Interpolation
by Gisle Hannemyr
Interpolation is a mathematical technique where a specific
alghortim is used to construct new intermediate data points from an
existing set of known data points. The result of the interpolation
(the new data points) depend on which algorithm is used.
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To test how well interpolation works, I tried the
following: I cropped a 400 x 400 px portion from an image
(Original, below), downsampled it, (using Photoshop's
bicubic sharper algorithm) to 127 x 127 px
(i.e 10 %, left ). This was then interpolated
back to the original size by means of various algorithms (the
equivalent of doing a 1000 % enlargement).
Note: Nearest Neighbor is only included for reference
(Nearest Neighbor is enlarging without interpolation). |
| 10 % |
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| Original |
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| Nearest Neighbor (1000 %) |
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| Qimage Pyramid (1000 %) |
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| Lanczos Interpolation (1000 %) |
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| Bicubic (1000 %) |
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| Qimage Vector (1000 %) |
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| Bicubic Smoother (1000 %) |
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| Extensis pxl Smartscale (1000 %) |
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As a rule of thumb, I've found that the number of kilobytes (Kb) in
a file after lossless compression is a good measure for the amount of
detail in a file. So, for what it is worth, here is the file
sizes:
|
| Original: | 301 Kb | 100 % |
| Qimage Pyramid: | 189 Kb | 63 % |
| Lanczos Interpolation: | 185 Kb | 61 % |
| Bicubic: | 183 Kb | 61 % |
| Qimage Vector: | 176 Kb | 58 % |
| Bicubic Smoother: | 172 Kb | 57 % |
| Extensis pxl Smartscale: | 166 Kb | 55 % |
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| Nearest Neighbor: | 53 Kb | 18 % |
| 10 %: | 35 Kb | 12 % |
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I think it is interesting that this table appears to give the same
result as visual inspection: Qimage Pyramid has a less
prominent pixelized structure (see hair and highlight on upper eyelid)
than the other methods. I also think
Lanczos looks nice.
The Qimage
results have been submitted by Bart van der Wolf. Please note that
Qimage is a printing interpolator, designed to do the much
larger interpolations required by inkjet printers. Screen crops of
print ready results may appear a bit ugly on screen.
Richardson-Lucy
Richardson-Lucy is a well known algorithm for image restoration
using a statistical model for image formation based on the Bayes
formula. It is not an interpolation method, but a post-processing
technique (like sharpening). Applying Richardson-Lucy to
interpolated images may create an artifical look for screen images,
but usually improves prints.
Below, courtesy of Bart van der Wolf, are examples of the results
of applying Richardson-Lucy to the Qimage Pyramid and
Vector 1000 images. For easy comparison I've also
included the Original, the Nearest Neighbor and the
unrestored crops.
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| Original |
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| Nearest Neighbor (1000 %) |
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| Qimage Pyramid R-L (1000 %) |
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| Qimage Vector R-L (1000 %) |
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| Qimage Pyramid (1000 %) |
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| Qimage Vector (1000 %) |
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Challenge
In the Usenet newsgroup rec.photo.digital, someone with the
handle Ryadia is making extraordinary claims about what
interpolation can do to an image.
After I complained about Kodak's Ofoto site stating that a 1600 x
1200 pixel (about 2 Mpx) image would give a "high quality"
print up to 30 x 20 inches (i.e. 53 ppi), Ryadia responded:
"What you don't understand here Gisle is precisely how these images are
printed. The firm are limiting the upload size to save bandwidth. They
then Interpolate the image to the print size at whatever pixel density
they need for their printer.
[...]
"Agfa labs, particular the ones using Durst, 'Lambda', continuous tone
laser printers use a highly refined Interpolation program capable of
2000% enlargements with only very minimal loss of detail. At 1000%
and below there is no loss of discernable detail. Look here for some
information;
http://www.technoaussie.com/ryadia/"
(The full text is in
Google Groups.)
Unless your ability to discern detail is seriously impaired,
downsampling (to conserve bandwidth or whatever) and interpolating
back up to "restore" the original detail does not work
Among other things, this process violates the second law of
thermodynamics (only half a :-) - which is one of the fundamental laws
of nature. The second law of thermodynamics tells us that the
decrease of order within a closed system is an irreversable process.
If detail is destroyed, there nothing that can restore it.
Standing offer to Ryadia: Download the 10 % crop above, and run
it through whatever means you use to make a 1000 % enlargement,
and email me the result. I'll put it up here along with the others.
Challenge posted Sep. 22, 2004.
Ryadia has elected not to submit a 1000 % enlargement that
can be compared to the other examples. However, on May 8, 2005, he
requested that
this comment
was added to the blog.
Interpolation Links
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