问题描述:AAL脑图谱（自动解剖标记图谱）包含116个脑区。利用matlab程序计算各个脑区的质心坐标。

步骤：

第一步：

首先建立一个.m文件，命名为y_CenterOfMass.m :

function [Table] = y_CenterOfMass(AtlasFile)

%[Data Head]=y_Read('D:\PFC_ROI\aal\MFG_L.nii','all');
[Data Head]=y_Read(AtlasFile);

[nDim1 nDim2 nDim3]=size(Data);

[I J K] = ndgrid(1:nDim1,1:nDim2,1:nDim3);

Element = unique(Data);
Element(1) = []; % This is the background 0
Table = [];
for iElement=1:length(Element)
    
    ICenter = mean(I(Data==Element(iElement)));
    JCenter = mean(J(Data==Element(iElement)));
    KCenter = mean(K(Data==Element(iElement)));
    
    Center = Head.mat*[ICenter JCenter KCenter 1]';
    XCenter = Center(1);
    YCenter = Center(2);
    ZCenter = Center(3);

    Table = [Table;[iElement,Element(iElement),ICenter,JCenter,KCenter,XCenter,YCenter,ZCenter]];
end


% % 定义文件路径
% AtlasFile = 'D:/aal/MFG_L.nii';
% 
% % 调用 y_CenterOfMass 函数
% Table = y_CenterOfMass(AtlasFile);

注意：在这个文件中不能直接调用函数，因为在MATLAB中，一个 .m 文件如果第一行是以 function 关键字开头的函数定义（例如这里的 function [Table] = y_CenterOfMass(AtlasFile)），那么整个文件就会被MATLAB视为一个函数文件。
如果想要直接运行函数，可手动把[Data Head]=y_Read(AtlasFile);这一句的AtlasFile参数改成nii文件路径。

第二步:

在当前的工作目录下新建另一个.m文件，比如这里命名为test_center_of_mass.m ：

% test_center_of_mass.m (独立的脚本文件)
% 定义文件路径
AtlasFile = 'D:/PFC_ROI/aal/aal.nii';
% 调用 y_CenterOfMass 函数
Table = y_CenterOfMass(AtlasFile);
disp(Table)

运行此程序后，即可输出每个脑区的质心坐标：

>> test_center_of_mass

    1.0000    1.0000   51.3504  120.3167  122.9442  -39.6496   -5.6833   50.9442
    2.0000    2.0000  131.3746  117.7869  124.0920   40.3746   -8.2131   52.0920
    3.0000    3.0000   71.5543  160.8081  114.2017  -19.4457   34.8081   42.2017
    4.0000    4.0000  111.8997  157.1201  115.8154   20.8997   31.1201   43.8154
    5.0000    5.0000   73.4396  173.3247   58.6932  -17.5604   47.3247  -13.3068
    6.0000    6.0000  108.4947  174.0980   57.9799   17.4947   48.0980  -14.0201
    7.0000    7.0000   56.5682  158.7318  107.4556  -34.4318   32.7318   35.4556
    8.0000    8.0000  127.5948  159.0619  106.0351   36.5948   33.0619   34.0351
    9.0000    9.0000   59.3543  176.4297   62.3810  -31.6457   50.4297   -9.6190
   10.0000   10.0000  123.1817  178.5879   61.2688   32.1817   52.5879  -10.7312
   11.0000   11.0000   41.5662  138.7333   91.0225  -49.4338   12.7333   19.0225
   12.0000   12.0000  140.2040  140.9765   93.4118   49.2040   14.9765   21.4118
   13.0000   13.0000   44.4168  155.9140   85.9904  -46.5832   29.9140   13.9904
   14.0000   14.0000  140.3297  156.1618   86.1734   49.3297   30.1618   14.1734
   15.0000   15.0000   54.0152  156.7074   59.8902  -36.9848   30.7074  -12.1098
   16.0000   16.0000  131.2244  158.2303   60.0890   40.2244   32.2303  -11.9110
   17.0000   17.0000   42.8415  117.5245   85.9507  -48.1585   -8.4755   13.9507
   18.0000   18.0000  142.6468  119.7478   86.6347   51.6468   -6.2522   14.6347
   19.0000   19.0000   84.6760  130.8485  133.3755   -6.3240    4.8485   61.3755
   20.0000   20.0000   98.6158  126.1714  133.8538    7.6158    0.1714   61.8538
   21.0000   21.0000   81.9372  141.0531   60.5447   -9.0628   15.0531  -11.4553
   22.0000   22.0000  100.4269  141.9121   60.7437    9.4269   15.9121  -11.2563
   23.0000   23.0000   85.2006  175.1687  102.8937   -5.7994   49.1687   30.8937
   24.0000   24.0000   99.0994  176.8406  102.2193    8.0994   50.8406   30.2193
   25.0000   25.0000   84.8260  180.0571   64.6032   -6.1740   54.0571   -7.3968
   26.0000   26.0000   98.1611  177.6710   64.8659    7.1611   51.6710   -7.1341
   27.0000   27.0000   84.9181  163.0724   53.8638   -6.0819   37.0724  -18.1362
   28.0000   28.0000   98.3533  161.6447   53.9560    7.3533   35.6447  -18.0440
   29.0000   29.0000   54.8690  132.6518   75.4409  -36.1310    6.6518    3.4409
   30.0000   30.0000  129.0191  132.2451   74.0775   38.0191    6.2451    2.0775
   31.0000   31.0000   85.9634  161.3999   85.9529   -5.0366   35.3999   13.9529
   32.0000   32.0000   98.4557  163.0056   87.8398    7.4557   37.0056   15.8398
   33.0000   33.0000   84.5236  111.0802  113.5694   -6.4764  -14.9198   41.5694
   34.0000   34.0000   98.0204  117.1736  111.7910    7.0204   -8.8264   39.7910
   35.0000   35.0000   85.1524   83.0821   96.6697   -5.8476  -42.9179   24.6697
   36.0000   36.0000   97.4375   84.1850   93.8666    6.4375  -41.8150   21.8666
   37.0000   37.0000   64.9732  105.2588   61.8665  -26.0268  -20.7412  -10.1335
   38.0000   38.0000  119.2307  106.2168   61.6688   28.2307  -19.7832  -10.3312
   39.0000   39.0000   68.8289  110.0497   51.2957  -22.1711  -15.9503  -20.7043
   40.0000   40.0000  115.3818  110.8532   51.5298   24.3818  -15.1468  -20.4702
   41.0000   41.0000   66.7311  125.3329   54.8586  -24.2689   -0.6671  -17.1414
   42.0000   42.0000  117.3191  126.6387   54.4972   26.3191    0.6387  -17.5028
   43.0000   43.0000   82.8583   47.3330   78.4392   -8.1417  -78.6670    6.4392
   44.0000   44.0000  105.9942   52.8517   81.4048   14.9942  -73.1483    9.4048
   45.0000   45.0000   84.0660   45.8664   99.2235   -6.9340  -80.1336   27.2235
   46.0000   46.0000  103.5110   46.6418  100.2284   12.5110  -79.3582   28.2284
   47.0000   47.0000   75.3831   58.4450   67.3671  -15.6169  -67.5550   -4.6329
   48.0000   48.0000  106.2899   59.0741   68.1253   15.2899  -66.9259   -3.8747
   49.0000   49.0000   73.4593   41.7377  100.1653  -17.5407  -84.2623   28.1653
   50.0000   50.0000  114.2915   45.1461  102.5870   23.2915  -80.8539   30.5870
   51.0000   51.0000   57.6115   45.2684   88.1148  -33.3885  -80.7316   16.1148
   52.0000   52.0000  127.3877   46.2954   91.4158   36.3877  -79.7046   19.4158
   53.0000   53.0000   53.6413   47.7070   64.1557  -37.3587  -78.2930   -7.8443
   54.0000   54.0000  128.1587   44.0069   64.3868   37.1587  -81.9931   -7.6132
   55.0000   55.0000   58.8407   85.7022   51.7718  -32.1593  -40.2978  -20.2282
   56.0000   56.0000  123.9681   86.8983   51.8216   32.9681  -39.1017  -20.1784
   57.0000   57.0000   47.5376  103.3687  120.9172  -43.4624  -22.6313   48.9172
   58.0000   58.0000  131.4284  100.5069  124.5450   40.4284  -25.4931   52.5450
   59.0000   59.0000   66.5464   66.4428  130.9601  -24.4536  -59.5572   58.9601
   60.0000   60.0000  116.1058   66.8202  134.0618   25.1058  -59.1798   62.0618
   61.0000   61.0000   47.1963   80.1803  118.7405  -43.8037  -45.8197   46.7405
   62.0000   62.0000  136.4620   79.7103  121.5351   45.4620  -46.2897   49.5351
   63.0000   63.0000   34.2119   92.3622  102.4495  -56.7881  -33.6378   30.4495
   64.0000   64.0000  147.6107   94.4951  106.4800   56.6107  -31.5049   34.4800
   65.0000   65.0000   45.8587   65.1842  107.5872  -45.1413  -60.8158   35.5872
   66.0000   66.0000  135.5077   66.0153  110.6277   44.5077  -59.9847   38.6277
   67.0000   67.0000   82.7592   69.9291  120.0090   -8.2408  -56.0709   48.0090
   68.0000   68.0000   99.9796   69.9505  115.7694    8.9796  -56.0495   43.7694
   69.0000   69.0000   82.3699  100.6354  142.0703   -8.6301  -25.3646   70.0703
   70.0000   70.0000   97.4771   94.4130  140.0941    6.4771  -31.5870   68.0941
   71.0000   71.0000   78.5381  136.9960   81.2391  -12.4619   10.9960    9.2391
   72.0000   72.0000  104.8362  138.0743   81.4152   13.8362   12.0743    9.4152
   73.0000   73.0000   66.0863  129.8553   74.4013  -24.9137    3.8553    2.4013
   74.0000   74.0000  117.7787  130.9129   74.4647   26.7787    4.9129    2.4647
   75.0000   75.0000   72.2503  125.9685   72.2105  -18.7497   -0.0315    0.2105
   76.0000   76.0000  111.2006  126.1755   72.2281   20.2006    0.1755    0.2281
   77.0000   77.0000   79.1516  108.4355   79.9761  -11.8484  -17.5645    7.9761
   78.0000   78.0000  102.9977  108.4476   80.0868   11.9977  -17.5524    8.0868
   79.0000   79.0000   48.0083  107.1247   81.9784  -42.9917  -18.8753    9.9784
   80.0000   80.0000  135.8569  108.8533   82.4060   44.8569  -17.1467   10.4060
   81.0000   81.0000   36.8435  105.3224   79.1348  -54.1565  -20.6776    7.1348
   82.0000   82.0000  148.1460  104.2194   78.8014   57.1460  -21.7806    6.8014
   83.0000   83.0000   50.1214  141.1441   51.8173  -40.8786   15.1441  -20.1827
   84.0000   84.0000  138.2468  140.7452   55.1368   47.2468   14.7452  -16.8632
   85.0000   85.0000   34.4761   92.2002   69.7990  -56.5239  -33.7998   -2.2010
   86.0000   86.0000  147.4735   88.7720   70.5319   56.4735  -37.2280   -1.4681
   87.0000   87.0000   53.6801  140.5869   37.9191  -37.3199   14.5869  -34.0809
   88.0000   88.0000  134.2204  140.5516   39.7668   43.2204   14.5516  -32.2332
   89.0000   89.0000   40.2293   97.9484   48.8316  -50.7707  -28.0516  -23.1684
   90.0000   90.0000  143.6922   94.9308   49.6811   52.6922  -31.0692  -22.3189
   91.0000   91.0000   54.9330   59.2803   43.0656  -36.0670  -66.7197  -28.9344
   92.0000   92.0000  128.4559   58.8632   42.4525   37.4559  -67.1368  -29.5475
   93.0000   93.0000   62.3642   52.7397   33.7963  -28.6358  -73.2603  -38.2037
   94.0000   94.0000  123.0575   56.9841   32.0513   32.0575  -69.0159  -39.9487
   95.0000   95.0000   82.1996   88.7771   53.4188   -8.8004  -37.2229  -18.5812
   96.0000   96.0000  103.3187   91.5344   52.6088   12.3187  -34.4656  -19.3912
   97.0000   97.0000   75.9960   82.5139   55.0671  -15.0040  -43.4861  -16.9329
   98.0000   98.0000  108.1987   83.1391   53.8492   17.1987  -42.8609  -18.1508
   99.0000   99.0000   67.7621   66.8993   49.8694  -23.2379  -59.1007  -22.1306
  100.0000  100.0000  115.6914   67.6837   48.3549   24.6914  -58.3163  -23.6451
  101.0000  101.0000   58.6422   66.1798   26.5505  -32.3578  -59.8202  -45.4495
  102.0000  102.0000  124.1392   62.8220   23.5428   33.1392  -63.1780  -48.4572
  103.0000  103.0000   65.2486   71.4809   24.3154  -25.7514  -54.5191  -47.6846
  104.0000  104.0000  116.0640   69.6602   22.5320   25.0640  -56.3398  -49.4680
  105.0000  105.0000   80.0526   77.0495   26.0971  -10.9474  -48.9505  -45.9029
  106.0000  106.0000  100.4602   76.5005   25.6732    9.4602  -49.4995  -46.3268
  107.0000  107.0000   68.3858   92.2002   30.2352  -22.6142  -33.7998  -41.7648
  108.0000  108.0000  116.9945   92.1617   30.6531   25.9945  -33.8383  -41.3469
  109.0000  109.0000   91.7574   87.2079   51.9505    0.7574  -38.7921  -20.0495
  110.0000  110.0000   92.3804   86.0692   60.6021    1.3804  -39.9308  -11.3979
  111.0000  111.0000   92.2207   73.6384   65.8862    1.2207  -52.3616   -6.1138
  112.0000  112.0000   92.1414   58.9415   56.8769    1.1414  -67.0585  -15.1231
  113.0000  113.0000   92.1458   54.0697   46.8593    1.1458  -71.9303  -25.1407
  114.0000  114.0000   92.1521   61.5706   37.9201    1.1521  -64.4294  -34.0799
  115.0000  115.0000   91.8647   71.1251   37.1039    0.8647  -54.8749  -34.8961
  116.0000  116.0000   91.3558   80.2002   40.3169    0.3558  -45.7998  -31.6831

输出解读：
第一列：ROI的索引，即标签序号。
第二列：区域的标签值，即该ROI的像素值。
第三列：质心在图像坐标系中的 I 坐标。
第四列：质心在图像坐标系中的 J 坐标。
第五列：质心在图像坐标系中的 K 坐标。
第六列：质心在物理坐标系中的 X 坐标。
第七列：质心在物理坐标系中的 Y 坐标。
第八列：质心在物理坐标系中的 Z 坐标。

注：此程序也可用来计算单一脑区的质心坐标，输入一个ROI，会输出相应的单个质心坐标。

参考资料：
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