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Image Processing using  2D-Convolution

Example of 2D Convolution on single Pixel, using 3 X 3 Kernel,
Kernel (n, n') can be any size.  3x3 kernel requires 9 passes: normalizer = 9.  3D Convolution would use Time as the 3rd dimension.
2D Convolution (image processing)

An image processing operation that is used to spatially filter an image. 

A convolution is defined by a kernel that is a small matrix of fixed numbers (coefficients). 

The size of the kernel, the numbers within it, and a single normalizer value define the operation that is applied to the image. 

The kernel is applied to the image by placing the kernel over the image to be convolved and sliding it around to center it over every pixel in the original image. At each placement the numbers (pixel values) from the original image are multiplied by the kernel number that is currently aligned above it. 

The sum of all these products is tabulated and divided by the kernel's normalizer. This result is placed into the new image at the position of the kernel's center. The kernel is translated to the next pixel position and the process repeats until all image pixels have been processed. 

As an example, a 3x3 kernel holding all 1's with a normalizer of 9 performs a neighborhood averaging operation. Each pixel in the new image is the average of its 9 neighbors from the original. 

In a raster type image, only one Kernel coefficient operates during a single pass; after 9 passes, all 3x3 coefficients will have operated on the image.

Examples of Function ver Kernel coefficient values
-1 -1 -1
-1  9 -1
-1 -1 -1
1/16 1/16 1/16
1/16 1/2 1/16
1/16 1/16 1/16
-1 -1 -1
-1  8 -1
-1 -1 -1
High-Pass mask Low-Pass Filter Edge-Detector

This page is merely an introduction, 
for much more on Convolution, 
please see: Tim Dettmers Blog Post


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