# Matrix Average of neighbour values

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Kiwala Martin on 19 Feb 2020
Edited: Kiwala Martin on 19 Feb 2020
After creating a matrix of order MxM it will then output a new matrix in which each element is calculated from the original matrix by finding the average of each element adjacent (horizontally, vertically, excluding diagonal elements) to the original element including the element itself.
For example
M=3
then matrix is
[1,2,3;6,5,4;7,8,9]
element
�(1,1) = (1 + 2 + 6 )/ 3 = 3
(1,2) = (1 + 2 + 3 + 5 ) /4 = 3
Kiwala Martin on 19 Feb 2020
I have tried using :
Result = conv2(M, ones(3), 'same')./conv2(ones(3),ones(3), 'same')
But this approach includes the diagonal neighbours, how can i exclude them.

Marta G on 19 Feb 2020
Hello!
I think using conv2 was a great idea. However, you should use it like this
DIM=3;
aa=[0 1 0;1 1 1;0 1 0];
matrix=[1,2,3;6,5,4;7,8,9];
conv2(matrix, aa, 'same')./conv2(ones(DIM),aa, 'same')
This way of convolution does not account for diagonal neighbours. Afterwards, if you do not want decimals, use ceil or round depending on your desire.
Hope this helps :)
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Marta G on 19 Feb 2020
Edited: Marta G on 19 Feb 2020
You are welcome! The good thing is that you dont need to change de aa matrix.
M=4
N=3
matrix=[1,2,3;6,5,4;7,8,9;7,8,9]
aa=[0 1 0;1 1 1;0 1 0];
conv2(matrix, aa, 'same')./conv2(ones(M,N),aa, 'same')
Since you are using 'same' : returns the central part of the convolution that is the same size as matrix.
You still have the same dimensions as before while using aa still. With matrix being:
1 2 3
6 5 4
7 8 9
7 8 9
you get
ans =
3.0000 2.7500 3.0000
4.7500 5.0000 5.2500
7.0000 7.4000 7.5000
7.3333 8.0000 8.6667
Kiwala Martin on 19 Feb 2020
Edited: Kiwala Martin on 19 Feb 2020
Thank you very much Marta.