Defining a pixel neighborhood in an array in MATLAB

I am working with matrix operations in MATLAB, and I would have the following problem. I have matrix containing zero elements:

a=zeros(100,100)

and another matrix with significantly smaller dimension containing value 6:

b=6*ones(3,3)

I define some coordinates in matrix a: a(45,50). I also consider this point as center of matrix b(2,2). I need to copy to matrix a the elements from matrix b, whose center is defined by b(2,2). I just know that it can be done manually by defining coordinates in matrix a. Please, is there any way, or inbuilt MATLAB function how to do it automatically? I am just MATLAB beginner.

• Are there additional details you would share to help improve answers? – Laurent Duval Sep 3 '16 at 17:09

Just for the display, the following works as long as you are doing right: you do not try to copy b values outside of a, because you did not specify what should be done when you are at a(100,100). My choice is a circular shift, with a toroidal topology.

% a = zeros(100); aX = 45 ; aY = 50;
a = zeros(12); aCenter = [4 6];
b = 6 * ones(3); bCenter = ceil(size(b)/2);

Basically, this creates a 2D logical indexing of b of the same size as a, with ones in the top left:

then circshift moves this pattern by the vector aCenter-bCenter:

circshift(...)

Finally, the elements of a with the above logical indexing are affected with the values in b.

You can easily do this by using the sparse function, which allows you to construct matrices by supplying a list of non-zero indices. Here is a short example. Note that I have formatted the local blocks to show the matrix structure, even though they are represented as vectors.

% Define i indices in local coordinates
i = [-1,  0,  1,...
-1   0   1,...
-1   0   1];
% Define j indices in local coordinates
j = [ 1,  1,  1,...
0   0   0,...
-1  -1  -1];
% Construct 100 x 100 sparse matrix by using offsets
a = sparse(i + 45, j + 50, 6, 100, 100);
% Show subset of matrix
full(a(43:47, 48:52))
• Thank you very much for response, but, unfortunately, I would need to make it without using of sparse matrix. Please, is there any way how to make it with using common matrix format (zeros (100,100))? Thank you very much. – jendula11 Aug 26 '16 at 12:18