How to crop arrays using a vector? (reverse of padarray)

*Short version: I'm looking for the reverse of padarray, where you can do padarray(a,[2 2 2]), but instead have it crop [2 2 2] instead of pad [2 2 2]. (Or alternatively, imcrop for more then two dimensions); *

Long version: I have a cell arrays of unknown size K, each cell in the array contains an numerical array with dimensions (m,n,k,... )importantly:

          1. I don't know beforehand how many dimensions there will be for the 
             numerical arrays in the different cell arrays, but I
             know that within a cell array all the numerical arrays will have 
             the same number of dimensions. 

          2. While all the arrays have the same number of dimensions, they 
             differ in size.

Basically I want to make a functions that crops the numerical arrays to the smallest dimensions, and then concatenates them, i.e. if

      a{1} = zeros(10,10)
      a{2} = zeros(16,6)
      a{3} = zeros(6,6)

I want the outcome to be an array c with size (6,6,3).

I guess the problem is that I don't know how to index the arrays for a variable amount of dimensions. That is, I can get the size to which I need to crop (or the number by which I need to crop) in vector form like [6 6] or [15 4 8], but I don't know how to use this vector to index my arrays.

Thanks in advance!

Edit: Just thought of something, but it's very ugly: if we know we want to crop to an array of size (30,30,30)

minSize = [30 30 30]
c = []

for ii = length(a);
  temp = a{ii}(:);

    mask = zeros(minSize)
    padding = (minSize - size(a{ii})./2;
    mask = padarray(mask,padding,1,'both');
    mask = logical(mask);
    temp(mask)= [];

    temp = reshape(temp,minSize);
    c = cat(ndim(a{ii})+1,c,temp);
  end

[Jan]

Do you know an upper limit for the number of dimensions?

[Kerwin]

No, they can theoretically be of any nr.

Answer 1

[Sean de Wolski]

So something along the lines of:

x = rand(10,6,8,9);
nd = ndims(x);
c = repmat({':'},nd-1,1);
for ii = 1:nd;
  x = shiftdim(x,1);
  x = x(3:end-2,c{:});
end

[Kerwin]

Definitely better than my solution, thanks!

On second inspection, for large arrays this operation is fairly slow, because shiftdim is quite intensive. I really wish there was a way to use vectors for dimensions.

Answer 2

[nanren888]

Sorry I do not know paddarray, so maybe I am answering the wrong question.

I can give you parts of a way to do it. There may be more elegant ways. Indexing any number of dimensions is supported by Matlab's cool mechanism of using cell arrays as parameters;

Short version:

(1) Find the size you want with size & min

(2) Create a cell array of the ranges you want indC = {1:4 1:5 1:6 1:2 ...}

(3) Use < for all cells k > c{k} = c{k}(indC{:});

Longer version:

It seems finding the size you want to crop to is easy, just go through all cells with some sort of min(), eg collect all sizes & use min(?,dim), or manually take minimum values.

Maybe for the indexing, this will help

gg = randn([2 3 4 2]);

szVec = size(gg);

nDim = length(szVec);

.... cropSize = [nDim,1] array of desired dimensions as above

ind = {};

for k = 1:nDim

 ind = [ind 1:cropSize(k)]; % I presume you want 1:cropSize

end

smallerGg = gg(ind{:});

Hope it helps

[nanren888]

Yeah, Mine won't suffer to the same extent from the extremely slow moves, I guess.

Maybe you could profile them for us, on a reasonable number of trials?

I guess what you asked for "vectors for dimensions" I did with cells for dimensions.

%% timeMultiDimStuff.m

x = rand(10,6,8,9,5,6,4,5,5);

y = zeros(size(x));

nDim = ndims(x);

cropSize = [8,6,7,3,4,5,3,5,4];

ind = {};

for k = 1:nDim

   ind = [ind 1:cropSize(k)];

end

nTrial = 1000;

tic();

for k = 1:nTrial

    y = x(ind{:}); %#ok<NASGU>

end

toc();

Run with your solution & compare?

Elapsed time is 5.751869 seconds. (You have to run both on the same machine :))

[Kerwin]

sorry for the late reply!

Your solution works very well, I quickly tested it on some arrays, the largest being 4 arrays of each 5 dimensions, with the largest array having approx 40 million elements.

The earlier proposed solution with shiftdim took 9.87 seconds. Your solution took 2.01 seconds, a very nice speed-up! I expect that on my larger arrays this difference will become even more pronounced.

Thanks again!