Home > Image Processing > 1. Digital Scanning

1. Digital Scanning

A reproduction of a graph was performed by relating the pixel locations of its data points to their actual physical values.  Here I used a hand-plotted graph, drawn from The Journal of Experimental Zoology (1916), which shows the relation of pulsation rate with temperature for the organism Holothuria captiva (Figure 1).

Figure 1. Graph taken from the Journal of Experimental Zoology (1916).

Using a drawing tool (Microsoft Paint) and a spreadsheet software (OpenOffice Calc), a ratio-and-proportion approach was applied to replicate the plot.  With the help of the mouse-over location tool of Paint, the pixel coordinates of the tick marks were recorded and were related to their axis values.  Considering the possible imperfections contained in the hand-drawn image, an averaged relation was sought for all the tick marks on both axes to obtain more accurate proportionality constants.  It was found that for the x-axis 1C temperature is represented by 11.27 pixels, while for the y-axis 1 second is represented by 6.08 pixels.

After finding the pixel locations for all data points, their x and y coordinates were converted using the ratios obtained.  It is important to note that for MS Paint, the origin is located on the upper left corner of the window.  Furthermore, it is significant to observe the range of values focused on the plot, x:(10,40) and y:(25,85).  Necessary inversion and shifting of the converted values were thus performed to achieve the actual values for the points.  Figure 2 shows the resulting graph produced using the charting function in the spreadsheet.

Figure 2. Reconstruction of the graph using ratio and proportion.

The digital replica of the graph was compared to the original scanned image by overlaying one on top of the other.  Using the Chart Area tool in Calc, the bitmap image of the original plot was embedded behind the new graph.

Finishing touches include making sure that the bitmap background is set as Autofit, as opposed to the default Tile option, which somehow produces an unsatisfactory embedding depending on the bitmap size.  Figure 3 shows the resemblance of the reproduced graph with the original scanned image.

Figure 3. The digital replica overlaid on the original plot.

It is remarkable that some aspects of the manually drawn graph were corrected on the reconstructed plot (i.e. axis tilts and misalignment).  However, it can be observed that though the calculated points fall fairly well on their proper locations, the curve produced is not similar to the original plot.  This can be accounted on the limitations of the curve smoothening function for charting under OpenOffice Calc, which restricts to including all points within the smoothened curve.  A workaround will somehow require more sophisticated approaches in performing array statistics.

I would like to acknowledge Gladys Regalado for sharing a few software tips, and Dr. Soriano for the helpful assistance.  For this activity, I would give myself a grade of 9 for applying the basic methods and being able to reconstruct the essential parts of the plot.

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References:

  1. Applied Physics 186 Activity 1 manual.
  2. Soriano, 2008.  Inserting images as background for OpenOffice Calc graphs.
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  1. LS
    May 23, 2013 at 10:55 pm

    Excuse the necromancy, but these days you can do it online, in web apps, such as http://arohatgi.info/WebPlotDigitizer/app/

  2. May 26, 2014 at 5:45 pm

    Excellent post! We will be linking to this particularly great content
    on our website. Keep up the great writing.

  1. June 27, 2010 at 8:25 am
  2. July 1, 2010 at 12:28 pm

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