Is plotting log(z) or sqrt(z) considered as a filtering technique?

Norwid Behrnd — Wed, 11 Dec 2019 12:01:16 -0000

On gnuplotting.org, the presentation of color palettes includes the raw data to replicate the plots displayed there. Likely known to whose using gnuplot for longer, I recognized the representation of the third dimension, and overall perception of the maps plots depend on calling the quantity 'directly', e.g.

plot 'test_colormap.txt' u ($1/3.0):($2/3.0):($3/1000.0) matrix with image

or 'square-root transformed',

plot 'test_colormap.txt' u ($1/3.0):($2/3.0):(sqrt ($3/1000.0)) matrix with image

or 'logarithm transformed'

plot 'test_colormap.txt' u ($1/3.0):($2/3.0):(log ($3/1000.0)) matrix with image

In my perception of using the cubehelix palette and in reference to the 'direct output', small z-values more than proportionally benefit from the square-root transformation; they seem to be «lifted» from the otherwise more dark region of the palette. Applying the logarithm on z equally yields a brighter plot in general; though areas with larger z-values, already displayed with more brightness, than others, seem to gain more brightness, than the areas with lower z-values.

My two questions are:

Is applying such transformations already considered as a kind of filtering, similar to low-pass filters in acoustics?
If so, is there a name commonly used to describe the processing better than for example "data were displayed as their square-root transformation"?

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Is plotting log(z) or sqrt(z) considered as a filtering technique?