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Topic: Lambda In Fractal Interpolation?

Hello,

I am student of photography and I have read an article about your programm Image Analyzer on

http://digi.zive.cz/h/fotoskola/AR.asp?ARI=657

I think it is an interesting programm, but I don´t understand the parametr Smoothing lamba in using Fractal interpolation.

If in use, the pre-set value is Lambda = 0,1 and I understand the term Smoothing, but in which interval can I use it and how does it work on the quality of resized picture to get the best result? Is there any
dependence on the size of picture?

Thank you for your answer.

Milos Vorel, Prague

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Re: Lambda In Fractal Interpolation?

A common and fast way of doubling the size of a picture is to insert new pixels between the existing ones, where the new ones are simply the average of the surronding original pixels. This is called bilinear interpolation.
This plugin instead uses a weighted average of the surronding pixels, and the weights are determined by examining the local structure of the image. The new pixels inserted is just a guess from the program, and in some cases this guess is very bad and here using a simple average would actually be better. By increasing this smoothing parameter you will get some closer to a simple average (bilinear interpolation). Allowed values are in the range 0-1.
Synthesizing the new pixels in the enlarged image involves solving a system of linear equations (via matrices), and this parameter is actually a regularization parameter (for Tikhonov regularization) as this system tends to be unstable and produce "wild" results. And since few people knows what Tikhonov regularization is I just chose to call it Smoothing as this describes very well what it does.
Try comparing the same picture enlarged with the value 0 and the value 1. I don't think it has anything to do with the size of the picture, but it the picture is noisy you will probably need a greater value.

Michael Vinther

> software developer <

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Re: Lambda In Fractal Interpolation?

Well, thank you, I can imagine... a little   smile
And (as I´ve read and seen in your commmentary on http://meesoft.logicnet.dk/Analyzer/help/help3.htm ) how can I compare the fractal resizing with the bicubic interpolation via the increasing step 10% and then 10%... and so on up to resizing of image to the 100%, as some authors recommend in their practical books on photography? Is it really so good way or is it only a wish? I´ve tried this way and normally bicubic interpolation and didn´t seen so big differences...  sad
Thanks

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Re: Lambda In Fractal Interpolation?

I'm not sure I understand... Do they recommend enlarging the same picture several times by 10% every time until the desired size is achieved?

Using the Fractal plugin to double the size and then reducing the size to e.g. 75% with the standard resize feature (A 150% increase in total) seems to give quite good result.  The will give you a bigger image, but without the "noise" sometimes introduced by the fractal method.

Michael Vinther

> software developer <

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Re: Lambda In Fractal Interpolation?

>> Do they recommend enlarging the same picture several times by 10% every time until the desired size is achieved?
====================
Yes, that´s true. For example Scott Kelby, Ben Willmore and others...

http://www.fredmiranda.com/Interpolation_Plugin
http://shop.scottkelbybooks.com/index.php
http://www.digitalmastery.com/companionsit...rces/index.html

They explain this way by reason of much smaller damage of enlarged pixels than the straight bicubic way. Are they right?
Perhaps they don´t know your programme...  B)

Bye

Milos Vorel

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Re: Lambda In Fractal Interpolation?

appendix from the link above:
..............
Everyone involved with digital imaging has heard about Genuine Fractals. This utility claimed to do a better job interpolating digital images than Photoshop's bicubic engine. SI Pro 2 uses a different approach to Fractals, which allows interpolated files to maintain a high level of detail while keeping your photograph's natural look. (Without the creation of fractal artifacts) - It's also only a fraction of the price. :-)

Using the Stair Interpolation Pro 2 Plugin, will make your interpolated images appear sharper, therefore producing beautiful prints. After running the plugin, SI Pro 2 images are superior to Genuine Fractal's and much better than just using Photoshop Bicubic (Or Bicubic Smoother) alone.
=======================================================

WHERE THE TRUE IS ?  ......    sad    :angry:    :unsure:

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Re: Lambda In Fractal Interpolation?

In my opinion no - using bicubic interpolation sevaral times in stead of just one does not give better results.
I tried with 9 different pictures (from a wide range of scenes), and none of them seemed to be better with the many-step enlargement. Only the text in an image looked a bit better, but in natural images some artefacts were introduced. There are also some mathematical resons why a single-step anlargement should be better than multi-step becuase each step will throw away some information.
But this is also something that is very different between different algorithms. With bicubic interpolation the multi-step approach is ok (but not good), but with bilinear interpolation the result is quite hopeless (too smoothed).

If you are comparing different image-enlargement algorithms I can also recommend trying the Wiener methods in Image Analyzer. They are superior to bicubic interpolation on most pictures. Actually they are related to the fractal method, but much faster and with less risk of producing strange artifacts (and then its free  wink ).

But which algorithm performs best probably always depends on the individual picture and how much enlargement you want... Many programs exists for enlarging pictures in many different ways and I think the ones available in Image Analyzer are okay, but I wont claim they are the best.

Michael Vinther

> software developer <

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Re: Lambda In Fractal Interpolation?

Thanks!
I think you are right. My experiencies are similar, but I´m only photographer, not mathematician. But I know from the practical life that perpetuum mobile doesn´t exist.   tongue

Re: Lambda In Fractal Interpolation?

admin,Nov 19 2005, 11:31 PM wrote:

In my opinion no - using bicubic interpolation sevaral times in stead of just one does not give better results.
I tried with 9 different pictures (from a wide range of scenes), and none of them seemed to be better with the many-step enlargement.

There are also some mathematical resons why a single-step anlargement should be better than multi-step becuase each step will throw away some information.

I agree

This "multiple step" mantra sounds like a good idea is not backed up by fact. It's (IMO) akin to the search for the elixir of life or turning base-metal to gold.  It becomes a fad ... underneath though it fails.

I too have  tried it in photoshop with several types of images (graphic and photo) and found the results no better than single step.


The weakness of classic bicubic is that it can exaggerate grain. I've wondered why no-one has implimented a bi-(constrained-cubic spline) interpolation.  I've done it myself in VB ( roll ) but it's too slow and has no visual interface.  It has all the advantages of bicubic but never increases noise.

Mpemba

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Re: Lambda In Fractal Interpolation?

My favorite filter (on the few progs which have it) is the haNNing filter (NOT haMMing). It's high quality, fast, and works for shrinking as well as enlarging. I'd love to see it added to IA. The wiener filters get better results than haNNing when enlarging, but haNNing is faster and works for reducing. Also, haNNing is very good at keeping text readable, which is something most filters are terrible at.

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Re: Lambda In Fractal Interpolation?

Hello,
I´ve tried that filter of Fred Miranda - SI Pro 2 - Stair Interpolation™ Pro - at my friend in comparision with fractal and wiener methods and this amazingly advertised (and sold) filter is really only a toy and childish fakement...
But I´ve got another question on fractal enlargement:
When (or where) can strange artifacts be produced? On which type of photos? If is there some experience? Usually my photos are landscapes, nature, faces and still-lifes free of text.
Thanks

Milos

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Re: Lambda In Fractal Interpolation?

One thing that my fractal method sometimes handles bad is text, very sharp details, and pixel noise (like from bad JPEG compression). What happens is that it produces a number of parallel horizontal or vertical lines.
(see example in attached picture of polar bear fur)
This is an example where the smoothing parameter should be increased, or the Wiener filter method used instead.

Michael Vinther

> software developer <

Re: Lambda In Fractal Interpolation?

I've never understood the advice to increment image size expansions either, since the results have always been poorer that one (or at most, two) to the final size. This holds on every image manipulation programme I've ever used (and this dates back to the "dear" old DOS days, some 11 years ago).

I suffered congenital cataracts, and wear glasses all the time as a result, and can clearly see the difference (even with scratched lenses), so it makes me wonder if those who advocate such a procedure even have eyes at all. (LOL).

<shrugs>

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Re: Lambda In Fractal Interpolation?

An updated version is now available with a filter for reducing the problem with the thin horizontal/vertical lines. This leads to a significant improvement with many images.

Michael Vinther

> software developer <

Re: Lambda In Fractal Interpolation?

Thanks for your effort.I like the new version.