How to use matrix elements as indices to access elements of another matrix

I have a 5*4 matrix 'Id'

Id = [1 2 1 1; 
      1 2 2 2; 
      3 1 3 1;
      1 2 3 1; 
      2 2 3 3]

I have another matrix Values of size 5*4*3

Values(:,:,1) = [0 0 1 2;
                 2 2 1 1;
                 2 1 0 0;
                 1 1 2 1;
                 2 1 2 2]

Values(:,:,2) = [1 0 1 2;
                 2 0 2 1;
                 1 1 2 0;
                 1 0 2 1;
                 1 2 2 0]

Values(:,:,3) = [1 2 1 0;
                 2 0 2 1;
                 2 0 1 2;
                 0 0 2 1;
                 1 1 2 2]

I want the resultant matrix of size 5*4 to be using the value in Id as the index to pick corresponding elements from Values ie.

Result(i,j) = Values(i,j,Id(i,j)) 

Result = [0 0 1 2;
          2 0 2 1;
          2 1 1 0;
          1 0 2 1;
          1 2 2 2]

How do I do this without a for loop?

Answer 1

[Azzi Abdelmalek]

Values(:,:,1) = [0 0 1 2 
  2 2 1 1 
  2 1 0 0 
  1 1 2 1 
  2 1 2 2]
Values(:,:,2) = [1 0 1 2 
  2 0 2 1 
  1 1 2 0 
  1 0 2 1 
  1 2 2 0]
Values(:,:,3) = [1 2 1 0 
  2 0 2 1 
  2 0 1 2 
  0 0 2 1 
  1 1 2 2]
Id = [1 2 1 1 
  1 2 2 2 
  3 1 3 1 
  1 2 3 1 
  2 2 3 3]
[n,m]=size(Id)
[x,y]=ndgrid(1:n,1:m)
idl=sub2ind(size(Values),x,y,Id)
Result=Values(idl)

Answer 2

[Stephen23]

>> S = size(Values);
>> [R,C] = ndgrid(1:S(1),1:S(2));
>> X = sub2ind(S,R,C,Id);
>> out = Values(X)
out =
   0     0     1     2
   2     0     2     1
   2     1     1     0
   1     0     2     1
   1     2     2     2