在R语言中实现Matlab专用函数

我需要计算R中的结构相似性（SSIM）指数，并且只能找到在Matlab中实现的方法。除了两种Matlab方法“fspecial”和“filter2”，在R中重新编写该方法似乎非常简单

F特殊返回11x11矩阵中的二维高斯分布，标准偏差为1.5：

h = fspecial('gaussian', 11, 1.5)

因此，我在R中实现了一个功能，该功能也可以在网上找到一些帮助：

gaussian2D <- function(amplitude) {
  # Defining limits of grid
  x_min <- 1
  x_max <- 11
  y_min <- x_min
  y_max <- x_max

  # Setting parameters of the two-dimensional Gaussian function 
  # The distribution is centred in [6,6]
  x_zero <- 6
  y_zero <- 6

  # Setting the spread of the filter
  sigma_x <- 1.5
  sigma_y <- sigma_x

  # Running through all x and y combinations applying the 2d-gaussian equation
  df <- NULL
  for (x_val in c(x_min:x_max)){
    for (y_val in c(y_min:y_max)){
      cell_value <- amplitude*exp(-( (((x_val-x_zero)^2)/(2*(sigma_x^2))) +     (((y_val-y_zero)^2)/(2*(sigma_y^2))) ))
      df = rbind(df,data.frame(x_val,y_val, cell_value))
    }
  }

  # Axis labels
  x_axis <- c(x_min:x_max)
  y_axis <- c(y_min:y_max)

  # Populating matrix
  gauss_matrix <- matrix(df[,3], nrow = 11, ncol = 11, dimnames = list(x_axis,     y_axis))

  return(gauss_matrix)
}

h2 = gaussian2D(1)

---

有人对我做错了什么有意见吗？

您缺少调整条件：1/（2*pi*sigma1*sigma2）

---

请注意，在MATLAB中，2*pi*1.5*1.5=14.13717

，

fspecial

还规范化了内核，使内核中所有元素的总和等于1。这是因为当使用该内核执行卷积时，它避免产生任何超出与您试图过滤的信号相关联的数据类型动态范围的输出值

这也避免了使用@imo之前所述的任何调整术语。非常简单，您没有在代码中规范化内核。因此，在循环中有一个额外的求和项，它对每个高斯项求和，那么最终的矩阵应该将每个项除以这个量：

  df <- NULL
  s <- 0 # Added
  for (x_val in c(x_min:x_max)){
    for (y_val in c(y_min:y_max)){
      cell_value <- amplitude*exp(-( (((x_val-x_zero)^2)/(2*(sigma_x^2))) +     (((y_val-y_zero)^2)/(2*(sigma_y^2))) ))
      df = rbind(df,data.frame(x_val,y_val, cell_value))
      s <- s + cell_value # Added
    }
  }

要再次检查，在MATLAB中，这是调用

fspecial

时得到的结果：

>> format long g
>> h = fspecial('gaussian', 11, 1.5)

h =

  Columns 1 through 3

      1.05756559815326e-06       7.8144115330536e-06      3.70224770827489e-05
       7.8144115330536e-06      5.77411251978637e-05      0.000273561160085806
      3.70224770827489e-05      0.000273561160085806        0.0012960555938432
      0.000112464355116679      0.000831005429087199       0.00393706926284678
      0.000219050652866017       0.00161857756253439       0.00766836382523672
      0.000273561160085806       0.00202135875836257       0.00957662749024029
      0.000219050652866017       0.00161857756253439       0.00766836382523672
      0.000112464355116679      0.000831005429087199       0.00393706926284678
      3.70224770827489e-05      0.000273561160085806        0.0012960555938432
       7.8144115330536e-06      5.77411251978637e-05      0.000273561160085806
      1.05756559815326e-06       7.8144115330536e-06      3.70224770827489e-05

  Columns 4 through 6

      0.000112464355116679      0.000219050652866017      0.000273561160085806
      0.000831005429087199       0.00161857756253439       0.00202135875836257
       0.00393706926284678       0.00766836382523672       0.00957662749024029
         0.011959760410037        0.0232944324734871        0.0290912256485504
        0.0232944324734871        0.0453713590956603        0.0566619704916846
        0.0290912256485504        0.0566619704916846         0.070762237763947
        0.0232944324734871        0.0453713590956603        0.0566619704916846
         0.011959760410037        0.0232944324734871        0.0290912256485504
       0.00393706926284678       0.00766836382523672       0.00957662749024029
      0.000831005429087199       0.00161857756253439       0.00202135875836257
      0.000112464355116679      0.000219050652866017      0.000273561160085806

  Columns 7 through 9

      0.000219050652866017      0.000112464355116679      3.70224770827489e-05
       0.00161857756253439      0.000831005429087199      0.000273561160085806
       0.00766836382523672       0.00393706926284678        0.0012960555938432
        0.0232944324734871         0.011959760410037       0.00393706926284678
        0.0453713590956603        0.0232944324734871       0.00766836382523672
        0.0566619704916846        0.0290912256485504       0.00957662749024029
        0.0453713590956603        0.0232944324734871       0.00766836382523672
        0.0232944324734871         0.011959760410037       0.00393706926284678
       0.00766836382523672       0.00393706926284678        0.0012960555938432
       0.00161857756253439      0.000831005429087199      0.000273561160085806
      0.000219050652866017      0.000112464355116679      3.70224770827489e-05

  Columns 10 through 11

       7.8144115330536e-06      1.05756559815326e-06
      5.77411251978637e-05       7.8144115330536e-06
      0.000273561160085806      3.70224770827489e-05
      0.000831005429087199      0.000112464355116679
       0.00161857756253439      0.000219050652866017
       0.00202135875836257      0.000273561160085806
       0.00161857756253439      0.000219050652866017
      0.000831005429087199      0.000112464355116679
      0.000273561160085806      3.70224770827489e-05
      5.77411251978637e-05       7.8144115330536e-06
       7.8144115330536e-06      1.05756559815326e-06

。。。最后在R中：

> h2
              1            2            3            4            5            6            7
1  1.057566e-06 7.814412e-06 3.702248e-05 0.0001124644 0.0002190507 0.0002735612 0.0002190507
2  7.814412e-06 5.774113e-05 2.735612e-04 0.0008310054 0.0016185776 0.0020213588 0.0016185776
3  3.702248e-05 2.735612e-04 1.296056e-03 0.0039370693 0.0076683638 0.0095766275 0.0076683638
4  1.124644e-04 8.310054e-04 3.937069e-03 0.0119597604 0.0232944325 0.0290912256 0.0232944325
5  2.190507e-04 1.618578e-03 7.668364e-03 0.0232944325 0.0453713591 0.0566619705 0.0453713591
6  2.735612e-04 2.021359e-03 9.576627e-03 0.0290912256 0.0566619705 0.0707622378 0.0566619705
7  2.190507e-04 1.618578e-03 7.668364e-03 0.0232944325 0.0453713591 0.0566619705 0.0453713591
8  1.124644e-04 8.310054e-04 3.937069e-03 0.0119597604 0.0232944325 0.0290912256 0.0232944325
9  3.702248e-05 2.735612e-04 1.296056e-03 0.0039370693 0.0076683638 0.0095766275 0.0076683638
10 7.814412e-06 5.774113e-05 2.735612e-04 0.0008310054 0.0016185776 0.0020213588 0.0016185776
11 1.057566e-06 7.814412e-06 3.702248e-05 0.0001124644 0.0002190507 0.0002735612 0.0002190507
              8            9           10           11
1  0.0001124644 3.702248e-05 7.814412e-06 1.057566e-06
2  0.0008310054 2.735612e-04 5.774113e-05 7.814412e-06
3  0.0039370693 1.296056e-03 2.735612e-04 3.702248e-05
4  0.0119597604 3.937069e-03 8.310054e-04 1.124644e-04
5  0.0232944325 7.668364e-03 1.618578e-03 2.190507e-04
6  0.0290912256 9.576627e-03 2.021359e-03 2.735612e-04
7  0.0232944325 7.668364e-03 1.618578e-03 2.190507e-04
8  0.0119597604 3.937069e-03 8.310054e-04 1.124644e-04
9  0.0039370693 1.296056e-03 2.735612e-04 3.702248e-05
10 0.0008310054 2.735612e-04 5.774113e-05 7.814412e-06
11 0.0001124644 3.702248e-05 7.814412e-06 1.057566e-06

---

。。。看起来和我很相配

切题地说，您可以查看

outer

和

expand.grid

。它们可以用来减轻嵌套的

for

循环。谢谢，我现在生成了我想要的！谢谢，我想知道那个号码是从哪里来的！我用圆周率尝试了各种各样的操作，但这是有意义的。

>> format long g
>> h = fspecial('gaussian', 11, 1.5)

h =

  Columns 1 through 3

      1.05756559815326e-06       7.8144115330536e-06      3.70224770827489e-05
       7.8144115330536e-06      5.77411251978637e-05      0.000273561160085806
      3.70224770827489e-05      0.000273561160085806        0.0012960555938432
      0.000112464355116679      0.000831005429087199       0.00393706926284678
      0.000219050652866017       0.00161857756253439       0.00766836382523672
      0.000273561160085806       0.00202135875836257       0.00957662749024029
      0.000219050652866017       0.00161857756253439       0.00766836382523672
      0.000112464355116679      0.000831005429087199       0.00393706926284678
      3.70224770827489e-05      0.000273561160085806        0.0012960555938432
       7.8144115330536e-06      5.77411251978637e-05      0.000273561160085806
      1.05756559815326e-06       7.8144115330536e-06      3.70224770827489e-05

  Columns 4 through 6

      0.000112464355116679      0.000219050652866017      0.000273561160085806
      0.000831005429087199       0.00161857756253439       0.00202135875836257
       0.00393706926284678       0.00766836382523672       0.00957662749024029
         0.011959760410037        0.0232944324734871        0.0290912256485504
        0.0232944324734871        0.0453713590956603        0.0566619704916846
        0.0290912256485504        0.0566619704916846         0.070762237763947
        0.0232944324734871        0.0453713590956603        0.0566619704916846
         0.011959760410037        0.0232944324734871        0.0290912256485504
       0.00393706926284678       0.00766836382523672       0.00957662749024029
      0.000831005429087199       0.00161857756253439       0.00202135875836257
      0.000112464355116679      0.000219050652866017      0.000273561160085806

  Columns 7 through 9

      0.000219050652866017      0.000112464355116679      3.70224770827489e-05
       0.00161857756253439      0.000831005429087199      0.000273561160085806
       0.00766836382523672       0.00393706926284678        0.0012960555938432
        0.0232944324734871         0.011959760410037       0.00393706926284678
        0.0453713590956603        0.0232944324734871       0.00766836382523672
        0.0566619704916846        0.0290912256485504       0.00957662749024029
        0.0453713590956603        0.0232944324734871       0.00766836382523672
        0.0232944324734871         0.011959760410037       0.00393706926284678
       0.00766836382523672       0.00393706926284678        0.0012960555938432
       0.00161857756253439      0.000831005429087199      0.000273561160085806
      0.000219050652866017      0.000112464355116679      3.70224770827489e-05

  Columns 10 through 11

       7.8144115330536e-06      1.05756559815326e-06
      5.77411251978637e-05       7.8144115330536e-06
      0.000273561160085806      3.70224770827489e-05
      0.000831005429087199      0.000112464355116679
       0.00161857756253439      0.000219050652866017
       0.00202135875836257      0.000273561160085806
       0.00161857756253439      0.000219050652866017
      0.000831005429087199      0.000112464355116679
      0.000273561160085806      3.70224770827489e-05
      5.77411251978637e-05       7.8144115330536e-06
       7.8144115330536e-06      1.05756559815326e-06

> h2
              1            2            3            4            5            6            7
1  1.057566e-06 7.814412e-06 3.702248e-05 0.0001124644 0.0002190507 0.0002735612 0.0002190507
2  7.814412e-06 5.774113e-05 2.735612e-04 0.0008310054 0.0016185776 0.0020213588 0.0016185776
3  3.702248e-05 2.735612e-04 1.296056e-03 0.0039370693 0.0076683638 0.0095766275 0.0076683638
4  1.124644e-04 8.310054e-04 3.937069e-03 0.0119597604 0.0232944325 0.0290912256 0.0232944325
5  2.190507e-04 1.618578e-03 7.668364e-03 0.0232944325 0.0453713591 0.0566619705 0.0453713591
6  2.735612e-04 2.021359e-03 9.576627e-03 0.0290912256 0.0566619705 0.0707622378 0.0566619705
7  2.190507e-04 1.618578e-03 7.668364e-03 0.0232944325 0.0453713591 0.0566619705 0.0453713591
8  1.124644e-04 8.310054e-04 3.937069e-03 0.0119597604 0.0232944325 0.0290912256 0.0232944325
9  3.702248e-05 2.735612e-04 1.296056e-03 0.0039370693 0.0076683638 0.0095766275 0.0076683638
10 7.814412e-06 5.774113e-05 2.735612e-04 0.0008310054 0.0016185776 0.0020213588 0.0016185776
11 1.057566e-06 7.814412e-06 3.702248e-05 0.0001124644 0.0002190507 0.0002735612 0.0002190507
              8            9           10           11
1  0.0001124644 3.702248e-05 7.814412e-06 1.057566e-06
2  0.0008310054 2.735612e-04 5.774113e-05 7.814412e-06
3  0.0039370693 1.296056e-03 2.735612e-04 3.702248e-05
4  0.0119597604 3.937069e-03 8.310054e-04 1.124644e-04
5  0.0232944325 7.668364e-03 1.618578e-03 2.190507e-04
6  0.0290912256 9.576627e-03 2.021359e-03 2.735612e-04
7  0.0232944325 7.668364e-03 1.618578e-03 2.190507e-04
8  0.0119597604 3.937069e-03 8.310054e-04 1.124644e-04
9  0.0039370693 1.296056e-03 2.735612e-04 3.702248e-05
10 0.0008310054 2.735612e-04 5.774113e-05 7.814412e-06
11 0.0001124644 3.702248e-05 7.814412e-06 1.057566e-06