Rearrange sliding blocks into columns for a 3D array (IM2COL in 3D) - MATLAB

Question

Given a matrix A(mxnxc) (c can be arbitrary), I want to sample patches(pxp) in sliding window scheme with stepsize d, and rearrange all the pxpxc patches into vectors. I can do it within nested for-loops, but it is very time consuming. How to do this quickly?

Answer 1

One can extend this solution to Efficient Implementation of im2col and col2im again with bsxfun for a 3D array case to solve your case.

Now, there are two possible interpretations to the question :

• Extract blocks of size p x p and as vectors each, do this for entire first 2D slice and then repeat this for all slices in 3D, resulting in a 3D output.

• Gather blocks of size p x p x c as vectors each and do this in a sliding manner across the entire array, resulting in a 2D output.

These two interpretations are implemented as im2col_3D_sliding_v1 and im2col_3D_sliding_v2 respectively and listed next.

im2col_3D_sliding_v1 :

function out = im2col_3D_sliding_v1(A,blocksize,stepsize)

%// Store blocksizes
nrows = blocksize(1);
ncols = blocksize(2);

%// Store stepsizes along rows and cols
d_row = stepsize(1);
d_col = stepsize(2);

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

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

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

%// 2D linear indices
lidx_2D = reshape(bsxfun(@plus,lin_row,[0:ncols-1]*m),nrows*ncols,[]);

%// 3D linear indices
lidx_3D = bsxfun(@plus,lidx_2D,m*n*permute((0:r-1),[1 3 2]));

%// Get linear indices based on row and col indices and get desired output
out = A(lidx_3D);

return;

im2col_3D_sliding_v2 :

function out = im2col_3D_sliding_v2(A,blocksize,stepsize)

%// Store blocksizes
nrows = blocksize(1);
ncols = blocksize(2);

%// Store stepsizes along rows and cols
d_row = stepsize(1);
d_col = stepsize(2);

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

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

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

%// 2D linear indices
lidx_2D = reshape(bsxfun(@plus,lin_row,[0:ncols-1]*m),nrows*ncols,[]);

%// 3D linear indices
lidx_3D = bsxfun(@plus,permute(lidx_2D,[1 3 2]),m*n*(0:r-1));

%// Final 2D linear indices
lidx_2D_final = reshape(lidx_3D,[],size(lidx_2D,2));

%// Get linear indices based on row and col indices and get desired output
out = A(lidx_2D_final);

return;

Sample runs

(I) Input array :

>> A
A(:,:,1) =
    23   109    63     1    37   153
   110    31   201    57    69   230
    66   127    19     1    45   240
    76   181   101    49    36    57
A(:,:,2) =
   124    18   244     2   141    95
    96   112   110   174    56   228
   134    45   246   181   197   219
    68     7   195   165    59   103

(II) Input parameters :

>> blocksize = [2,3]; %// blocksize along rows, cols
>> stepsize = [2,2];  %// stepsize along rows, cols

(III) Outputs with two versions :

>> im2col_3D_sliding_v1(A,blocksize,stepsize)
ans(:,:,1) =
    23    66    63    19
   110    76   201   101
   109   127     1     1
    31   181    57    49
    63    19    37    45
   201   101    69    36
ans(:,:,2) =
   124   134   244   246
    96    68   110   195
    18    45     2   181
   112     7   174   165
   244   246   141   197
   110   195    56    59

   >> im2col_3D_sliding_v2(A,blocksize,stepsize)
ans =
    23    66    63    19
   110    76   201   101
   109   127     1     1
    31   181    57    49
    63    19    37    45
   201   101    69    36
   124   134   244   246
    96    68   110   195
    18    45     2   181
   112     7   174   165
   244   246   141   197
   110   195    56    59