Image Processing Toolbox User's Guide

Convolution

Linear filtering of an image is accomplished through an operation called convolution. Convolution is a neighborhood operation in which each output pixel is the weighted sum of neighboring input pixels. The matrix of weights is called the convolution kernel, also known as the filter. A convolution kernel is a correlation kernel that has been rotated 180 degrees.

For example, suppose the image is

• A = [17  24   1   8  15
       23   5   7  14  16
        4   6  13  20  22
       10  12  19  21   3
       11  18  25   2   9]
  

and the convolution kernel is

• h = [8   1   6
       3   5   7
       4   9   2]
  

The following figure shows how to compute the (2,4) output pixel using these steps:

1. Rotate the convolution kernel 180 degrees about its center element.
2. Slide the center element of the convolution kernel so that it lies on top of the (2,4) element of A.
3. Multiply each weight in the rotated convolution kernel by the pixel of A underneath.
4. Sum the individual products from step 3.

Hence the (2,4) output pixel is

Computing the (2,4) Output of Convolution

Linear Filtering

Correlation

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