Efficient Implementation of `im2col` and `col2im`

Question

MATLAB's `im2col` and `col2im` are very important function for vectorization in MATLAB when dealing with images. Yet they require MATLAB's Image Processing Toolbox. My question is, is there an efficient (Vectorzied) way to implement the using MATLAB's functions (With no toolbox)? I need both the `sliding` and `distinct` mode. I don't need any padding. Thank You.

Accepted Answer

I can only hope that Mathworks guys don't sue you or me or `Stackoverflow` for that matter, trying to create vectorized implementations of their IP toolbox functions, as they have put price on that toolbox. But in any case, forgetting those issues, here are the implementations.

Replacement for `im2col` with `'sliding'` option

I wasn't able to vectorize this until I sat down to write solution to another problem on Stackoverflow. So, I would strongly encourage to look into it too.

```
function out = im2col_sliding(A,blocksize)

nrows = blocksize(1);
ncols = blocksize(2);

%// Get sizes for later usages
[m,n] = size(A);

%// Start indices for each block
start_ind = reshape(bsxfun(@plus,[1:m-nrows+1]',[0:n-ncols]*m),[],1); %//'

%// Row indices
lin_row = permute(bsxfun(@plus,start_ind,[0:nrows-1])',[1 3 2]);  %//'

%// Get linear indices based on row and col indices and get desired output
out = A(reshape(bsxfun(@plus,lin_row,[0:ncols-1]*m),nrows*ncols,[]));

return;
```

Replacement for `im2col` with `'distinct'` option

```
function out = im2col_distinct(A,blocksize)

nrows = blocksize(1);
ncols = blocksize(2);
nele = nrows*ncols;

row_ext = mod(size(A,1),nrows);
col_ext = mod(size(A,2),ncols);

padrowlen = (row_ext~=0)*(nrows - row_ext);
padcollen = (col_ext~=0)*(ncols - col_ext);

A1 = zeros(size(A,1)+padrowlen,size(A,2)+padcollen);
A1(1:size(A,1),1:size(A,2)) = A;

t1 = reshape(A1,nrows,size(A1,1)/nrows,[]);
t2 = reshape(permute(t1,[1 3 2]),size(t1,1)*size(t1,3),[]);
t3 =  permute(reshape(t2,nele,size(t2,1)/nele,[]),[1 3 2]);
out = reshape(t3,nele,[]);

return;
```

Some quick tests show that both these implementations particularly `sliding` one for small to decent sized input data and `distinct` for all datasizes perform much better than the in-built MATLAB function implementations in terms of runtime performance.

How to use

```
With in-built MATLAB function - 
B = im2col(A,[nrows ncols],'sliding')

With our custom function - 
B = im2col_sliding(A,[nrows ncols])

%// ------------------------------------

With in-built MATLAB function - 
B = im2col(A,[nrows ncols],'distinct')

With our custom function - 
B = im2col_distinct(A,[nrows ncols])
```

Efficient Implementation of `im2col` and `col2im`

Solution

Problem

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