2D-interpolation using Splines

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Hello,

I'm interested in interpolating an image using these iinstructions ;

(...)
Duplicate/O $str_spectre_source, $str_Interpolated_spectrum
ImageInterpolate  /DEST=$str_Interpolated_spectrum /f={8,8}/D=5 spline $str_spectre_source
(...)


As I read in http://bigwww.epfl.ch/publications/thevenaz9901.pdf, page 2 :
P.Thévenaz, T. Blu and M. Unser
Swiss Federal Institute of Technology—Lausanne
"The evaluation of the underlying continuous function at the sampling points yields the same value as the data themselves."

My problem is that this requirement is not fulfilled. As you can see on the attached files, the max values on the raw data are higher than on the interpolated data.

I can see that you refer to :
Unser, M., A. Aldroubi, and M. Eden, B-Spline Signal Processing: Part I-Theory, IEEE Transactions on Signal Processing, 41, 821-832, 1993.

Is this interpolation implemented as in :
http://bigwww.epfl.ch/publications/thevenaz9901.pdf, page 34-35
?

Would you know why the overall magnitude of the image has decreased ?

Thank you very much in advance for your support,

Kind regards
Hello Nasser,

You are right, the command line that you used results in an interpolated image with reduced peak values. The reference and the original code used by ImageInterpolate appear to be 6 years older than the 1999 paper you cite in which the authors may have improved on the performance of the original algorithm.

If you would like to perform 2D spline interpolation that retains the peak values just add the (undocumented) /FDS flag to your command line.

A.G.
WaveMetrics, Inc.

October 7, 2011 at 11:18 am - Permalink

Hello A.G.,

Thank you very much, now the magnitutes are preserved. Could you please give us more information about the /FDS flag and the associated algorithm ?
Can I ask you why you have not documented it in spite of its importance?

Thank you.

October 7, 2011 at 01:34 pm - Permalink

Hello Nasser,

"Importance" is subjective.

I consider the FDS implementation as experimental until I have resolved a number of issues. This is probably not going to happen until the IP7 release when this feature might have both a different syntax and options. In the meantime there is no reason why you should not benefit from the utility this provides.

A.G.
WaveMetrics, Inc.

October 7, 2011 at 02:07 pm - Permalink

That's subjective, you're right. For instance, that's not a big deal if it happens on photographs, but in the present case, amplitudes have to be preserved to quantify the response according to calibration curves; Fortunatelly, you noticed that.

Thanks a lot!

October 7, 2011 at 03:56 pm - Permalink

Hello A.G.,

We are going to submit a paper, and as you know, there are many ways to interpolate a signal. Yours (with the /FDS flag) is really convenient.
Could you please give me some more details about the algorithm please ? Even if it is experimental, it would be really helpful to know how this interpolation is performed. Of course, IgorPro will be cited in the paper.

Thank you very much in advance !

Best Regards

December 19, 2011 at 01:19 am - Permalink