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Filter parameters

The purpose of filtering is always the same:

Make the signal distinct and suppress the noise. We call it optimizing the signal/noise-ratio. In general signal processing there is an extensive theory and a huge variety of filters. For the Scorpion intensity profiles we have made a small, but effective subset available. They can be chosen by 5 integer parameters. The three first parameters decide a linear FIR filter consisting of a gaussian smooth filter and differentiation. In praxis there will be a small set of actual values of the possible ones. If we set the differentiation to zero, we get a clean smooth filter suited to remove noise with small frequent variations along the intensity profile. Below a set of such smooth filters is graphically shown. (The numbers in parentheses are the smooth base and smooth counter respectively.) 

Generally you can say that the wider and flatter the filter is, the more it smoothes. The filter becomes wider both when the smooth base and smooth counter increases. When the smooth counter increases the filter changes from rectangular to more gaussian. When the smooth base increases, the width increases more directly.

When searching for intensity profile jumps, it is suitable to differentiate to change the jumps into tops easy to detect. Differentiation however increases the high frequent noise in the image. Thus it is wise to always combine differentiation with smoothing. Below you see graphs of filters with first order differentiation and varying degree of smoothing. As earlier we see that the smooth base increases the width, while the smooth counter makes the filter more gaussian.

Higher order differentiation is also possible, but rarely used since the noise is increased. You may however compensate this by low pass filtering or smoothing the curve. This results in wide filters and is only suited to detect forms covering wider parts of the intensity profile. Second order differentiation is however useful to detect narrow dark or light stripes in the image. These will turn out as sharp tops and bottoms in the intensity profile. But they can be difficult to detect because they may lay on varying intensity levels and you get problems with finding a common threshold setting to select the tops and bottoms you really want. If you use a second order differentiation filter to see the sharp ripples in the intensity profile, you will get tops that can be separated by a common threshold setting. Below you see some examples of second order differentiation filters:

Observe again the filter width increases with the smooth base, while the gaussian form increases with the smooth counter. 


Scorpion Vision Version XII : Build 646 - Date: 20170225
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