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FX: Photoshop Tech Vault 3.0
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> Convolution -
Custom Filter
Convolution
is a basic operation found in
raster
image editing software. Building
custom convolution filter kernels is an elementary task for image
processing students, although this is often far from being the case for
the average Photoshop user from a GUI background. With regular filters
offering speed, flexibility and ease of use - Custom filtering is often
an esoteric subject that is forgotten in the exploration of more
powerful and user friendly filters. Custom filters still have limited
use, even in Photoshop - particularly so for feature detection beyond
the Find Edges or Glowing Edges filters.
The filter works by using the
rules defined in the custom filter, to affect brightness levels of the
centre pixel found in the kernel matrix, based on the values of
neighbouring pixels in the kernel matrix - for every pixel in the image
or selection. Positive or negative pixel values and mathematical
operations are entered to produce blurring, sharpening, embossing,
feature detection and some other basic filtering operations.
Adobe Custom Filter
Photoshop
offers a Custom Filter found under the filter/other menu which can be
used for constructing a simple 5x5 or smaller kernel matrix using
integer math. The save/load .acf file option is critical for productive
use of this filter - otherwise the coefficients, bias, scale
and offset have to be entered by hand for each filtering operation.
Alternatively, custom filter settings can be recorded into actions
which can be run or then used to generate any required .acf files for
use outside of the original action. 
Adobe
Custom Filter: The standard Custom Filter found under the
filter/other/custom menu. The simple kernel as shown above is often
known as the 'identity function' - input and output are the same, no
filtering takes place.
Reindeer Graphics Custom Filter
Reindeer
Graphics are the respected creators of Fovea Pro, Optipix and the Image
Processing Toolkit and their free Custom Convolution filter reflects
this background. There are many features offered by this third party
custom filter, most notable is the ability to use a larger 7x7 kernel matrix with floating point
math. One can also load Adobe Custom Filter .acf presets. Custom
filter kernel example text preset files are also provided for loading
into the filter. With the ability to process Photoshop high bit data -
sharpening, blurring and other basic filtering operations disabled in
Photoshop 5.x can now be applied.
Photoshop Custom Convolution Kernel Action Download
Actions
are a very flexible and productive method of storing and applying
multiple custom filter kernels or for quickly generating .acf files.
For maximum compatibility this action set is for Photoshop 5 or
higher. Custom filter actions are grouped into categories such as Low
Pass, Directional Derivative Feature Detection using Roberts, Robinson,
Sobel, Prewitt and Kirsch operators, Embossing, Laplacian Sharpening
and Edge Detection, High Pass, Weighted Blur/Sharpen, Band Pass DoM,
Band Pass DoG and Sub Pixel Motion Offset. Sharpening, blurring or
directional actions are ordered from light to heavy in application.
Directional operations borrow the Photoshop Emboss filter naming
convention for the eight compass angles, starting at 12 o'clock and
following in a clockwise direction. A manual in .RTF rich text format is also
included in the archive.

Download the 10KB .atn file .zip archive for:
Photoshop
5 or later
Further Reading
Two
excellent sources of information on custom convolution can be found at
the links below. Each site presents the topic of convolution with
interactive web browser based Java presentations which are an excellent
method of illustrating the custom filtering process. Arizona State
University - 2D Convolution, Java Primer
Molecular Expressions - DIP Convolution Kernels, Java Primer
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