PNG and MNG tools
MNG MAGN methods

MNG MAGN methods

This illustrates the two methods used in the MAGN proposal and an alternate methods using ImageMagick's method and L1 splines.

Method 1 Pixel Replication

Method 2 Linear Interpolation

Alternate 2 ImageMagick's Interpolation

Alternate 2 L1 Spline Interpolation

All three images originated from this 5x5 pgm file:

   P2 5 5 1
   0 0 0 0 0
   0 0 0 0 0
   0 0 1 0 0
   0 0 0 0 0
   0 0 0 0 0

It is a single white pixel in the middle of a black 5x5 array.

• To emulate Method 1 (pixel magnification), I used ImageMagick's

      convert -sample 33x33 5x5.pgm 33x33.pgm.
  

  This magnified the pixels 8x by pixel replication. The "-sample" method in ImageMagick uses the closest pixel, so the blocks are centered over the original pixels, not offset to the right and bottom as in the MAGN proposal [should the proposal be revised to do this?]

  Then I expanded the image another 8x for visbility, using

  convert -sample 264x264 33x33s.pgm 264x264s.pgm
  

  The simple magnification resulted in a sharp blocky image, as shown on the left.

• Method 2, linear interpretation is demonstrated by magnifying the 5x5 image using a "pmninterp" script provided by Adam Costello. It didn't properly scale the value "1" to full scale, so I edited the 5x5.pgm and changed the two "1" values to "255", then

      pmninterp 8 < p255_5x5.pgm > 40x40i.pgm
  

  then

      convert -sample 320x320 40x40s.pgm  320x320i.pgm
  

  and converted that to jpeg for use on this page.

• At first, to emulate Method 2 (linear interpolation, or "lerping"), I had used ImageMagick's

      convert -geom 33x33 5x5.pgm 33x33g.pgm.
  

  This magnified the intervals 8x approximately if not exactly by linear magnification. Then, as above, I expanded the image another 8x for visibility, using

      convert -sample 264x264 33x33g.pgm 264x264g.pgm
  

  The linear magnification resulted in a soft blurry image, as shown in the middle.
  It seems, however, that this is not linear interpolation, as I first thought.

• To emulate an alternate method (L1 splines), I used a research code provided by John Lavery, to produce a 33x33 interpolation of the original 5x5 image. This magnified the intervals 8x by L1 spline interpolation. Then, as above, I expanded the image another 8x for visibility, using

  convert -sample 264x264 33x33L.pgm 264x264L.pgm
  

  The linear magnification resulted in another soft blurry image, as shown on the right.
  

Finally, I cropped away some of the uninteresting black area from each image, and converted the results to JPEG to make the three 180x180 images that appear in the table, above.