The Convolution Method

EM 1110-2-2907

1 October 2003

The Convolution Method

Convolution is carried out by overlaying a kernel onto the pixel image and

centering its middle value over the pixel of interest. The kernel is first placed

above the pixel located at the top left corner of the image and moved from top

to bottom, left to right. Each kernel position will create an output pixel value,

which is calculated by multiplying each input pixel value with the kernel

coefficient above it. The product of the input data and kernel is then averaged

over the array (sum of the product divided by the number of pixels evaluated);

the output value is assigned this average. The kernel then moves to the next

pixel, always using the original input data set for calculating averages. Go to

http://www.cla.sc.edu/geog/rslab/Rscc/rscc-frames.html for an in-depth

description and examples of the convolution method.

The pixels at the edges create a problem owing to the absence of neighboring

pixels. This problem can be solved by inventing input data values. A simpler

solution for this problem is to clip the bottom row and right column of pixels

at the margin.

(b) The Laplacian filter measures the changes in spectral frequency or pixel in-

tensity. In areas of the image where the pixel intensity is constant, the filter assigns a

digital number value of 0. Where there are changes in intensity, the filter assigns a posi-

tive or negative value to designate an increase or decrease in the intensity change. The

resulting image will appear black and white, with white pixels defining the areas of

changes in intensity.

Table 5-2

Variety in 9-Matix Kernel Filters Used in a Convolution Enhancement.

Each graphic shows a

kernel, an example of raw DN data array, and the resultant enhanced data array.

See

http://www.cee.hw.ac.uk/hipr/html/filtops.html for further information on kernels and the filtering methods.

a. Low Pass: simple mean kernel.

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Raw data

Output data

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