灰度共生矩阵（GLCM）并计算能量、熵、惯性矩、相关性（matlab）（待总结）
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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.****.net/chuminnan2010/article/details/22035751
http://blog.****.net/xuezhisd/article/details/8908824
http://blog.****.net/xuexiang0704/article/details/8713204
http://cn.mathworks.com/help/images/ref/imlincomb.html?refresh=true
理论介绍
http://blog.****.net/lskyne/article/details/8659225
http://blog.****.net/light_lj/article/details/26098815
http://blog.****.net/kezunhai/article/details/42001477
共生矩阵的物理意义
http://blog.****.net/light_lj/article/details/26098815
下面给出不同的NumLevels的例子
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gray = [1 1 5 6 8
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2 3 5 7 1
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4 5 7 1 2
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8 5 1 2 5];
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GLCM = graycomatrix(gray,'GrayLimits',[])
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GLCM =
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1 2 0 0 1 0 0 0
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0 0 1 0 1 0 0 0
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0 0 0 0 1 0 0 0
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0 0 0 0 1 0 0 0
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1 0 0 0 0 1 2 0
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0 0 0 0 0 0 0 1
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2 0 0 0 0 0 0 0
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0 0 0 0 1 0 0 0
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GLCM = graycomatrix(gray, 'GrayLimits',[],'offset', [0 1])
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GLCM =
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1 2 0 0 1 0 0 0
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0 0 1 0 1 0 0 0
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0 0 0 0 1 0 0 0
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0 0 0 0 1 0 0 0
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1 0 0 0 0 1 2 0
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0 0 0 0 0 0 0 1
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2 0 0 0 0 0 0 0
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0 0 0 0 1 0 0 0
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GLCM = graycomatrix(gray, 'GrayLimits',[],'offset', [0 1],'NumLevels',8)
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GLCM =
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1 2 0 0 1 0 0 0
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0 0 1 0 1 0 0 0
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0 0 0 0 1 0 0 0
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0 0 0 0 1 0 0 0
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1 0 0 0 0 1 2 0
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0 0 0 0 0 0 0 1
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2 0 0 0 0 0 0 0
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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
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gray = [1 1 5 6 8
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2 3 5 7 1
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4 5 7 1 2
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8 5 1 2 5];
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GL(2) = max(max(gray));
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GL(1) = min(min(gray));
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if GL(2) == GL(1)
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SI = ones(size(gray));
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else
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slope = NumLevels/(GL(2) - GL(1));
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intercept = 1 - (slope*(GL(1)));
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SI = floor(imlincomb(slope,gray,intercept,'double'));
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end
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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SI =
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1 1 2 3 4
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1 1 2 3 1
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2 2 3 1 1
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4 2 1 1 2
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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SI(SI > NumLevels) = NumLevels;
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SI(SI < 1) = 1;
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SI =
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1 1 2 3 3
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1 1 2 3 1
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2 2 3 1 1
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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；
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gray = [1 1 5 6 8
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2 3 5 7 1
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4 5 7 1 2
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8 5 1 2 5];
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[GLCM,SI] = graycomatrix(gray,'NumLevels',3,'G',[])
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GLCM =
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4 3 0
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1 1 3
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2 1 1
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SI =
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1 1 2 3 3
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1 1 2 3 1
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2 2 3 1 1
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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
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gray = [1 1 5 6 8
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2 3 5 7 1
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4 5 7 1 2
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8 5 1 2 5];
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offsets = [0 1;-1 1;-1 0;-1 -1];
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m = 3; % 3阶灰度级
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[GLCMS,SI] = graycomatrix(gray,'GrayLimits',[],'Of',offsets,'NumLevels',m);
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P = GLCMS;
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[kk,ll,mm] = size(P);
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% 对共生矩阵归一化
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%---------------------------------------------------------
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for n = 1:mm
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P(:,:,n) = P(:,:,n)/sum(sum(P(:,:,n)));
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end
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%-----------------------------------------------------------
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%对共生矩阵计算能量、熵、惯性矩、相关4个纹理参数
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%-----------------------------------------------------------
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H = zeros(1,mm);
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I = H;
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Ux = H; Uy = H;
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deltaX= H; deltaY = H;
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C =H;
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for n = 1:mm
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E(n) = sum(sum(P(:,:,n).^2)); %能量
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for i = 1:kk
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for j = 1:ll
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if P(i,j,n)~=0
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H(n) = -P(i,j,n)*log(P(i,j,n))+H(n); %熵
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end
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I(n) = (i-j)^2*P(i,j,n)+I(n); %惯性矩
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Ux(n) = i*P(i,j,n)+Ux(n); %相关性中μx
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Uy(n) = j*P(i,j,n)+Uy(n); %相关性中μy
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end
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end
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end
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for n = 1:mm
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for i = 1:kk
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for j = 1:ll
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deltaX(n) = (i-Ux(n))^2*P(i,j,n)+deltaX(n); %相关性中σx
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deltaY(n) = (j-Uy(n))^2*P(i,j,n)+deltaY(n); %相关性中σy
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C(n) = i*j*P(i,j,n)+C(n);
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end
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end
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C(n) = (C(n)-Ux(n)*Uy(n))/deltaX(n)/deltaY(n); %相关性
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end
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%--------------------------------------------------------------------------
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%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
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%--------------------------------------------------------------------------
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a1 = mean(E)
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b1 = sqrt(cov(E))
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a2 = mean(H)
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b2 = sqrt(cov(H))
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a3 = mean(I)
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b3 = sqrt(cov(I))
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a4 = mean(C)
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b4 = sqrt(cov(C))
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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;
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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;
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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;
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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.
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gray = [1 1 5 6 8
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2 3 5 7 1
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4 5 7 1 2
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8 5 1 2 5];
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offsets = [0 1;-1 1;-1 0;-1 -1];
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[GLCMS,SI] = graycomatrix(gray,'GrayLimits',[],'Of',offsets)
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GLCMS(:,:,1) =
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1 2 0 0 1 0 0 0
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0 0 1 0 1 0 0 0
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0 0 0 0 1 0 0 0
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0 0 0 0 1 0 0 0
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1 0 0 0 0 1 2 0
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0 0 0 0 0 0 0 1
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2 0 0 0 0 0 0 0
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0 0 0 0 1 0 0 0
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GLCMS(:,:,2) =
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2 0 0 0 0 0 0 0
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1 1 0 0 0 0 0 0
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0 0 0 0 1 0 0 0
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0 0 1 0 0 0 0 0
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0 0 0 0 1 1 1 0
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0 0 0 0 0 0 0 0
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0 0 0 0 0 0 1 1
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0 0 0 0 1 0 0 0
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GLCMS(:,:,3) =
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0 0 0 0 0 0 2 1
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3 0 0 0 0 0 0 0
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1 0 0 0 0 0 0 0
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0 1 0 0 0 0 0 0
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0 1 1 0 2 0 0 0
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0 0 0 0 0 0 0 0
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0 0 0 0 1 1 0 0
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0 0 0 1 0 0 0 0
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GLCMS(:,:,4) =
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0 0 0 0 2 1 0 0
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0 0 0 0 0 0 2 0
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1 0 0 0 0 0 0 0
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0 0 0 0 0 0 0 0
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2 1 0 1 0 0 0 0
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0 0 0 0 0 0 0 0
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0 0 1 0 1 0 0 0
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0 0 0 0 0 0 0 0
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SI =
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1 1 5 6 8
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2 3 5 7 1
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4 5 7 1 2
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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
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I = imread('circuit.tif');
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GLCM2 = graycomatrix(I,'GrayLimits',[],'Offset',[0 1;-1 1;-1 0;-1 -1]);
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stats = GLCM_Features1(GLCM2,0)
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I = imread('circuit.tif');
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AllGLCMFeatureb= caluateglcmfeature(I);
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function [newglcm] = caluateglcmfeature(I);
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GLCM2 = graycomatrix(I,'GrayLimits',[],'Offset',[0 1;-1 1;-1 0;-1 -1]);
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stats = GLCM_Features1(GLCM2,0)
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newstats = struct2cell(stats);
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[statsx,statsy] = size(newstats);
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newglcm = [];
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for i = 1:statsx
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element = [];
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newelement = [];
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glcm = [];
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element = newstats(i,1);
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newelement = element{1,1};
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average = mean(newelement);
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variance = sqrt(cov(newelement));
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glcm = [newelement average variance];
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newglcm = [newglcm glcm];
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end
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end
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% http://www.mathworks.com/matlabcentral/fileexchange/22187-glcm-texture-features
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% This code from the upper website but we have changed some.
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function [out] = GLCM_Features1(glcmin,pairs)
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% GLCM_Features1 helps to calculate the features from the different GLCMs
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% that are input to the function. The GLCMs are stored in a i x j x n
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% matrix, where n is the number of GLCMs calculated usually due to the
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% different orientation and displacements used in the algorithm. Usually
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% the values i and j are equal to 'NumLevels' parameter of the GLCM
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% computing function graycomatrix(). Note that matlab quantization values
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% belong to the set {1,..., NumLevels} and not from {0,...,(NumLevels-1)}
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% as provided in some references
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% http://www.mathworks.com/access/helpdesk/help/toolbox/images/graycomatrix
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% .html
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%
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% Although there is a function graycoprops() in Matlab Image Processing
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% Toolbox that computes four parameters Contrast, Correlation, Energy,
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% and Homogeneity. The paper by Haralick suggests a few more parameters
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% that are also computed here. The code is not fully vectorized and hence
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% is not an efficient implementation but it is easy to add new features
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% based on the GLCM using this code. Takes care of 3 dimensional glcms
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% (multiple glcms in a single 3D array)
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%
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% If you find that the values obtained are different from what you expect
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% or if you think there is a different formula that needs to be used
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% from the ones used in this code please let me know.
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% A few questions which I have are listed in the link
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% http://www.mathworks.com/matlabcentral/newsreader/view_thread/239608
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%
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% I plan to submit a vectorized version of the code later and provide
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% updates based on replies to the above link and this initial code.
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%
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% Features computed
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% Autocorrelation: [2] (out.autoc)
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% Contrast: matlab/[1,2] (out.contr)
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% Correlation: matlab (out.corrm)
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% Correlation: [1,2] (out.corrp)
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% Cluster Prominence: [2] (out.cprom)
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% Cluster Shade: [2] (out.cshad)
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% Dissimilarity: [2] (out.dissi)
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% Energy: matlab / [1,2] (out.energ)
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% Entropy: [2] (out.entro)
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% Homogeneity: matlab (out.homom)
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% Homogeneity: [2] (out.homop)
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% Maximum probability: [2] (out.maxpr)
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% Sum of sqaures: Variance [1] (out.sosvh)
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% Sum average [1] (out.savgh)
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% Sum variance [1] (out.svarh)
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% Sum entropy [1] (out.senth)
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% Difference variance [1] (out.dvarh)
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% Difference entropy [1] (out.denth)
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% Information measure of correlation1 [1] (out.inf1h)
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% Informaiton measure of correlation2 [1] (out.inf2h)
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% Inverse difference (INV) is homom [3] (out.homom)
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% Inverse difference normalized (INN) [3] (out.indnc)
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% Inverse difference moment normalized [3] (out.idmnc)
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%
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% The maximal correlation coefficient was not calculated due to
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% computational instability
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% http://murphylab.web.cmu.edu/publications/boland/boland_node26.html
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%
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% Formulae from MATLAB site (some look different from
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% the paper by Haralick but are equivalent and give same results)
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% Example formulae:
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% Contrast = sum_i(sum_j( (i-j)^2 * p(i,j) ) ) (same in matlab/paper)
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% Correlation = sum_i( sum_j( (i - u_i)(j - u_j)p(i,j)/(s_i.s_j) ) ) (m)
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% Correlation = sum_i( sum_j( ((ij)p(i,j) - u_x.u_y) / (s_x.s_y) ) ) (p[2])
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% Energy = sum_i( sum_j( p(i,j)^2 ) ) (same in matlab/paper)
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% Homogeneity = sum_i( sum_j( p(i,j) / (1 + |i-j|) ) ) (as in matlab)
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% Homogeneity = sum_i( sum_j( p(i,j) / (1 + (i-j)^2) ) ) (as in paper)
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%
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% Where:
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% u_i = u_x = sum_i( sum_j( i.p(i,j) ) ) (in paper [2])
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% u_j = u_y = sum_i( sum_j( j.p(i,j) ) ) (in paper [2])
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% s_i = s_x = sum_i( sum_j( (i - u_x)^2.p(i,j) ) ) (in paper [2])
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% s_j = s_y = sum_i( sum_j( (j - u_y)^2.p(i,j) ) ) (in paper [2])
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%
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%
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% Normalize the glcm:
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% Compute the sum of all the values in each glcm in the array and divide
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% each element by it sum
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%
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% Haralick uses 'Symmetric' = true in computing the glcm
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% There is no Symmetric flag in the Matlab version I use hence
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% I add the diagonally opposite pairs to obtain the Haralick glcm
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% Here it is assumed that the diagonally opposite orientations are paired
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% one after the other in the matrix
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% If the above assumption is true with respect to the input glcm then
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% setting the flag 'pairs' to 1 will compute the final glcms that would result
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% by setting 'Symmetric' to true. If your glcm is computed using the
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% Matlab version with 'Symmetric' flag you can set the flag 'pairs' to 0
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%
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% References:
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% 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
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% 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
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% function of grey level quantization, Can. J. Remote Sensing, vol. 28, no.
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% 1, pp. 45-62, 2002
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% 4. http://murphylab.web.cmu.edu/publications/boland/boland_node26.html
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%
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%
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% Example:
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%
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% Usage is similar to graycoprops() but needs extra parameter 'pairs' apart
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% from the GLCM as input
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% I = imread('circuit.tif');
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% GLCM2 = graycomatrix(I,'GrayLimits',[],'Offset',[0 1;-1 1;-1 0;-1 -1]);
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% stats = GLCM_Features1(GLCM2,0)
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% The output is a structure containing all the parameters for the different
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% GLCMs
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%
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% [Avinash Uppuluri: [email protected]: Last modified: 11/20/08]
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% If 'pairs' not entered: set pairs to 0
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if ((nargin > 2) || (nargin == 0))
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error('Too many or too few input arguments. Enter GLCM and pairs.');
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elseif ( (nargin == 2) )
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if ((size(glcmin,1) <= 1) || (size(glcmin,2) <= 1))
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error('The GLCM should be a 2-D or 3-D matrix.');
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elseif ( size(glcmin,1) ~= size(glcmin,2) )
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error('Each GLCM should be square with NumLevels rows and NumLevels cols');
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end
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elseif (nargin == 1) % only GLCM is entered
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pairs = 0; % default is numbers and input 1 for percentage
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if ((size(glcmin,1) <= 1) || (size(glcmin,2) <= 1))
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error('The GLCM should be a 2-D or 3-D matrix.');
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elseif ( size(glcmin,1) ~= size(glcmin,2) )
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error('Each GLCM should be square with NumLevels rows and NumLevels cols');
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end
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end
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format long e
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if (pairs == 1)
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newn = 1;
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for nglcm = 1:2:size(glcmin,3)
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glcm(:,:,newn) = glcmin(:,:,nglcm) + glcmin(:,:,nglcm+1);
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newn = newn + 1;
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end
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elseif (pairs == 0)
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glcm = glcmin;
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end
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size_glcm_1 = size(glcm,1);
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size_glcm_2 = size(glcm,2);
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size_glcm_3 = size(glcm,3);
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% checked
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out.autoc = zeros(1,size_glcm_3); % Autocorrelation: [2]
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out.contr = zeros(1,size_glcm_3); % Contrast: matlab/[1,2]
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out.corrm = zeros(1,size_glcm_3); % Correlation: matlab
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out.corrp = zeros(1,size_glcm_3); % Correlation: [1,2]
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out.cprom = zeros(1,size_glcm_3); % Cluster Prominence: [2]
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out.cshad = zeros(1,size_glcm_3); % Cluster Shade: [2]
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out.dissi = zeros(1,size_glcm_3); % Dissimilarity: [2]
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out.energ = zeros(1,size_glcm_3); % Energy: matlab / [1,2]
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out.entro = zeros(1,size_glcm_3); % Entropy: [2]
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out.homom = zeros(1,size_glcm_3); % Homogeneity: matlab
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out.homop = zeros(1,size_glcm_3); % Homogeneity: [2]
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out.maxpr = zeros(1,size_glcm_3); % Maximum probability: [2]
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out.sosvh = zeros(1,size_glcm_3); % Sum of sqaures: Variance [1]
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out.savgh = zeros(1,size_glcm_3); % Sum average [1]
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out.svarh = zeros(1,size_glcm_3); % Sum variance [1]
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out.senth = zeros(1,size_glcm_3); % Sum entropy [1]
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out.dvarh = zeros(1,size_glcm_3); % Difference variance [4]
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%out.dvarh2 = zeros(1,size_glcm_3); % Difference variance [1]
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out.denth = zeros(1,size_glcm_3); % Difference entropy [1]
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out.inf1h = zeros(1,size_glcm_3); % Information measure of correlation1 [1]
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out.inf2h = zeros(1,size_glcm_3); % Informaiton measure of correlation2 [1]
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%out.mxcch = zeros(1,size_glcm_3);% maximal correlation coefficient [1]
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%out.invdc = zeros(1,size_glcm_3);% Inverse difference (INV) is homom [3]
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out.indnc = zeros(1,size_glcm_3); % Inverse difference normalized (INN) [3]
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out.idmnc = zeros(1,size_glcm_3); % Inverse difference moment normalized [3]
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% correlation with alternate definition of u and s
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%out.corrm2 = zeros(1,size_glcm_3); % Correlation: matlab
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%out.corrp2 = zeros(1,size_glcm_3); % Correlation: [1,2]
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glcm_sum = zeros(size_glcm_3,1);
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glcm_mean = zeros(size_glcm_3,1);
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glcm_var = zeros(size_glcm_3,1);
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% http://www.fp.ucalgary.ca/mhallbey/glcm_mean.htm confuses the range of
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% i and j used in calculating the means and standard deviations.
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% As of now I am not sure if the range of i and j should be [1:Ng] or
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% [0:Ng-1]. I am working on obtaining the values of mean and std that get
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% the values of correlation that are provided by matlab.
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u_x = zeros(size_glcm_3,1);
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u_y = zeros(size_glcm_3,1);
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s_x = zeros(size_glcm_3,1);
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s_y = zeros(size_glcm_3,1);
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% % alternate values of u and s
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% u_x2 = zeros(size_glcm_3,1);
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% u_y2 = zeros(size_glcm_3,1);
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% s_x2 = zeros(size_glcm_3,1);
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% s_y2 = zeros(size_glcm_3,1);
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% checked p_x p_y p_xplusy p_xminusy
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p_x = zeros(size_glcm_1,size_glcm_3); % Ng x #glcms[1]
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p_y = zeros(size_glcm_2,size_glcm_3); % Ng x #glcms[1]
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p_xplusy = zeros((size_glcm_1*2 - 1),size_glcm_3); %[1]
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p_xminusy = zeros((size_glcm_1),size_glcm_3); %[1]
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% checked hxy hxy1 hxy2 hx hy
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hxy = zeros(size_glcm_3,1);
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hxy1 = zeros(size_glcm_3,1);
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hx = zeros(size_glcm_3,1);
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hy = zeros(size_glcm_3,1);
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hxy2 = zeros(size_glcm_3,1);
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%Q = zeros(size(glcm));
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