`im2col` 和 `col2im` 的高效实现 [英] Efficient Implementation of `im2col` and `col2im`

问题描述

MATLAB 的 im2col 和 col2im 是 MATLAB 中矢量化非常重要的函数，当处理图像.
然而，他们需要 MATLAB 的图像处理工具箱.

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.

我的问题是，是否有一种有效的(Vectorzied)方法来实现使用 MATLAB 的函数(没有工具箱)?
我需要 sliding 和 distinct 模式.

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.

我不需要任何填充.

谢谢.

推荐答案

我只能希望 Mathworks 的人不要就此起诉你或我或 Stackoverflow，试图创建他们的 IP 工具箱功能，因为他们为该工具箱定价.但无论如何，忘记这些问题，这里是实现.

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.

用'sliding'选项替换im2col

Replacement for im2col with 'sliding' option

直到我坐下来编写Stackoverflow 上另一个问题的解决方案之前，我无法将其矢量化.因此，我强烈建议您也研究一下.

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;

用'distinct'选项替换im2col

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;

<小时>

一些快速测试表明，这两种实现特别是 sliding 一个用于小到体面大小的输入数据和 distinct 对于所有数据大小的性能比内置的 MATLAB 函数好得多运行时性能方面的实现.

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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.

如何使用

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])

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