matlab函數: graycomatrix()
功 能：建立灰階共生矩陣
Gray-level co-occurrence matrix from an image
圖像的灰階共生矩陣
灰階共生矩陣是像素距離和角度的矩陣函數，它通過計算圖像中一定距離和一定方向的兩點灰階之間的相關性，來反映圖像在方向、間隔、變化幅度及快慢上的綜合資訊。
使用方法：
glcm = graycomatrix(I)
glcms = graycomatrix(I,param1,val1,param2,val2,...)
[glcms,SI] = graycomatrix(...)
描述：
glcms = graycomatrix(I) 産生圖像I的灰階共生矩陣GLCM。它是通過計算兩灰階值 i,j 在圖像 I 中水準相鄰的次數而得到的 (你也可以通過調整' Offsets' 參數來指定其它的像素空間關系），GLCM中的每一個元素（i,j）代表灰階 i 與灰階 j 在圖像 I 中水準相鄰的次數。
graycomatrix()先将圖像 I 歸一化到指定的灰階級，再計算GLCM；這是因為動态地求取圖像的GLCM區間代價過高。如果I是一個二值圖像，那麼灰階共生矩陣就将圖像轉換到二值灰階級（黑和白）。如果I是一個灰階圖像， 那将轉換到8灰階級(預設)。灰階的級數決定了GLCM的大小尺寸，假設灰階級為L，則GLCM的尺寸是L x L。你可以通過設定參數“NumLevels”來指定灰階級數目，還可以通過設定“GrayLimits"參數來設定灰階共生矩陣的轉換方式。
下圖在一個4x5的圖像I中顯示了如何求解灰階共生矩陣，以（1，1）點為例，在圖像 I 中水準相鄰的像素對的灰階值都為1的情況隻出現了1次，是以GLCM(1,1)的值是1。，同理，在圖像 I 中水準相鄰的像素對的灰階值分别為 1和2 的情況出現了2次，是以GLCM(1,2)的值是2。 graycomatrix疊代以上過程，就可以計算出GLCM的所有位置(L^2)的取值。
glcms = graycomatrix(I,param1,val1,param2,val2,...) 傳回一個或多個灰階灰階共生矩陣，根據指定的參數對的值。參數可以簡寫，并且對大小寫不敏感。
參數
下面按照字母的順序列寫了參數：
'GrayLimits' 是兩個元素的向量[low,high]，指明了圖像 I 中的灰階值如何線性歸一化到灰階級别。低于或等于low的灰階值置成1，大于或等于high的灰階值置成NumLevels。如果其設為[]，灰階共生矩陣将使用圖像I的最小和最大灰階值分别作為GrayLimits的low和high，即[min(I(:) , max(I(:)))]。
'NumLevels' 一個整數，指定灰階級的數目。例如，如果NumLevels為8，意思就是将圖像I的灰階映射到1到8之間，它也決定了灰階共生矩陣的大小。預設值是8。
'Offset' 一個p*2的整數矩陣，指定了感興趣像素對之間的距離和方向。矩陣中的每一行是一個兩元素的向量，[row_offset , col_offset]，它指定了一對像素之間的關系，或者說是位移。row_offset是感興趣像素對間隔的行的數目；col_offset是感興趣像素對間隔的列的數目。offset通常表示一個角度，下面列寫的offset的值指定了常見角度。D代表是目前像素與鄰居的距離。
Angle Offset
0 [0 D]
45 [-D D]
90 [-D 0]
135 [-D -D]
下圖說明了數組：offset = [0 1; -1 1; -1 0; -1 -1]
'Symmetric' 一個布爾型數(邏輯型)，指定建立GLCM時像素對中的兩像素的順序是否考慮。例如，當 'Symmetric' 是true時，graycomatrix計算1連接配接2的次數時，(1,2)和(2,1)這兩種數對都計算在内。當'Symmetric'是false時，graycomatrix隻是計算(1,2)或(2,1).
[glcm,SI] = graycomatrix(....) 傳回歸一化(灰階級的)圖像,SI,它被用來計算灰階共生矩陣(GLCM)，SI圖像的取值範圍是[1,NumLevels]。
支援類型
I可以是數字型或邏輯型，但必須是二維的，實數的，非稀疏的矩陣。SI是一個double型矩陣，它和I的尺寸相同。glcms是一個‘NumLevels’ x ‘NumLevels’ x P的double型矩陣，P是offsets的數目(即‘Offset’參數值的列數)。
說明：
灰階共生矩陣(GLCM)的另一個名字是灰階空間相關矩陣(gray-level spatial dependence matrix)。另一方面，co-occurrence在文獻中使用時經常不帶連字元，即cooccurrence。
如果像素對中的一個像素值為NaN，graycomatrix忽略該像素對。
graycomatrix用NumLevels值替代positive Inf，用1代替negative Inf。
如果邊界像素的鄰居落在圖像邊界的外邊，graycomatrix忽略該邊界像素。
當'Symmetric'設定成'true'時，GLCM 是關于對角線對稱的，就是Haralick (1973)描述的GLCM。下面句法（1）使用'Symmetric'為'true'時建立了GLCM等于句法（2）和句法（3）使用'Symmetric'為‘false’時産生的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：
計算灰階共生矩陣，并且傳回縮放後的圖像，SI
I = [ 1 1 5 6 8 8; 2 3 5 7 0 2; 0 2 3 5 6 7]; % 生成圖像I矩陣
[glcm,SI] = graycomatrix(I,'NumLevels',9,'G',[]) % 計算灰階共生矩陣(glcm)和歸一化圖像(SI)
計算灰階圖像的灰階共生矩陣
I = imread('circuit.tif'); % 讀入circuit.tif圖像
glcm = graycomatrix(I,'Offset',[2 0]);
參考文獻
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.
灰階共生矩陣的特征：
角二階矩（Angular Second Moment, ASM)
也稱為 能量
ASM=sum(p(i,j).^2) p(i,j)指歸一化後的灰階共生矩陣
角二階矩是圖像灰階分布均勻程度和紋理粗細的一個度量，當圖像紋理絞細緻、灰階分布均勻時，能量值較大，反之，較小。
熵（Entropy, ENT)
ENT=sum(p(i,j)*(-ln(p(i,j)))
是描述圖像具有的資訊量的度量，表明圖像的複雜程式，當複雜程式高時，熵值較大，反之則較小。
反差分矩陣（Inverse Differential Moment, IDM)
IDM=sum(p(i,j)/(1+(i-j)^2))
反映了紋理的清晰程度和規則程度，紋理清晰、規律性較強、易于描述的，值較大；雜亂無章的，難于描述的，值較小。
************************************************************************************************************************************************************************
************************************************************* graycomatrix源程式代碼 *****************************************************************************
************************************************************************************************************************************************************************
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