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Understanding Columnwise Processing Using Column Processing with Sliding Neighborhood Operations |

Performing sliding neighborhood and distinct block operations columnwise, when possible, can reduce the execution time required to process an image.

For example, suppose the operation you are performing involves
computing the mean of each block. This computation is much faster
if you first rearrange the blocks into columns, because you can compute
the mean of every column with a single call to the `mean` function,
rather than calling `mean` for each block individually.

To use column processing, use the `colfilt` function
. This function

For a sliding neighborhood operation, `colfilt` creates
a temporary matrix that has a separate column for each pixel in the
original image. The column corresponding to a given pixel contains
the values of that pixel's neighborhood from the original image.

The following figure illustrates this process. In this figure,
a 6-by-5 image matrix is processed in 2-by-3 neighborhoods. `colfilt` creates
one column for each pixel in the image, so there are a total of 30
columns in the temporary matrix. Each pixel's column contains the
value of the pixels in its neighborhood, so there are six rows. `colfilt` zero-pads
the input image as necessary. For example, the neighborhood of the
upper left pixel in the figure has two zero-valued neighbors, due
to zero padding.

**colfilt Creates a Temporary Matrix for Sliding
Neighborhood**

The temporary matrix is passed to a function, which must return
a single value for each column. (Many MATLAB^{®} functions work this
way, for example, `mean`, `median`, `std`, `sum`,
etc.) The resulting values are then assigned to the appropriate pixels
in the output image.

`colfilt` can produce the same results as `nlfilter` with
faster execution time; however, it might use more memory. The example
below sets each output pixel to the maximum value in the input pixel's
neighborhood, producing the same result as the `nlfilter` example
shown in Implementing Linear and Nonlinear Filtering as Sliding Neighborhood
Operations.

I2 = colfilt(I,[3 3],'sliding',@max);

For a distinct block operation, `colfilt` creates
a temporary matrix by rearranging each block in the image into a column. `colfilt` pads
the original image with 0's, if necessary, before creating the temporary
matrix.

The following figure illustrates this process. A 6-by-16 image
matrix is processed in 4-by-6 blocks. `colfilt` first
zero-pads the image to make the size 8-by-18 (six 4-by-6 blocks),
and then rearranges the blocks into six columns of 24 elements each.

**colfilt Creates a Temporary Matrix for Distinct
Block Operation**

After rearranging the image into a temporary matrix, `colfilt` passes
this matrix to the function. The function must return a matrix of
the same size as the temporary matrix. If the block size is `m`-by-`n`,
and the image is `mm`-by-`nn`, the
size of the temporary matrix is `(m*n)`-by-(`ceil(mm/m)*ceil(nn/n))`.
After the function processes the temporary matrix, the output is rearranged
into the shape of the original image matrix.

This example sets all the pixels in each 8-by-8 block of an image to the mean pixel value for the block.

I = im2double(imread('tire.tif')); f = @(x) ones(64,1)*mean(x); I2 = colfilt(I,[8 8],'distinct',f);

The anonymous function in the example computes the mean of the block and then multiplies the result by a vector of ones, so that the output block is the same size as the input block. As a result, the output image is the same size as the input image.

You can use `colfilt` to implement many of
the same distinct block operations that `blockproc` performs.
However, `colfilt` has certain restrictions that `blockproc` does
not:

The output image must be the same size as the input image.

The blocks cannot overlap.

For situations that do not satisfy these constraints, use `blockproc`.

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