Matlab中的函数movmean是否创建了矩阵的所有维度的平均值？

Question

I am trying to smooth the temporal history of each pixel in my matrix- in other words, trying to smooth each pixel through both 'space' (mxn) and 'time'(third dimension). I am using the function movmean to create an average of each pixel in time of a 1000x1000x8 matrix.

I am currently using the following code to take an average, using a window size of 5, operating along the third dimension:

av_matrix = movmean(my_matrix,5,3)

This is creating an average as expected, but I'm wondering if the window is just operating in the mxn direction and not taking the average along the third dimension as well.

Answer 1

To compute a moving average along the n dimensions of an n -dimensional array (the "window" is an n -dimensional rectangle), the simplest way is to use convolution (see convn ).

You need to be careful with edge effects , that is, when the convolution kernel (or n -dimensional window) partially slides out of the data. What movmean does is average over the actual data points only. To achieve that behaviour you can

1. compute the sum over the kernel via convolution with the 'same' option; and then
2. divide each entry by the number of actual data points from which it was computed. This number can also be obtaind via convolution, namely, applying the kernel to an array of ones.

So, all you need is:

my_matrix = randi(9,5,5,3); % example 3D array
sz = [3 3 2]; % 3D window size
av_matrix = convn(my_matrix, ones(sz), 'same') ...          % step 1
          ./convn(ones(size(my_matrix)), ones(sz), 'same'); % step 2

Check :

The following examples use

>> my_matrix
my_matrix(:,:,1) =
     6     8     2     1     8
     4     6     7     9     8
     4     5     1     4     3
     5     5     8     7     9
     3     6     6     4     9
my_matrix(:,:,2) =
     8     8     5     3     6
     8     9     6     9     1
     9     5     6     2     2
     1     7     4     1     2
     5     4     7     4     9
my_matrix(:,:,3) =
     6     5     8     6     6
     1     6     8     6     1
     5     5     1     6     7
     1     1     2     9     8
     1     2     6     1     2

With edge effects:

>> mean(mean(mean(my_matrix(1:2,1:2,1:2))))
ans =
   7.125000000000000
>> av_matrix(1,1,1)
ans =
   7.125000000000000

Without edge effects:

>> mean(mean(mean(my_matrix(1:3,1:3,1:2))))
ans =
   5.944444444444445

>> av_matrix(2,2,1)
ans =
   5.944444444444445