graycomatrix 计算(图像)灰度共生矩阵(CLCM)——matlab相关函数说明，很详细

matlab函数: graycomatrix()

功           能：创建灰度共生矩阵

Gray-level co-occurrence matrix from an image

图像的灰度共生矩阵

灰度共生矩阵是像素距离和角度的矩阵函数，它通过计算图像中一定距离和一定方向的两点灰度之间的相关性，来反映图像在方向、间隔、变化幅度及快慢上的综合信息。

使用方法：
glcm = graycomatrix(I)
glcms = graycomatrix(I,param1,val1,param2,val2,...)
[glcms,SI] = graycomatrix(...)

描述：
glcms = graycomatrix(I) 产生图像I的灰度共生矩阵GLCM。它是通过计算两灰度值 i,j 在图像 I 中水平相邻的次数而得到的 (你也可以通过调整' Offsets' 参数来指定其它的像素空间关系），GLCM中的每一个元素（i,j）代表灰度 i 与灰度 j 在图像 I 中水平相邻的次数。

graycomatrix()先将图像 I 归一化到指定的灰度级，再计算GLCM；这是因为动态地求取图像的GLCM区间代价过高。如果I是一个二值图像，那么灰度共生矩阵就将图像转换到二值灰度级（黑和白）。如果I是一个灰度图像， 那将转换到8灰度级(默认)。灰度的级数决定了GLCM的大小尺寸，假设灰度级为L，则GLCM的尺寸是L x L。你可以通过设定参数“NumLevels”来指定灰度级数目，还可以通过设置“GrayLimits"参数来设置灰度共生矩阵的转换方式。

下图在一个4x5的图像I中显示了如何求解灰度共生矩阵，以（1，1）点为例，在图像 I 中水平相邻的像素对的灰度值都为1的情况只出现了1次，所以GLCM(1,1)的值是1。，同理，在图像 I 中水平相邻的像素对的灰度值分别为 1和2 的情况出现了2次，所以GLCM(1,2)的值是2。 graycomatrix迭代以上过程，就可以计算出GLCM的所有位置(L^2)的取值。

  

glcms = graycomatrix(I,param1,val1,param2,val2,...) 返回一个或多个灰度灰度共生矩阵，根据指定的参数对的值。参数可以简写，并且对大小写不敏感。

参数
下面按照字母的顺序列写了参数：
     'GrayLimits'  是两个元素的向量[low,high]，指明了图像 I 中的灰度值如何线性归一化到灰度级别。低于或等于low的灰度值置成1，大于或等于high的灰度值置成NumLevels。如果其设为[]，灰度共生矩阵将使用图像I的最小和最大灰度值分别作为GrayLimits的low和high，即[min(I(:) , max(I(:)))]。

     'NumLevels'    一个整数，指定灰度级的数目。例如，如果NumLevels为8，意思就是将图像I的灰度映射到1到8之间，它也决定了灰度共生矩阵的大小。默认值是8。

     'Offset'   一个p*2的整数矩阵，指定了感兴趣像素对之间的距离和方向。矩阵中的每一行是一个两元素的向量，[row_offset , col_offset]，它指定了一对像素之间的关系，或者说是位移。row_offset是感兴趣像素对间隔的行的数目；col_offset是感兴趣像素对间隔的列的数目。offset通常表示一个角度，下面列写的offset的值指定了常见角度。D代表是当前像素与邻居的距离。

Angle        Offset
  0              [0 D]
 45             [-D D]
 90             [-D 0]
135            [-D -D]
     下图说明了数组：offset = [0 1; -1 1; -1 0; -1 -1]

 

     'Symmetric'  一个布尔型数(逻辑型)，指定创建GLCM时像素对中的两像素的顺序是否考虑。例如，当 'Symmetric' 是true时，graycomatrix计算1连接2的次数时，(1,2)和(2,1)这两种数对都计算在内。当'Symmetric'是false时，graycomatrix只是计算(1,2)或(2,1).

[glcm,SI] = graycomatrix(....) 返回归一化(灰度级的)图像,SI,它被用来计算灰度共生矩阵(GLCM)，SI图像的取值范围是[1,NumLevels]。

支持类型

      I可以是数字型或逻辑型，但必须是二维的，实数的，非稀疏的矩阵。SI是一个double型矩阵，它和I的尺寸相同。glcms是一个‘NumLevels’ x ‘NumLevels’ x P的double型矩阵，P是offsets的数目(即‘Offset’参数值的列数)。
说明：

      灰度共生矩阵(GLCM)的另一个名字是灰度空间相关矩阵(gray-level spatial dependence matrix)。另一方面，co-occurrence在文献中使用时经常不带连字符，即cooccurrence。

     如果像素对中的一个像素值为NaN，graycomatrix忽略该像素对。

     graycomatrix用NumLevels值替代positive Inf，用1代替negative Inf。

      如果边界像素的邻居落在图像边界的外边，graycomatrix忽略该边界像素。

     当'Symmetric'设置成'true'时，GLCM 是关于对角线对称的，就是Haralick (1973)描述的GLCM。下面句法（1）使用'Symmetric'为'true'时创建了GLCM等于句法（2）和句法（3）使用'Symmetric'为‘false’时产生的GLCM的和。

 graycomatrix(I, 'offset', [0 1], 'Symmetric', true)    (1)

 graycomatrix(I,'offset',  [0,1], 'Symmetric', false)   (2)

 graycomatrix(I,'offset',  [0,-1], 'Symmetric',false)   (3)

 

示例：

计算灰度共生矩阵，并且返回缩放后的图像，SI
I = [ 1 1 5 6 8 8; 2 3 5 7 0 2; 0 2 3 5 6 7];     % 生成图像I矩阵
[glcm,SI] = graycomatrix(I,'NumLevels',9,'G',[])  % 计算灰度共生矩阵(glcm)和归一化图像(SI)

计算灰度图像的灰度共生矩阵
I = imread('circuit.tif');     % 读入circuit.tif图像
glcm = graycomatrix(I,'Offset',[2 0]);

参考文献

Haralick, R.M., K. Shanmugan, and I. Dinstein, "Textural Features for Image Classification", IEEE Transactions on Systems, Man, and Cybernetics, Vol. SMC-3, 1973, pp. 610-621.

Haralick, R.M., and L.G. Shapiro. Computer and Robot Vision: Vol. 1, Addison-Wesley, 1992, p. 459.

 

灰度共生矩阵的特征：

角二阶矩（Angular Second Moment, ASM)

也称为 能量
ASM=sum(p(i,j).^2)    p(i,j)指归一化后的灰度共生矩阵
角二阶矩是图像灰度分布均匀程度和纹理粗细的一个度量，当图像纹理绞细致、灰度分布均匀时，能量值较大，反之，较小。

熵（Entropy, ENT)
ENT=sum(p(i,j)*(-ln(p(i,j)))    
是描述图像具有的信息量的度量，表明图像的复杂程序，当复杂程序高时，熵值较大，反之则较小。

反差分矩阵（Inverse Differential Moment, IDM)
IDM=sum(p(i,j)/(1+(i-j)^2))
反映了纹理的清晰程度和规则程度，纹理清晰、规律性较强、易于描述的，值较大；杂乱无章的，难于描述的，值较小。

************************************************************************************************************************************************************************

  *************************************************************  graycomatrix源程序代码  *****************************************************************************

 ************************************************************************************************************************************************************************

 function [GLCMS,SI] = graycomatrix(varargin)
 %GRAYCOMATRIX Create gray-level co-occurrence matrix.
 %   GLCMS = GRAYCOMATRIX(I) analyzes pairs of horizontally adjacent pixels
 %   in a scaled version of I.  If I is a binary image, it is scaled to 2
 %   levels. If I is an intensity image, it is scaled to 8 levels. In this
 %   case, there are 8 x 8 = 64 possible ordered combinations of values for
 %   each pixel pair. GRAYCOMATRIX accumulates the total occurrence of each
 %   such combination, producing a 8-by-8 output array, GLCMS. The row and
 %   column subscripts in GLCMS correspond respectively to the first and
 %   second (scaled) pixel-pair values.
 %
 %   GLCMS = GRAYCOMATRIX(I,PARAM1,VALUE1,PARAM2,VALUE2,...) returns one or
 %   more gray-level co-occurrence matrices, depending on the values of the
 %   optional parameter/value pairs. Parameter names can be abbreviated, and
 %   case does not matter.
 %
 %   Parameters include:
 %
 %   'Offset'         A p-by-2 array of offsets specifying the distance
 %                    between the pixel-of-interest and its neighbor. Each
 %                    row in the array is a two-element vector,
 %                    [ROW_OFFSET COL_OFFSET], that specifies the
 %                    relationship, or 'Offset', between a pair of pixels.
 %                    ROW_OFFSET is the number of rows between the
 %                    pixel-of-interest and its neighbor.  COL_OFFSET is the
 %                    number of columns between the pixel-of-interest and
 %                    its neighbor. For example, if you want the number of
 %                    occurrences where the pixel of interest is one pixel
 %                    to the left of its neighbor, then
 %                    [ROW_OFFSET COL_OFFSET] is [0 1].
 %
 %                    Because this offset is often expressed as an angle,
 %                    the following table lists the offset values that
 %                    specify common angles, given the pixel distance D.
 %
 %                    Angle     OFFSET
 %                    -----     ------
 %                    0         [0 D]
 %                    45        [-D D]
 %                    90        [-D 0]
 %                    135       [-D -D]
 %
 %                    ROW_OFFSET and COL_OFFSET must be integers.
 %
 %                    Default: [0 1]
 %
 %   'NumLevels'      An integer specifying the number of gray levels to use when
 %                    scaling the grayscale values in I. For example, if
 %                    'NumLevels' is 8, GRAYCOMATRIX scales the values in I so
 %                    they are integers between 1 and 8.  The number of gray levels
 %                    determines the size of the gray-level co-occurrence matrix
 %                    (GLCM).
 %
 %                    'NumLevels' must be an integer. 'NumLevels' must be 2 if I
 %                    is logical.
 %
 %                    Default: 8 for numeric
 %                             2 for logical
 %
 %   'GrayLimits'     A two-element vector, [LOW HIGH], that specifies how
 %                    the grayscale values in I are linearly scaled into
 %                    gray levels. Grayscale values less than or equal to
 %                    LOW are scaled to 1. Grayscale values greater than or
 %                    equal to HIGH are scaled to HIGH.  If 'GrayLimits' is
 %                    set to [], GRAYCOMATRIX uses the minimum and maximum
 %                    grayscale values in I as limits,
 %                    [min(I(:)) max(I(:))].
 %
 %                    Default: the LOW and HIGH values specified by the
 %                    class, e.g., [LOW HIGH] is [0 1] if I is double and
 %                    [-32768 32767] if I is int16.
 %
 %   'Symmetric'      A Boolean that creates a GLCM where the ordering of
 %                    values in the pixel pairs is not considered. For
 %                    example, when calculating the number of times the
 %                    value 1 is adjacent to the value 2, GRAYCOMATRIX
 %                    counts both 1,2 and 2,1 pairings, if 'Symmetric' is
 %                    set to true. When 'Symmetric' is set to false,
 %                    GRAYCOMATRIX only counts 1,2 or 2,1, depending on the
 %                    value of 'offset'. The GLCM created in this way is
 %                    symmetric across its diagonal, and is equivalent to
 %                    the GLCM described by Haralick (1973).
 %
 %                    The GLCM produced by the following syntax,
 %
 %                    graycomatrix(I, 'offset', [0 1], 'Symmetric', true)
 %
 %                    is equivalent to the sum of the two GLCMs produced by
 %                    these statements.
 %
 %                    graycomatrix(I, 'offset', [0 1], 'Symmetric', false)
 %                    graycomatrix(I, 'offset', [0 -1], 'Symmetric', false)
 %
 %                    Default: false
 %
 %
 %   [GLCMS,SI] = GRAYCOMATRIX(...) returns the scaled image used to
 %   calculate GLCM. The values in SI are between 1 and 'NumLevels'.
 %
 %   Class Support
 %   -------------
 %   I can be numeric or logical.  I must be 2D, real, and nonsparse. SI is
 %   a double matrix having the same size as I.  GLCMS is an
 %   'NumLevels'-by-'NumLevels'-by-P double array where P is the number of
 %   offsets in OFFSET.
 %
 %   Notes
 %   -----
 %   Another name for a gray-level co-occurrence matrix is a gray-level
 %   spatial dependence matrix.
 %
 %   GRAYCOMATRIX ignores pixels pairs if either of their values is NaN. It
 %   also replaces Inf with the value 'NumLevels' and -Inf with the value 1.
 %
 %   GRAYCOMATRIX ignores border pixels, if the corresponding neighbors
 %   defined by 'Offset' fall outside the image boundaries.
 %
 %   References
 %   ----------
 %   Haralick, R.M., K. Shanmugan, and I. Dinstein, "Textural Features for
 %   Image Classification", IEEE Transactions on Systems, Man, and
 %   Cybernetics, Vol. SMC-3, 1973, pp. 610-621.
 %
 %   Haralick, R.M., and L.G. Shapiro. Computer and Robot Vision: Vol. 1,
 %   Addison-Wesley, 1992, p. 459.
 %
 %   Example 1
 %   ---------
 %   Calculate the gray-level co-occurrence matrix (GLCM) and return the
 %   scaled version of the image, SI, used by GRAYCOMATRIX to generate the
 %   GLCM.
 %
 %        I = [1 1 5 6 8 8;2 3 5 7 0 2; 0 2 3 5 6 7];
 %       [GLCMS,SI] = graycomatrix(I,'NumLevels',9,'G',[])
 %
 %   Example 2
 %   ---------
 %   Calculate the gray-level co-occurrence matrix for a grayscale image.
 %
 %       I = imread('circuit.tif');
 %       GLCMS = graycomatrix(I,'Offset',[2 0])
 %
 %   Example 3
 %   ---------
 %   Calculate gray-level co-occurrences matrices for a grayscale image
 %   using four different offsets.
 %
 %       I = imread('cell.tif');
 %       offsets = [0 1;-1 1;-1 0;-1 -1];
 %       [GLCMS,SI] = graycomatrix(I,'Of',offsets);
 %
 %   Example 4
 %   ---------
 %   Calculate the symmetric gray-level co-occurrence matrix (the Haralick
 %   definition) for a grayscale image.
 %
 %       I = imread('circuit.tif');
 %       GLCMS = graycomatrix(I,'Offset',[2 0],'Symmetric', true)
 %
 %   See also GRAYCOPROPS.

 %   Copyright 1993-2008 The MathWorks, Inc.
 %   $Revision.1 $  $Date: 2008/04/03 03:10:53 $

 [I, Offset, NL, GL, makeSymmetric] = ParseInputs(varargin{:});

 % Scale I so that it contains integers between 1 and NL.
 if GL(2) == GL(1)
   SI = ones(size(I));
 else
   slope = (NL-1) / (GL(2) - GL(1));
   intercept = 1 - (slope*(GL(1)));
   SI = round(imlincomb(slope,I,intercept,'double'));
 end

 % Clip values if user had a value that is outside of the range, e.g.,
 % double image = [0 .5 2;0 1 1]; 2 is outside of [0,1]. The order of the
 % following lines matters in the event that NL = 0.
 SI(SI > NL) = NL;
 SI(SI < 1) = 1;

 numOffsets = size(Offset,1);

 if NL ~= 0

   % Create vectors of row and column subscripts for every pixel and its
   % neighbor.
   s = size(I);
   [r,c] = meshgrid(1:s(1),1:s(2));
   r = r(:);
   c = c(:);

   % Compute GLCMS
   GLCMS = zeros(NL,NL,numOffsets);
   for k = 1 : numOffsets
     GLCMS(:,:,k) = computeGLCM(r,c,Offset(k,:),SI,NL);

     if makeSymmetric
         % Reflect glcm across the diagonal
         glcmTranspose = GLCMS(:,:,k).';
         GLCMS(:,:,k) = GLCMS(:,:,k) + glcmTranspose;
     end
   end

 else
   GLCMS = zeros(0,0,numOffsets);
 end

 %-----------------------------------------------------------------------------
 function oneGLCM = computeGLCM(r,c,offset,si,nl)
 % computes GLCM given one Offset

 r2 = r + offset(1);
 c2 = c + offset(2);

 [nRow nCol] = size(si);
 % Determine locations where subscripts outside the image boundary
 outsideBounds = find(c2 < 1 | c2 > nCol | r2 < 1 | r2 > nRow);

 % Create vector containing si(r1,c1)
 v1 = shiftdim(si,1);
 v1 = v1(:);
 v1(outsideBounds) = [];

 % Create vector containing si(r2,c2). Not using sub2ind for performance
 % reasons
 r2(outsideBounds) = []; %#ok
 c2(outsideBounds) = []; %#ok
 Index = r2 + (c2 - 1)*nRow;
 v2 = si(Index);

 % Remove pixel and its neighbor if their value is NaN.
 bad = isnan(v1) | isnan(v2);
 if any(bad)
     wid = sprintf('Images:%s:scaledImageContainsNan',mfilename);
     warning(wid, ...
         'GLCM does not count pixel pairs if either of their values is NaN.');
 end

 Ind = [v1 v2];
 Ind(bad,:) = [];

 if isempty(Ind)
     oneGLCM = zeros(nl);
 else
     % Tabulate the occurrences of pixel pairs having v1 and v2.
     oneGLCM = accumarray(Ind, 1, [nl nl]);
 end

 %-----------------------------------------------------------------------------
 function [I, offset, nl, gl, sym] = ParseInputs(varargin)

 iptchecknargin(1,9,nargin,mfilename);

 % Check I
 I = varargin{1};
 iptcheckinput(I,{'logical','numeric'},{'2d','real','nonsparse'}, ...
               mfilename,'I',1);

 % Assign Defaults
 offset = [0 1];
 if islogical(I)
   nl = 2;
 else
   nl = 8;
 end
 gl = getrangefromclass(I);
 sym = false;

 % Parse Input Arguments
 if nargin ~= 1

   paramStrings = {'Offset','NumLevels','GrayLimits','Symmetric'};

   for k = 2:2:nargin

     param = lower(varargin{k});
     inputStr = iptcheckstrs(param, paramStrings, mfilename, 'PARAM', k);
     idx = k + 1;  %Advance index to the VALUE portion of the input.
     if idx > nargin
       eid = sprintf('Images:%s:missingParameterValue', mfilename);
       error(eid,'Parameter ''%s'' must be followed by a value.', inputStr);
     end

     switch (inputStr)

      case 'Offset'

       offset = varargin{idx};
       iptcheckinput(offset,{'logical','numeric'},...
                     {'2d','nonempty','integer','real'},...
                     mfilename, 'OFFSET', idx);
       if size(offset,2) ~= 2
         eid = sprintf('Images:%s:invalidOffsetSize',mfilename);
         error(eid, 'OFFSET must be an N-by-2 array.');
       end
       offset = double(offset);

      case 'NumLevels'

       nl = varargin{idx};
       iptcheckinput(nl,{'logical','numeric'},...
                     {'real','integer','nonnegative','nonempty','nonsparse'},...
                     mfilename, 'NL', idx);
       if numel(nl) > 1
         eid = sprintf('Images:%s:invalidNumLevels',mfilename);
         error(eid, 'NL cannot contain more than one element.');
       elseif islogical(I) && nl ~= 2
         eid = sprintf('Images:%s:invalidNumLevelsForBinary',mfilename);
         error(eid, 'NL must be two for a binary image.');
       end
       nl = double(nl);

      case 'GrayLimits'

       gl = varargin{idx};
       iptcheckinput(gl,{'logical','numeric'},{'vector','real'},...
                     mfilename, 'GL', idx);
       if isempty(gl)
         gl = [min(I(:)) max(I(:))];
       elseif numel(gl) ~= 2
         eid = sprintf('Images:%s:invalidGrayLimitsSize',mfilename);
         error(eid, 'GL must be a two-element vector.');
       end
       gl = double(gl);

       case 'Symmetric'
         sym = varargin{idx};
         iptcheckinput(sym,{'logical'}, {'scalar'}, mfilename, 'Symmetric', idx);

     end
   end
 end