vector representating the different distances in  
% which the color distribution is calculated.  % Output:  
% correlogram_vector=This is a straight vector representating the  
% probabilities of occurence of 64 quantized colors. Its total dimension is  
% 64n X 1; where n is the number of different inf-norm distances  % Usage: (To create the auto-correlogram vector for user-defined distances)  
% I=imread('peppers.png'); distance_vector=[1 3];  
% correlogram_vector=color_auto_correlogram(I,distance_vector);  % Contact Author:  
% Soumyabrata Dev  
% E-mail: soumyabr001@e.ntu.edu.sg  
% http://www3.ntu.edu.sg/home2012/soumyabr001/  correlogram_vector=[];  
[Y,X]=size(rgb2gray(I));  % quantize image into 64 colors = 4x4x4, in RGB space  
[img_no_dither, ~] = rgb2ind(I, 64, 'nodither');  
% figure, imshow(img_no_dither, map);  
%rgb = ind2rgb(img_no_dither, map); % rgb = double(rgb)  [~,d]=size(distance_vector);  
count_matrix=zeros(64,d);   total_matrix=zeros(64,d);  
prob_dist=cell(1,d);  for serial_no=1:1:d  for x=1:X  for y=1:Y  color=img_no_dither(y,x);  % At the given distance   [positive_count,total_count]=get_n(distance_vector(serial_no),x,y,color,img_no_dither,X,Y);  count_matrix(color+1,serial_no)=count_matrix(color+1,serial_no)+positive_count;  total_matrix(color+1,serial_no)=total_matrix(color+1,serial_no)+total_count;         end  end  prob_dist{serial_no}=count_matrix(:,serial_no)./(1+total_matrix(:,serial_no));  end  for serial_no=1:d  correlogram_vector=cat(1,correlogram_vector,prob_dist{serial_no});  
end  end  

function [positive_count,total_count]=get_n(n,x,y,color,img_no_dither,X,Y)  
% This function is useful to get the validity map of the neighborhood case.  
% It can handle any number of neighborhood distances.  % Input  
% n=The order of the neighborhood  
% x & y= x y co-ordinates of the given pixel  
% color= particular quantized color  
% img_no_dither= The color quantized image matrix  
% X & Y= The original dimensions of the input image  % Output  
% positive_count= The number of occurences which have the same color  
% total_count= The total number of valid cases for this particular instant  valid_vector8n=zeros(1,8*n); % This is because of the propoerty of inf-norm. Each distance has 8 times the order  positive_count=0;   total_count=0;  nbrs_x=zeros(1,8*n);    nbrs_y=zeros(1,8*n);  % The counting of the pixels is done in the following manner: From the  % given pixel, go left-->up-->right-->down-->left-->up  % Y co-ordinates of nbrs  nbrs_y(1)=y;  d=1;  for k=2:1+n  nbrs_y(k)=y-d;  d=d+1;  end  nbrs_y(1+n:1:3*n+1)=y-n;  d=0;  for k=3*n+1:5*n+1  nbrs_y(k)=y-n+d;  d=d+1;  end  nbrs_y(5*n+1:1:7*n+1)=y+n;  d=0;  for k=7*n+1:1:7*n+1+(n-1)  nbrs_y(k)=y+n-d;  d=d+1;  end  % X co-ordinates of nbrs  nbrs_x(1)=x-n;  nbrs_x(2:1:1+n)=x-n;  d=0;  for k=1+n:1:3*n+1  nbrs_x(k)=x-n+d;  d=d+1;  end  nbrs_x(3*n+1:5*n+1)=x+n;  d=0;  for k=5*n+1:7*n+1  nbrs_x(k)=x+n-d;  d=d+1;  end  nbrs_x(7*n+1:7*n+1+(n-1))=x-n;  % Assigning the validity of the neighborhood  for i=1:8*n  if nbrs_x(i)>0 && nbrs_x(i)<=X && nbrs_y(i)>0 && nbrs_y(i)<=Y  valid_vector8n(i)=1;  else  valid_vector8n(i)=0;  end  end  % Couting the number of common colors in the valid areas of the  % neighborhood.  for j=1:8*n  if valid_vector8n(j)==1  data= img_no_dither(nbrs_y(j),nbrs_x(j));  if (data==color)  positive_count=positive_count+1;  end  total_count=total_count+1;  end  end  end