Low Pass Filters (Mean and Gaussian Filters) : Smoothing a DEM and Reducing Noise (Especially for GATE-Geospatial 2022)

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  • Low pass filters remove high-frequency features from an image, by diminishing the deviations from the central parameter. The bigger the moving window is, the more blurred will be the output image; sometimes it would be necessary to perform a contrast stretch after that filter, in order to use the full dynamic range of grey values.
  • These filters will be used mainly to remove noises from an image. Noises in an image can be classified in two according to their structure: random noise, and systematic or repetitive noise. Systematic noise is usually due to problems in the sensor. Random noise might occur (for example) on a camera film when some points on the film itself were damaged.
  • Such filters can be used also to lower the variability between pixels that belong to the same category and thus might help in performing a better classification.
  • The low-pass filters of MEAN and GAUSSIAN are used to smooth an image. In the MEAN filter all pixels have an equal weight, while in the GAUSSIAN, the far a pixel is located from the central pixel, its weight is smaller (according to Gaussian [bell] distribution) ; a filter where the weight of a pixel depends on its distance from the central pixel is termed “distance weighted” – these filters smooth more gently than “equal weighted” filters.

These filters are also applicable in GIS, for example:

  • Smoothing a DEM created from contours.
  • Computing density from point data.
These Filters Are Also Applicable in GIS
  • In the MEDIAN and MODE filters, there are no kernel values, and the value of the new pixel in the filtered output image is just the value of the median or mode of the pixels in the moving window. The MEDIAN filter is good for removing random noise. The MODE filter is good for filling in empty areas between polygons after a vector-to-raster conversion, or after performing classification in order to remove isolated pixels that belong to a different category than their neighbours. A MODE filter does not create a new value, in the sense that, for example, the data type remains the same. If the values of the input image are integers, the same will be in the output image (notice the first figure presented in this section, where applying the MEAN filter changed the values from integer to real) .
  • An example of applying filters will be given using a SONAR image in which we can see a pipeline. The SONAR image is quite noisy (similar to speckles seen on a Side Looking RADAR) .
SONAR Profile Line

Comparison of Various Low Pass Filters

In the following figure, the different effect of four different low-pass filters on the image can be seen, comparing them on a vertical profile line.

Vertical Distance

Notice the following:

  • The pipeline՚s location on the profile is above the “a” in the X title “Vertical Distance” .
  • The high-pass features reduced to the maximum with the MEAN filter, leaving only low-pass features.
  • The GAUSSIAN filter is following the original profile better than the MEAN, which might create a negative spike where it is actually positive.
  • The MEDIAN filter leaving many small spikes.
  • The MODE filter being the most unsuitable here, not removing much of the noise, and even creating grouped spikes.

For visual comparison are given the images produced by the MEAN and MODE filters:

MEAN and MODE Filters
  • In low-pass filters, the sum of the kernel values equals 1 (in some software, it is possible to define the kernel values in integer numbers – thus avoiding the need to calculate the exact numbers - and then define that the values should be normalized) .
  • Another characteristic of low-pass filters is that they maintain the units of the variable being filtered (unlike high-pass filters, as will be seen) .

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