Linear Filtering

Clifford Watson,
Department of Applied Mathematics,
University of Washington,
Seattle, Washington 98195

The topics discussed here are:

Low Pass Filters

Low pass filtering, otherwise known as "smoothing", is employed to remove high spatial frequency noise from a digital image. Noise is often introduced during the analog-to-digital conversion process as a side-effect of the physical conversion of patterns of light energy into electrical patterns [Tanimoto].

There are several common approaches to removing this noise:

Moving Window Operations

(Select digital convolution for a more detailed derivation of this section.)

The form that low-pass filters usually take is as some sort of moving window operator. The operator usually affects one pixel of the image at a time, changing its value by some function of a "local" region of pixels ("covered" by the window). The operator "moves" over the image to affect all the pixels in the image. Some common types are:

The above filters are all space invariant in that the same operation is applied to each pixel location. A non-space invariant filtering, using the above filters, can be obtained by changing the type of filter or the weightings used for the pixels for different parts of the image. Non-linear filters also exist which are not space invariant; these attempt to locate edges in the noisy image before applying smoothing, a difficult task at best, in order to reduce the blurring of edges due to smoothing. These filters are not discussed in this tutorial.

High Pass Filters

This Section is under construction.

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