Matrix Average of neighbour values

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]

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.

Thanks in advance

Answer 1

[Marta G]

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 :)

[Kiwala Martin]

Hello Marta,

Thank you for your response.

It really does exactly what i need.

However in the case i have a MxN matrix how do i form the aa matrix of ones and zeros just like the one you have above

[Marta G]

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]

Thank you very much Marta.

This has been very helpful.