Correlation of 2D matrix and 3D Matrix

Hi,

I have a 3D matrix/array A and a 2D matrix/array B. I want to correlate index B(i,j) to A(i,j,k) where the element (1,1) of B is equal to element (1,1,k) of A. How do I do this?

Answer 1

[BhaTTa]

To correlate an element B(i,j) of a 2D matrix B with an element A(i,j,k) of a 3D matrix A where B(i,j) is equal to A(i,j,k) for some k, you essentially need to find the k value for each (i,j) pair where this condition is satisfied. This implies searching through the third dimension of A for each (i,j) pair to find the k that makes A(i,j,k) equal to B(i,j).

Assuming that for each (i,j) there is only one such k, and also assuming that the matrices A and B are related as described, you can perform this search using MATLAB. Here's a conceptual approach:

Step-by-step Approach

1. Initialize: Create an output matrix K of the same size as B to store the k values.
2. Loop through B: For each element in B, search through the corresponding stack in A to find the matching k.
3. Store the k value: Once the correct k is found, store it in K.

% Assuming A is your 3D matrix and B is your 2D matrix
A = rand(5,5,10); % Example 3D matrix (for demonstration)
B = A(:,:,5);     % Example 2D matrix taken from the 5th layer of A

% Initialize K with zeros
K = zeros(size(B));

% Loop through each element in B
for i = 1:size(B,1) % Rows
    for j = 1:size(B,2) % Columns
        % Find the k for which A(i,j,k) is equal to B(i,j)
        % This example assumes there's always a match
        for k = 1:size(A,3) % Depth/3rd dimension
            if A(i,j,k) == B(i,j)
                K(i,j) = k; % Store the k value
                break; % Exit the loop once the match is found
            end
        end
    end
end

% Display the K matrix
disp(K);

This method provides a basic framework to correlate elements between a 2D and a 3D matrix based on your specified condition. Adjustments may be necessary depending on the exact nature of your data and requirements.