6.5. NL Filter
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### 6.5. NL Filter

#### Overview

This filter is found in Filters->Enhance->NL Filter. NL means "Non Linear". Derived from the Unix pnmnlfilt program, it joins smoothing, despeckle and sharpen enhancement functions. It works on the whole image, not on the selection.

This is something of a swiss army knife filter. It has 3 distinct operating modes. In all of the modes each pixel in the image is examined and processed according to it and its surrounding pixels values. Rather than using the 9 pixels in a 3x3 block, 7 hexagonal area samples are taken, the size of the hexagons being controlled by the radius parameter. A radius value of 0.3333 means that the 7 hexagons exactly fit into the center pixel (ie. there will be no filtering effect). A radius value of 1.0 means that the 7 hexagons exactly fit a 3x3 pixel array.

#### Options

Preview

  When Do preview is checked, parameter setting results are interactively displayed in preview.

Parameter settings

  - Alpha: Meaning of this value depends on the selected option.

  - Radius: Controls the strength of the filter (0.33-1.00).

#### Operating Modes

This filter can perform several distinct functions, depending on the value of the parameter `alpha`.

Alpha trimmed mean filter. (0.0 <= `alpha` <= 0.5)

  The value of the center pixel will be replaced by the mean of the 7 hexagon values, but the 7 values are sorted by size and the top and bottom `alpha` portion of the 7 are excluded from the mean. This implies that an `alpha` value of 0.0 gives the same sort of output as a normal convolution (ie. averaging or smoothing filter), where `radius` will determine the "strength" of the filter. A good value to start from for subtle filtering is `alpha` = 0.0, `radius` = 0.55. For a more blatant effect, try `alpha` 0.0 and `radius` 1.0.

  An `alpha` value of 0.5 will cause the median value of the 7 hexagons to be used to replace the center pixel value. This sort of filter is good for eliminating "pop" or single pixel noise from an image without spreading the noise out or smudging features on the image. Judicious use of the `radius` parameter will fine tune the filtering. Intermediate values of `alpha` give effects somewhere between smoothing and "pop" noise reduction. For subtle filtering try starting with values of `alpha` = 0.4, `radius` = 0.6. For a more blatant effect try `alpha` = 0.5, `radius` = 1.0 .

Optimal estimation smoothing. (1.0 <= `alpha` <= 2.0)

  This type of filter applies a smoothing filter adaptively over the image. For each pixel the variance of the surrounding hexagon values is calculated, and the amount of smoothing is made inversely proportional to it. The idea is that if the variance is small then it is due to noise in the image, while if the variance is large, it is because of "wanted" image features. As usual the `radius` parameter controls the effective radius, but it probably advisable to leave the radius between 0.8 and 1.0 for the variance calculation to be meaningful. The `alpha` parameter sets the noise threshold, over which less smoothing will be done. This means that small values of `alpha` will give the most subtle filtering effect, while large values will tend to smooth all parts of the image. You could start with values like ``alpha` = 1.2` , ``radius` = 1.0` , and try increasing or decreasing the `alpha` parameter to get the desired effect. This type of filter is best for filtering out dithering noise in both bitmap and color images.

Edge enhancement. (-0.1 >= `alpha` >= -0.9)

  This is the opposite type of filter to the smoothing filter. It enhances edges. The `alpha` parameter controls the amount of edge enhancement, from subtle (-0.1) to blatant (-0.9). The `radius` parameter controls the effective radius as usual, but useful values are between 0.5 and 0.9. Try starting with values of ``alpha` = 0.3` , ``radius` = 0.8` .

Combination use

  The various operating modes can be used one after the other to get the desired result. For instance to turn a monochrome dithered image into grayscale image you could try one or two passes of the smoothing filter, followed by a pass of the optimal estimation filter, then some subtle edge enhancement. Note that using edge enhancement is only likely to be useful after one of the non-linear filters (alpha trimmed mean or optimal estimation filter), as edge enhancement is the direct opposite of smoothing.

  For reducing color quantization noise in images (ie. turning .gif files back into 24 bit files) you could try a pass of the optimal estimation filter (`alpha` 1.2, `radius` 1.0), a pass of the median filter (`alpha` 0.5, `radius` 0.55), and possibly a pass of the edge enhancement filter. Several passes of the optimal estimation filter with declining `alpha` values are more effective than a single pass with a large `alpha` value. As usual, there is a tradeoff between filtering effectiveness and losing detail. Experimentation is encouraged.

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