On Mar 10, 2009, at 8:56 AM, Nicolas Robidoux wrote:

> Hello Rahul:
>> i m a student and interested in gsoc project:Fast Adaptive Resampler
>> Tailored For Transformations Which Mostly Downsample
>> I have read the requirements properly for this project which also
>> includes jacobian transformation,box filtering algorithm and
>> bilinear resampling.But i am having some problem in relating all
>> these in one algorithm. Please guide me.Also I would like to know
>> the status of this project progress.
> The >>programming<< for this project has not started. "No progress" is
> consequently a fair description.
> Computing jacobian information (for an arbitrary point transformation)
> approximately using finite differences is probably too ambitious. My
> current opinion is that this method should only be used when the point
> transformation "communicates" this information to the sampler. ...

Numerical Jacobian calculation is not so bad in terms of coding effort  
you can use the method I implemented for PDL::Transform (available as  
of the PDL package for Perl, or at pdl.perl.org), and it's  
to code.  The PDL::Transform resampling code switches its sampling  
based on user input; Jacobian based spatially variable filters are used
where artifact avoidance is most important.  It might make a nice  
point for you to look at.

On the other hand, you will need to think a bit about the "Fast" part,  
the PDL Jacobian-driven sampling is not -- mostly because of the need to
supply input and output filtering.  I did that by padding the singular  
of the Jacobian to approximate the effect of convolving one-pixel-wide  
and output filter kernels with the calculated sampling kernel.  That  
subjecting a matrix to singular value decomposition for every pixel -  
is almost certainly a faster way to do it. For linear transformations  
the Jacobian is constant) the method is much faster.

Dodgson is a great reference (in Nicolas' email).  You might also like  
read Ken Turkowski's nice overview of resampling theory:

My own paper on the subject (in the context of image resampling for  
applications) is here:

> You need to understand exact area methods, and in particular, exact
> area box filtering (basically, you understand images as being a
> piecewise constant surface, with the pieces determined by the set of
> points which are closer to a pixel center than any other pixel center,
> and you (approximately) integrate this surface over an area associated
> with the new pixel centers (determined by the point transformation).
> References which may help understand what is going on are
> @TechReport{Dodgson,
>  author =       {N. A. Dodgson},
>  title =        {Image resampling},
>  institution =  {University of Cambridge Computer Lab.},
>  year =         1992,
>  number =       {UCAM--CL--TR--261},
>  address =      {15 JJ Thomson Avenue, Cambridge CB3 0FD, UK},
>  month =        {Aug.}
> }
> and
> @inproceedings{DBLP:conf/iciar/RobidouxTGT08,
>  author    = {Nicolas Robidoux and
>               Adam Turcotte and
>               Minglun Gong and
>               Annie Tousignant},
>  title     = {Fast Exact Area Image Upsampling with Natural  
> Biquadratic
>               Histosplines},
>  pages     = {85-96},
>  ee        = {http://dx.doi.org/10.1007/978-3-540-69812-8_9},
>  bibsource = {DBLP, http://dblp.uni-trier.de},
>  crossref  = {DBLP:conf/iciar/2008}
> }
> Also, a student and I programmed a C filter (for 8-bit ppm/pgm) which
> does exact area box filtering in the very simple case of pure image
> resizing. If you're still interested, we'll put this on the web.
> The proposed method is none of the above. More precisely, it is a
> composite method: It "fits" a new fast but accurate downsampling
> method (related to box filtering) and bilinear together so that
> Frankenstein is flexible and "smoothly varying."
> Note: French is my mother tongue. If you are more comfortable in
> French, you can communicate with me---not this list---in
> French. Obviously, English is fine too.
> Best of luck,
> Nicolas Robidoux
> Universite Laurentienne
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