MATLAB: How to reduce the computation time for adding 3D-array

Question

Hi, I am trying to add multiple 3D-arrays to a bigger 3D-array at a specific index (x,y,z)

Below is the code, and it does work and compute the answer but it seems very ineffecient.

In this example, i only have 4 sets of coordiantes (x,y,z) but in real code, i have more than 1e6 sets of points.

It takes very long to compute the result with that many points.

Is there any way to reduce the computation time?

Thank you in advance

Regards

J

Big=zeros(500,500,500); %%%% Bigger Array
Small=rand(250,250,250);
x=[245; 220; 256; 270];
y=[245; 220; 256; 270];
z=[245; 220; 256; 270];
     for n = 1 : length(x)
        x_cord=x(n)-length(Small)/2; 
        y_cord=y(n)-length(Small)/2;
        z_cord=z(n)-length(Small)/2;
        x_end= x_cord + length(Small) -1 ;
        y_end= y_cord + length(Small) -1;
        z_end=z_cord + length(Small) -1;
            if x_end <= length(Big)    
                Big(x_cord:x_end, y_cord:y_end,z_cord:z_end)=Big(x_cord:x_end, y_cord:y_end,z_cord:z_end)+Small();
            end 
         
     end

Answer 1

You can reformulate the loop as convolution of

A = accumarray([x(:) y(:) z(:)]-length(Small)/2,1,[500 500 500])

and

B = flip(flip(flip(Small,1),2),3)

(I left out the detail of overflowed for simplicity)

You might look at convn function. The problem I see is that A is sparse (1/125 in density) and might not be efficient as for loop.

You also might try this FEX to see if you can exploit the sparsity

https://www.mathworks.com/matlabcentral/fileexchange/41310-sparse-matrix-convolution

Or this one using different method of compute convolution

https://www.mathworks.com/matlabcentral/fileexchange/24504-fft-based-convolution