我需要在R中计算结构相似度（SSIM）索引，并且只能找到在Matlab中实现的方法。在R中重写方法似乎很简单，除了两个Matlab方法“fspecial”和“filter2”。
fspecial返回标准除数为1.5的11x11矩阵中的二维高斯分布：
h = fspecial('gaussian', 11, 1.5)
所以我已经实现了一个功能，它应该在R中做同样的事情，并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)
然而，奇怪的是，当我运行这两种方法时，我得不到相同的结果，而是得到一个由14.13缩放的矩阵：
h2/h
1 2 3 4 5 6 7 8 9 10 11
1 14.13137 14.13185 14.13201 14.13238 14.13187 14.13189 14.13187 14.13238 14.13201 14.13185 14.13137
2 14.13185 14.13186 14.13189 14.13175 14.13164 14.13154 14.13164 14.13175 14.13189 14.13186 14.13185
3 14.13201 14.13189 14.13135 14.13172 14.13176 14.13187 14.13176 14.13172 14.13135 14.13189 14.13201
4 14.13238 14.13175 14.13172 14.13155 14.13209 14.13194 14.13209 14.13155 14.13172 14.13175 14.13238
5 14.13187 14.13164 14.13176 14.13209 14.13194 14.13182 14.13194 14.13209 14.13176 14.13164 14.13187
6 14.13189 14.13154 14.13187 14.13194 14.13182 14.13188 14.13182 14.13194 14.13187 14.13154 14.13189
7 14.13187 14.13164 14.13176 14.13209 14.13194 14.13182 14.13194 14.13209 14.13176 14.13164 14.13187
8 14.13238 14.13175 14.13172 14.13155 14.13209 14.13194 14.13209 14.13155 14.13172 14.13175 14.13238
9 14.13201 14.13189 14.13135 14.13172 14.13176 14.13187 14.13176 14.13172 14.13135 14.13189 14.13201
10 14.13185 14.13186 14.13189 14.13175 14.13164 14.13154 14.13164 14.13175 14.13189 14.13186 14.13185
11 14.13137 14.13185 14.13201 14.13238 14.13187 14.13189 14.13187 14.13238 14.13201 14.13185 14.13137
有没有人建议我做错了什么？
答案 0 :(得分：2)
您缺少调整期限：1 /（2 * pi * sigma1 * sigma2）
注意2 * pi * 1.5 * 1.5 = 14.13717
答案 1 :(得分：1)
在MATLAB中，fspecial也规范化内核，以便内核中所有元素的总和等于1.这是因为在使用此内核执行卷积时，它会避免产生超出与您尝试过滤的信号相关联的数据类型的动态范围的任何输出值。
这也避免了必须使用@imo之前所述的任何调整术语。很简单，您并没有在代码中规范化内核。因此，在你的循环中有一个额外的求和项，它对每个高斯项求和，那么最终矩阵应该将每个条目除以这个数量：
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
}
}
最后，当你返回矩阵时：
return(gauss_matrix / s)
要仔细检查，在MATLAB中，这是您拨打fspecial时所获得的信息：
>> 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：
> 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
......看起来和我匹配！