本文介绍了灰度共生矩阵(GLCM)的计算方法及其在不同灰度级别下的应用，并展示了如何使用MATLAB实现灰度共生矩阵的构造及从该矩阵中提取纹理特征的过程。
转
灰度共生矩阵（GLCM）并计算能量、熵、惯性矩、相关性（matlab）（待总结）
关于灰度共生矩阵的介绍可参考
http://blog.youkuaiyun.com/chuminnan2010/article/details/22035751
http://blog.youkuaiyun.com/xuezhisd/article/details/8908824
http://blog.youkuaiyun.com/xuexiang0704/article/details/8713204
http://cn.mathworks.com/help/images/ref/imlincomb.html?refresh=true
理论介绍
http://blog.youkuaiyun.com/lskyne/article/details/8659225
http://blog.youkuaiyun.com/light_lj/article/details/26098815
http://blog.youkuaiyun.com/kezunhai/article/details/42001477
共生矩阵的物理意义
http://blog.youkuaiyun.com/light_lj/article/details/26098815
下面给出不同的NumLevels的例子
-
gray = [
1
1
5
6
8
-
2
3
5
7
1
-
4
5
7
1
2
-
8
5
1
2
5];
-
GLCM = graycomatrix(gray,
'GrayLimits',[])
-
-
GLCM =
-
-
1
2
0
0
1
0
0
0
-
0
0
1
0
1
0
0
0
-
0
0
0
0
1
0
0
0
-
0
0
0
0
1
0
0
0
-
1
0
0
0
0
1
2
0
-
0
0
0
0
0
0
0
1
-
2
0
0
0
0
0
0
0
-
0
0
0
0
1
0
0
0
-
-
-
GLCM = graycomatrix(gray,
'GrayLimits',[],
'offset', [
0
1])
-
-
GLCM =
-
-
1
2
0
0
1
0
0
0
-
0
0
1
0
1
0
0
0
-
0
0
0
0
1
0
0
0
-
0
0
0
0
1
0
0
0
-
1
0
0
0
0
1
2
0
-
0
0
0
0
0
0
0
1
-
2
0
0
0
0
0
0
0
-
0
0
0
0
1
0
0
0
-
-
GLCM = graycomatrix(gray,
'GrayLimits',[],
'offset', [
0
1],
'NumLevels',
8)
-
-
GLCM =
-
-
1
2
0
0
1
0
0
0
-
0
0
1
0
1
0
0
0
-
0
0
0
0
1
0
0
0
-
0
0
0
0
1
0
0
0
-
1
0
0
0
0
1
2
0
-
0
0
0
0
0
0
0
1
-
2
0
0
0
0
0
0
0
-
0
0
0
0
1
0
0
0
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上图显示了如何求解灰度共生矩阵，以（1，1）点为例，GLCM（1，1）值为1说明只有一对灰度为1的像素水平相邻。GLCM（1，2）值为2，是因为有两对灰度为1和2的像素水平相邻。（1,5）出现一次，所以在（1.5）位置上标记1，没出现（1,6)所以为0；
上面所有的参数都是默认设置，NumLevels=8， 下面考虑NumLevels=3 的情况
-
gray = [
1
1
5
6
8
-
2
3
5
7
1
-
4
5
7
1
2
-
8
5
1
2
5];
-
-
GL(
2) = max(max(gray));
-
GL(
1) = min(min(gray));
-
if
GL(
2) ==
GL(
1)
-
SI = ones(size(gray));
-
else
-
slope =
NumLevels/(
GL(
2) -
GL(
1));
-
intercept =
1 - (slope*(
GL(
1)));
-
SI = floor(imlincomb(slope,gray,intercept,
'double'));
-
end
-
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SI =
-
-
1
1
2
3
4
-
1
1
2
3
1
-
2
2
3
1
1
-
4
2
1
1
2
-
%%%
%%%
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%%%%
-
-
-
SI(
SI >
NumLevels) =
NumLevels;
-
SI(
SI <
1) =
1;
-
-
SI =
-
-
1
1
2
3
3
-
1
1
2
3
1
-
2
2
3
1
1
-
3
2
1
1
2
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上面给出了如何将初始矩阵gray变成3阶的灰度级，SI就是gray的3阶灰度级矩阵。
上图显示了如何求解3级灰度共生矩阵，以（1，1）点为例，GLCM（1，1）值为4说明只有4对灰度为1的像素水平相邻。GLCM（3，1）值为2，是因为有两对灰度为3和1的像素水平相邻。（2,1）出现一次，所以在（2.1）位置上标记1，没出现（1,3)所以为0；
-
gray = [
1
1
5
6
8
-
2
3
5
7
1
-
4
5
7
1
2
-
8
5
1
2
5];
-
[
GLCM,SI] = graycomatrix(gray,
'NumLevels',
3,
'G',[])
-
-
GLCM =
-
-
4
3
0
-
1
1
3
-
2
1
1
-
-
-
SI =
-
-
1
1
2
3
3
-
1
1
2
3
1
-
2
2
3
1
1
-
3
2
1
1
2
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用3阶灰度级去计算四个共生矩阵P,取距离为1，角度分别为0,45,90,135
-
gray =
[1 1 5 6 8
-
2
3
5
7
1
-
4
5
7
1
2
-
8
5
1
2
5];
-
offsets =
[0 1;-1 1;-1 0;-1 -1];
-
m =
3;
% 3阶灰度级
-
[GLCMS,SI] = graycomatrix(gray,
'GrayLimits',
[],
'Of',offsets,
'NumLevels',m);
-
P = GLCMS;
-
[kk,ll,mm] =
size(P);
-
% 对共生矩阵归一化
-
%---------------------------------------------------------
-
for n =
1
:mm
-
P(
:,
:,n) = P(
:,
:,n)/sum(sum(P(
:,
:,n)));
-
end
-
-
%-----------------------------------------------------------
-
%对共生矩阵计算能量、熵、惯性矩、相关4个纹理参数
-
%-----------------------------------------------------------
-
H =
zeros(
1,mm);
-
I = H;
-
Ux = H; Uy = H;
-
deltaX= H; deltaY = H;
-
C =H;
-
for n =
1
:mm
-
E(n) = sum(sum(P(
:,
:,n).^
2));
%能量
-
for
i =
1
:kk
-
for
j =
1
:ll
-
if P(
i,
j,n)~=
0
-
H(n) = -P(
i,
j,n)*
log(P(
i,
j,n))+H(n);
%熵
-
end
-
I(n) = (
i-
j)^
2*P(
i,
j,n)+I(n);
%惯性矩
-
-
Ux(n) =
i*P(
i,
j,n)+Ux(n);
%相关性中μx
-
Uy(n) =
j*P(
i,
j,n)+Uy(n);
%相关性中μy
-
end
-
end
-
end
-
for n =
1
:mm
-
for
i =
1
:kk
-
for
j =
1
:ll
-
deltaX(n) = (
i-Ux(n))^
2*P(
i,
j,n)+deltaX(n);
%相关性中σx
-
deltaY(n) = (
j-Uy(n))^
2*P(
i,
j,n)+deltaY(n);
%相关性中σy
-
C(n) =
i*
j*P(
i,
j,n)+C(n);
-
end
-
end
-
C(n) = (C(n)-Ux(n)*Uy(n))/deltaX(n)/deltaY(n);
%相关性
-
end
-
-
%--------------------------------------------------------------------------
-
%求能量、熵、惯性矩、相关的均值和标准差作为最终8维纹理特征
-
%--------------------------------------------------------------------------
-
a1 = mean(E)
-
b1 =
sqrt(cov(E))
-
-
a2 = mean(H)
-
b2 =
sqrt(cov(H))
-
-
a3 = mean(I)
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b3 =
sqrt(cov(I))
-
-
a4 = mean(C)
-
b4 =
sqrt(cov(C))
-
-
sprintf(
'0,45,90,135方向上的能量依次为： %f, %f, %f, %f',E(
1),E(
2),E(
3),E(
4))
% 输出数据;
-
sprintf(
'0,45,90,135方向上的熵依次为： %f, %f, %f, %f',H(
1),H(
2),H(
3),H(
4))
% 输出数据;
-
sprintf(
'0,45,90,135方向上的惯性矩依次为： %f, %f, %f, %f',I(
1),I(
2),I(
3),I(
4))
% 输出数据;
-
sprintf(
'0,45,90,135方向上的相关性依次为： %f, %f, %f, %f',C(
1),C(
2),C(
3),C(
4))
% 输出数据;
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下面给出的是默认的设置下求四个方向的灰度共生矩阵，NumLevels=8.
-
gray = [
1
1
5
6
8
-
2
3
5
7
1
-
4
5
7
1
2
-
8
5
1
2
5];
-
offsets = [
0
1;
-1
1;
-1
0;
-1
-1];
-
[
GLCMS,SI] = graycomatrix(gray,
'GrayLimits',[],
'Of',offsets)
-
-
GLCMS(:,:,
1) =
-
-
1
2
0
0
1
0
0
0
-
0
0
1
0
1
0
0
0
-
0
0
0
0
1
0
0
0
-
0
0
0
0
1
0
0
0
-
1
0
0
0
0
1
2
0
-
0
0
0
0
0
0
0
1
-
2
0
0
0
0
0
0
0
-
0
0
0
0
1
0
0
0
-
-
-
GLCMS(:,:,
2) =
-
-
2
0
0
0
0
0
0
0
-
1
1
0
0
0
0
0
0
-
0
0
0
0
1
0
0
0
-
0
0
1
0
0
0
0
0
-
0
0
0
0
1
1
1
0
-
0
0
0
0
0
0
0
0
-
0
0
0
0
0
0
1
1
-
0
0
0
0
1
0
0
0
-
-
-
GLCMS(:,:,
3) =
-
-
0
0
0
0
0
0
2
1
-
3
0
0
0
0
0
0
0
-
1
0
0
0
0
0
0
0
-
0
1
0
0
0
0
0
0
-
0
1
1
0
2
0
0
0
-
0
0
0
0
0
0
0
0
-
0
0
0
0
1
1
0
0
-
0
0
0
1
0
0
0
0
-
-
-
GLCMS(:,:,
4) =
-
-
0
0
0
0
2
1
0
0
-
0
0
0
0
0
0
2
0
-
1
0
0
0
0
0
0
0
-
0
0
0
0
0
0
0
0
-
2
1
0
1
0
0
0
0
-
0
0
0
0
0
0
0
0
-
0
0
1
0
1
0
0
0
-
0
0
0
0
0
0
0
0
-
-
-
SI =
-
-
1
1
5
6
8
-
2
3
5
7
1
-
4
5
7
1
2
-
8
5
1
2
5
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下面给出更多的关于灰度共生矩阵的特征
-
I = imread(
'circuit.tif');
-
GLCM2 = graycomatrix(
I,
'GrayLimits',[],
'Offset',[
0
1;-
1
1;-
1
0;-
1 -
1]);
-
stats = GLCM_Features1(GLCM2,
0)
- 1
- 2
- 3
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- 2
- 3
-
I = imread(
'circuit.tif');
-
AllGLCMFeatureb= caluateglcmfeature(
I);
- 1
- 2
- 1
- 2
-
function [newglcm] = caluateglcmfeature(I);
-
GLCM2 = graycomatrix(I,
'GrayLimits',
[],
'Offset',
[0 1;-1 1;-1 0;-1 -1]);
-
stats = GLCM_Features1(GLCM2,
0)
-
newstats = struct2cell(stats);
-
[statsx,statsy] =
size(newstats);
-
newglcm =
[];
-
for
i =
1:statsx
-
element =
[];
-
newelement =
[];
-
glcm =
[];
-
element = newstats(
i,
1);
-
newelement = element
{1,1};
-
average = mean(newelement);
-
variance =
sqrt(cov(newelement));
-
glcm =
[newelement average variance];
-
newglcm =
[newglcm glcm];
-
end
-
end
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-
% http://www.mathworks.com/matlabcentral/fileexchange/22187-glcm-texture-features
-
% This code from the upper website but we have changed some.
-
function [out] = GLCM_Features1(glcmin,pairs)
-
% GLCM_Features1 helps to calculate the features from the different GLCMs
-
% that are input to the function. The GLCMs are stored in a i x j x n
-
% matrix, where n is the number of GLCMs calculated usually due to the
-
% different orientation and displacements used in the algorithm. Usually
-
% the values i and j are equal to 'NumLevels' parameter of the GLCM
-
% computing function graycomatrix(). Note that matlab quantization values
-
% belong to the set {1,..., NumLevels} and not from {0,...,(NumLevels-1)}
-
% as provided in some references
-
% http://www.mathworks.com/access/helpdesk/help/toolbox/images/graycomatrix
-
% .html
-
%
-
% Although there is a function graycoprops() in Matlab Image Processing
-
% Toolbox that computes four parameters Contrast, Correlation, Energy,
-
% and Homogeneity. The paper by Haralick suggests a few more parameters
-
% that are also computed here. The code is not fully vectorized and hence
-
% is not an efficient implementation but it is easy to add new features
-
% based on the GLCM using this code. Takes care of 3 dimensional glcms
-
% (multiple glcms in a single 3D array)
-
%
-
% If you find that the values obtained are different from what you expect
-
% or if you think there is a different formula that needs to be used
-
% from the ones used in this code please let me know.
-
% A few questions which I have are listed in the link
-
% http://www.mathworks.com/matlabcentral/newsreader/view_thread/239608
-
%
-
% I plan to submit a vectorized version of the code later and provide
-
% updates based on replies to the above link and this initial code.
-
%
-
% Features computed
-
% Autocorrelation: [2] (out.autoc)
-
% Contrast: matlab/[1,2] (out.contr)
-
% Correlation: matlab (out.corrm)
-
% Correlation: [1,2] (out.corrp)
-
% Cluster Prominence: [2] (out.cprom)
-
% Cluster Shade: [2] (out.cshad)
-
% Dissimilarity: [2] (out.dissi)
-
% Energy: matlab / [1,2] (out.energ)
-
% Entropy: [2] (out.entro)
-
% Homogeneity: matlab (out.homom)
-
% Homogeneity: [2] (out.homop)
-
% Maximum probability: [2] (out.maxpr)
-
% Sum of sqaures: Variance [1] (out.sosvh)
-
% Sum average [1] (out.savgh)
-
% Sum variance [1] (out.svarh)
-
% Sum entropy [1] (out.senth)
-
% Difference variance [1] (out.dvarh)
-
% Difference entropy [1] (out.denth)
-
% Information measure of correlation1 [1] (out.inf1h)
-
% Informaiton measure of correlation2 [1] (out.inf2h)
-
% Inverse difference (INV) is homom [3] (out.homom)
-
% Inverse difference normalized (INN) [3] (out.indnc)
-
% Inverse difference moment normalized [3] (out.idmnc)
-
%
-
% The maximal correlation coefficient was not calculated due to
-
% computational instability
-
% http://murphylab.web.cmu.edu/publications/boland/boland_node26.html
-
%
-
% Formulae from MATLAB site (some look different from
-
% the paper by Haralick but are equivalent and give same results)
-
% Example formulae:
-
% Contrast = sum_i(sum_j( (i-j)^2 * p(i,j) ) ) (same in matlab/paper)
-
% Correlation = sum_i( sum_j( (i - u_i)(j - u_j)p(i,j)/(s_i.s_j) ) ) (m)
-
% Correlation = sum_i( sum_j( ((ij)p(i,j) - u_x.u_y) / (s_x.s_y) ) ) (p[2])
-
% Energy = sum_i( sum_j( p(i,j)^2 ) ) (same in matlab/paper)
-
% Homogeneity = sum_i( sum_j( p(i,j) / (1 + |i-j|) ) ) (as in matlab)
-
% Homogeneity = sum_i( sum_j( p(i,j) / (1 + (i-j)^2) ) ) (as in paper)
-
%
-
% Where:
-
% u_i = u_x = sum_i( sum_j( i.p(i,j) ) ) (in paper [2])
-
% u_j = u_y = sum_i( sum_j( j.p(i,j) ) ) (in paper [2])
-
% s_i = s_x = sum_i( sum_j( (i - u_x)^2.p(i,j) ) ) (in paper [2])
-
% s_j = s_y = sum_i( sum_j( (j - u_y)^2.p(i,j) ) ) (in paper [2])
-
%
-
%
-
% Normalize the glcm:
-
% Compute the sum of all the values in each glcm in the array and divide
-
% each element by it sum
-
%
-
% Haralick uses 'Symmetric' = true in computing the glcm
-
% There is no Symmetric flag in the Matlab version I use hence
-
% I add the diagonally opposite pairs to obtain the Haralick glcm
-
% Here it is assumed that the diagonally opposite orientations are paired
-
% one after the other in the matrix
-
% If the above assumption is true with respect to the input glcm then
-
% setting the flag 'pairs' to 1 will compute the final glcms that would result
-
% by setting 'Symmetric' to true. If your glcm is computed using the
-
% Matlab version with 'Symmetric' flag you can set the flag 'pairs' to 0
-
%
-
% References:
-
% 1. R. M. Haralick, K. Shanmugam, and I. Dinstein, Textural Features of
-
% Image Classification, IEEE Transactions on Systems, Man and Cybernetics,
-
% vol. SMC-3, no. 6, Nov. 1973
-
% 2. L. Soh and C. Tsatsoulis, Texture Analysis of SAR Sea Ice Imagery
-
% Using Gray Level Co-Occurrence Matrices, IEEE Transactions on Geoscience
-
% and Remote Sensing, vol. 37, no. 2, March 1999.
-
% 3. D A. Clausi, An analysis of co-occurrence texture statistics as a
-
% function of grey level quantization, Can. J. Remote Sensing, vol. 28, no.
-
% 1, pp. 45-62, 2002
-
% 4. http://murphylab.web.cmu.edu/publications/boland/boland_node26.html
-
%
-
%
-
% Example:
-
%
-
% Usage is similar to graycoprops() but needs extra parameter 'pairs' apart
-
% from the GLCM as input
-
% I = imread('circuit.tif');
-
% GLCM2 = graycomatrix(I,'GrayLimits',[],'Offset',[0 1;-1 1;-1 0;-1 -1]);
-
% stats = GLCM_Features1(GLCM2,0)
-
% The output is a structure containing all the parameters for the different
-
% GLCMs
-
%
-
% [Avinash Uppuluri: avinash_uv@yahoo.com: Last modified: 11/20/08]
-
-
% If 'pairs' not entered: set pairs to 0
-
if ((nargin >
2) || (nargin ==
0))
-
error(
'Too many or too few input arguments. Enter GLCM and pairs.');
-
elseif ( (nargin ==
2) )
-
if ((
size(glcmin,
1) <=
1) || (
size(glcmin,
2) <=
1))
-
error(
'The GLCM should be a 2-D or 3-D matrix.');
-
elseif (
size(glcmin,
1) ~=
size(glcmin,
2) )
-
error(
'Each GLCM should be square with NumLevels rows and NumLevels cols');
-
end
-
elseif
(nargin ==
1
)
% only GLCM is entered
-
pairs =
0;
% default is numbers and input 1 for percentage
-
if
((
size
(glcmin,
1
) <=
1) || (
size(glcmin,
2) <=
1))
-
error(
'The GLCM should be a 2-D or 3-D matrix.');
-
elseif (
size(glcmin,
1) ~=
size(glcmin,
2) )
-
error(
'Each GLCM should be square with NumLevels rows and NumLevels cols');
-
end
-
end
-
-
-
format
long e
-
if
(pairs ==
1
)
-
newn =
1;
-
for nglcm =
1:
2:
size(glcmin,
3)
-
glcm(:,:,newn) = glcmin(:,:,nglcm) + glcmin(:,:,nglcm+
1);
-
newn = newn +
1;
-
end
-
elseif
(pairs ==
0
)
-
glcm = glcmin;
-
end
-
-
size_glcm_1 =
size(glcm,
1);
-
size_glcm_2 =
size(glcm,
2);
-
size_glcm_3 =
size(glcm,
3);
-
-
% checked
-
out.autoc =
zeros(
1,size_glcm_3);
% Autocorrelation: [2]
-
out.contr =
zeros(
1,size_glcm_3);
% Contrast: matlab/[1,2]
-
out.corrm =
zeros(
1,size_glcm_3);
% Correlation: matlab
-
out.corrp =
zeros(
1,size_glcm_3);
% Correlation: [1,2]
-
out.cprom =
zeros(
1,size_glcm_3);
% Cluster Prominence: [2]
-
out.cshad =
zeros(
1,size_glcm_3);
% Cluster Shade: [2]
-
out.dissi =
zeros(
1,size_glcm_3);
% Dissimilarity: [2]
-
out.energ =
zeros(
1,size_glcm_3);
% Energy: matlab / [1,2]
-
out.entro =
zeros(
1,size_glcm_3);
% Entropy: [2]
-
out.homom =
zeros(
1,size_glcm_3);
% Homogeneity: matlab
-
out.homop =
zeros(
1,size_glcm_3);
% Homogeneity: [2]
-
out.maxpr =
zeros(
1,size_glcm_3);
% Maximum probability: [2]
-
-
out.sosvh =
zeros(
1,size_glcm_3);
% Sum of sqaures: Variance [1]
-
out.savgh =
zeros(
1,size_glcm_3);
% Sum average [1]
-
out.svarh =
zeros(
1,size_glcm_3);
% Sum variance [1]
-
out.senth =
zeros(
1,size_glcm_3);
% Sum entropy [1]
-
out.dvarh =
zeros(
1,size_glcm_3);
% Difference variance [4]
-
%out.dvarh2 = zeros(1,size_glcm_3); % Difference variance [1]
-
out.denth =
zeros(
1,size_glcm_3);
% Difference entropy [1]
-
out.inf1h =
zeros(
1,size_glcm_3);
% Information measure of correlation1 [1]
-
out.inf2h =
zeros(
1,size_glcm_3);
% Informaiton measure of correlation2 [1]
-
%out.mxcch = zeros(1,size_glcm_3);% maximal correlation coefficient [1]
-
%out.invdc = zeros(1,size_glcm_3);% Inverse difference (INV) is homom [3]
-
out.
indnc =
zeros(
1,size_glcm_3);
% Inverse difference normalized (INN) [3]
-
out.
idmnc =
zeros(
1,size_glcm_3);
% Inverse difference moment normalized [3]
-
-
% correlation with alternate definition of u and s
-
%out.corrm2 = zeros(1,size_glcm_3); % Correlation: matlab
-
%out.corrp2 = zeros(1,size_glcm_3); % Correlation: [1,2]
-
-
glcm_sum =
zeros(size_glcm_3,
1);
-
glcm_mean =
zeros(size_glcm_3,
1);
-
glcm_var =
zeros(size_glcm_3,
1);
-
-
% http://www.fp.ucalgary.ca/mhallbey/glcm_mean.htm confuses the range of
-
% i and j used in calculating the means and standard deviations.
-
% As of now I am not sure if the range of i and j should be [1:Ng] or
-
% [0:Ng-1]. I am working on obtaining the values of mean and std that get
-
% the values of correlation that are provided by matlab.
-
u_x =
zeros(size_glcm_3,
1);
-
u_y =
zeros(size_glcm_3,
1);
-
s_x =
zeros(size_glcm_3,
1);
-
s_y =
zeros(size_glcm_3,
1);
-
-
% % alternate values of u and s
-
% u_x2 = zeros(size_glcm_3,1);
-
% u_y2 = zeros(size_glcm_3,1);
-
% s_x2 = zeros(size_glcm_3,1);
-
% s_y2 = zeros(size_glcm_3,1);
-
-
% checked p_x p_y p_xplusy p_xminusy
-
p_x =
zeros(size_glcm_1,size_glcm_3);
% Ng x #glcms[1]
-
p_y =
zeros(size_glcm_2,size_glcm_3);
% Ng x #glcms[1]
-
p_xplusy =
zeros((size_glcm_1*
2 -
1),size_glcm_3);
%[1]
-
p_xminusy =
zeros((size_glcm_1),size_glcm_3);
%[1]
-
% checked hxy hxy1 hxy2 hx hy
-
hxy =
zeros(size_glcm_3,
1);
-
hxy1 =
zeros(size_glcm_3,
1);
-
hx =
zeros(size_glcm_3,
1);
-
hy =
zeros(size_glcm_3,
1);
-
hxy2 =
zeros(size_glcm_3,
1);
-
-
%Q = zeros(size(glcm));
-
-
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