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

2019-12-11
2019-12-12
  • Norwid Behrnd

    Norwid Behrnd - 2019-12-11

    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"?
     
    • Ethan Merritt

      Ethan Merritt - 2019-12-11

      See "gamma correction", e.g. Wikipedia
      https://en.wikipedia.org/wiki/Gamma_correction

      On Wed, Dec 11, 2019 at 4:01 AM Norwid Behrnd nbehrnd@users.sourceforge.net
      wrote:

      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"?

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


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      • Norwid Behrnd

        Norwid Behrnd - 2019-12-12

        Thank you very much for telling me the keyword missing and indicating
        the address. The background and examples the site and its siblings
        provide (e.g., the Italian and Dutch analogue apply the technique on
        color images, too) are very helpful for me; they answer my questions.

        On Wed, 11 Dec 2019 16:57:49 -0000
        "Ethan Merritt" sfeam@users.sourceforge.net wrote:

        See "gamma correction", e.g. Wikipedia
        https://en.wikipedia.org/wiki/Gamma_correction

         

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