MATLAB: Fast interp on 1 dimension of 3d matrix

Question

1. Assume a Matrix A which is (M X N X P) array.

I want to upsample one dimension of the matrix, for example: upsample the third dimension by factor of 2.

Currently I'm using loops to make it happen:

B = zeros(M, N, 2 * P);

for ii = 1 : M

for jj = 1 : N

B(ii, jj, 🙂 = interp(double(A(ii, jj, :)), 2);

end

end

Is there any way to do so which doesn't include any use of loops?

Answer 1

Use interp3 or interpn:

>> A = randi(9,5,7,3)
A(:,:,1) =
   3   3   5   3   8   1   2
   8   7   3   4   9   9   2
   3   5   7   8   6   4   9
   2   9   1   7   3   6   6
   2   5   8   9   7   9   2
A(:,:,2) =
   3   6   9   5   3   5   4
   6   8   1   6   9   5   8
   8   5   5   9   4   2   9
   7   6   5   2   7   6   4
   8   4   2   6   1   6   4
A(:,:,3) =
   5   2   1   9   9   8   1
   9   8   5   5   8   8   2
   9   6   2   1   8   9   4
   5   1   4   9   7   4   2
   1   1   4   8   9   8   8
>> S = size(A);
>> Z = interpn(A,1:S(1),1:S(2),1:0.5:S(3)) % halve the step size
Z(:,:,1) =
   3.0   3.0   5.0   3.0   8.0   1.0   2.0
   8.0   7.0   3.0   4.0   9.0   9.0   2.0
   3.0   5.0   7.0   8.0   6.0   4.0   9.0
   2.0   9.0   1.0   7.0   3.0   6.0   6.0
   2.0   5.0   8.0   9.0   7.0   9.0   2.0
Z(:,:,2) =
   3.0   4.5   7.0   4.0   5.5   3.0   3.0
   7.0   7.5   2.0   5.0   9.0   7.0   5.0
   5.5   5.0   6.0   8.5   5.0   3.0   9.0
   4.5   7.5   3.0   4.5   5.0   6.0   5.0
   5.0   4.5   5.0   7.5   4.0   7.5   3.0
Z(:,:,3) =
   3.0   6.0   9.0   5.0   3.0   5.0   4.0
   6.0   8.0   1.0   6.0   9.0   5.0   8.0
   8.0   5.0   5.0   9.0   4.0   2.0   9.0
   7.0   6.0   5.0   2.0   7.0   6.0   4.0
   8.0   4.0   2.0   6.0   1.0   6.0   4.0
Z(:,:,4) =
   4.0   4.0   5.0   7.0   6.0   6.5   2.5
   7.5   8.0   3.0   5.5   8.5   6.5   5.0
   8.5   5.5   3.5   5.0   6.0   5.5   6.5
   6.0   3.5   4.5   5.5   7.0   5.0   3.0
   4.5   2.5   3.0   7.0   5.0   7.0   6.0
Z(:,:,5) =
   5.0   2.0   1.0   9.0   9.0   8.0   1.0
   9.0   8.0   5.0   5.0   8.0   8.0   2.0
   9.0   6.0   2.0   1.0   8.0   9.0   4.0
   5.0   1.0   4.0   9.0   7.0   4.0   2.0
   1.0   1.0   4.0   8.0   9.0   8.0   8.0

Generate the required indices either using the colon operator (as shown, e.g. to halve the step size) or linspace (e.g. to double the number of points):

Z = interpn(A,1:S(1),1:S(2),linspace(1,S(3),2*S(3))) % double the number of points
Z(:,:,1) =
   3.0   3.0   5.0   3.0   8.0   1.0   2.0
   8.0   7.0   3.0   4.0   9.0   9.0   2.0
   3.0   5.0   7.0   8.0   6.0   4.0   9.0
   2.0   9.0   1.0   7.0   3.0   6.0   6.0
   2.0   5.0   8.0   9.0   7.0   9.0   2.0
Z(:,:,2) =
   3.0   4.2   6.6   3.8   6.0   2.6   2.8
   7.2   7.4   2.2   4.8   9.0   7.4   4.4
   5.0   5.0   6.2   8.4   5.2   3.2   9.0
   4.0   7.8   2.6   5.0   4.6   6.0   5.2
   4.4   4.6   5.6   7.8   4.6   7.8   2.8
Z(:,:,3) =
   3.0   5.4   8.2   4.6   4.0   4.2   3.6
   6.4   7.8   1.4   5.6   9.0   5.8   6.8
   7.0   5.0   5.4   8.8   4.4   2.4   9.0
   6.0   6.6   4.2   3.0   6.2   6.0   4.4
   6.8   4.2   3.2   6.6   2.2   6.6   3.6
Z(:,:,4) =
   3.4   5.2   7.4   5.8   4.2   5.6   3.4
   6.6   8.0   1.8   5.8   8.8   5.6   6.8
   8.2   5.2   4.4   7.4   4.8   3.4   8.0
   6.6   5.0   4.8   3.4   7.0   5.6   3.6
   6.6   3.4   2.4   6.4   2.6   6.4   4.8
Z(:,:,5) =
   4.2   3.6   4.2   7.4   6.6   6.8   2.2
   7.8   8.0   3.4   5.4   8.4   6.8   4.4
   8.6   5.6   3.2   4.2   6.4   6.2   6.0
   5.8   3.0   4.4   6.2   7.0   4.8   2.8
   3.8   2.2   3.2   7.2   5.8   7.2   6.4
Z(:,:,6) =
   5.0   2.0   1.0   9.0   9.0   8.0   1.0
   9.0   8.0   5.0   5.0   8.0   8.0   2.0
   9.0   6.0   2.0   1.0   8.0   9.0   4.0
   5.0   1.0   4.0   9.0   7.0   4.0   2.0
   1.0   1.0   4.0   8.0   9.0   8.0   8.0