Unique concatenation of multi-dimensional cell arrays

I have 15, k x k x k cell arrays, stacked ontop of each other ,where each cell contians a row vector. I would like to concactenate each row vector living in the living the the same poisition cell for all 15 cell arrays such that each of the row vectors doesn't have any repetitions

For the sake of clarity, suppose we have only two cell arrays of size 3 x 3,

A(:,:,1) = {[1;2;3],[],[3];
    [],[],[4];
    [],[2;3],[]}
A(:,:,2) = {[2;3;4],[4],[3];
    [],[],[4];
    [],[2;4],[]}

%I'd like the output to be

C = {[1;2;3;4],[4],[3];
    [],[],[4];
    [],[2;3;4],[]}

%This is possible to do with a for loop where each step of the for loop
%looks like

C{i} = unique(cat(1,A{i},B{i}))

However, since k can be fairly large and vectors in each cell are very large this turns out to be very inefficent for me. I don't suppose anyone knows of a quick way to do this? Many Thanks.

Edit the uniqueness is no longer an issue since if say we are able to perform the concactenation to obtain;

D = {[1;2;3;1;2;3;4],[4],[3;3];
    [],[],[4;4];
    [],[2;2;3;4;4],[]}
C = cellfun(@(x)unique(x), D, 'UniformOutput', false);

What still remains unsolvable to me is how one could obtain D from A. I should add that I have tried

cat(1,A(:,:,1),A(:,:,2))
cat(2,A(:,:,1),A(:,:,2))
cat(3,A(:,:,1),A(:,:,2))

none of which yeild the desired result.

Answer 1

[Matt J]

A(:,:,1) = {[1;2;3],[],[3];
    [],[],[4];
    [],[2;3],[]};
A(:,:,2) = {[2;3;4],[4],[3];
    [],[],[4];
    [],[2;4],[]};

C = cellfun(@union,A(:,:,1),A(:,:,2),'UniformOutput',false)

C = 3×3 cell array
    {4×1 double}    {[       4]}    {[       3]}
    {0×1 double}    {0×1 double}    {[       4]}
    {0×1 double}    {3×1 double}    {0×1 double}

[Milos]

Ahh great this is even simpler! I'll accept this as the awnser now since it is simpler for me.

Answer 2

[Voss]

A(:,:,1) = {[1;2;3],[],[3];
    [],[],[4];
    [],[2;3],[]};
A(:,:,2) = {[2;3;4],[4],[3];
    [],[],[4];
    [],[2;4],[]};

C = cellfun(@(a,b)unique([a;b]),A(:,:,1),A(:,:,2),'UniformOutput',false)

C = 3×3 cell array
    {4×1 double}    {[       4]}    {[       3]}
    {0×1 double}    {0×1 double}    {[       4]}
    {0×1 double}    {3×1 double}    {0×1 double}

[Milos]

ohhh I didn't know you could do this. I'm quite new to matlab and I'm a bit confused as to how the @(a,b)unique([a;b]) part works in cellfun. Do you have anysuggestions as to where I could read more about this?

[Stephen23]

"Do you have anysuggestions as to where I could read more about this?"

https://www.mathworks.com/help/matlab/matlab_prog/anonymous-functions.html