Date: Fri, 9 Oct 2009 17:33:53 -0700 (PDT)
   From: grow <george...@gmail.com>

   Stefan,
   Thanks for your analysis of this.

   You asked about memory and responsiveness.

   My Mac has 5.5Gb of RAM ... when I have a large stitch to do I
   sometime restart the machine and re-open the Hugin project with only
   the Stitch tab open and no preview or anything else taking up
   memory ... that way I have about 4Gb of free memory at the start of
   the stitch.

   I have a box on the shelf with 2GB more RAM that I will install
   "soon"  - probably this weekend - but I said that last weekend also.
   That will take the RAM to 7Gb (as I will have to take out 2x256Mb in
   order to fit the the 2x1Gb  new cards).  I will of course try my
   problematic Hugin projects after the upgrade to check whether it makes
   a difference.

   On responsiveness ... I haven't been systematic in measuring and
   plotting the times.  These are all ROUGH NUMBERS FROM MEMORY - this is
   NOT the result of a carefully controlled and systematically logged
   analysis.

   But with that disclaimer out of the way it goes something like
   this ...
   If I launch a Hugin-stitch of one of the problematic projects at say
   2,000 x 1,000 it will take a few minutes (typically I will set a tiny-
   test-stitch running ... switch windows to check email and the like ...
   and by the time I check back on Hugin it has finished)
   at 5,000 x 2,500 it might take perhaps 30 minutes  ... (I go
   downstairs and watch an episode of The SImpsons ... when I get back to
   my desk the stitch is finishing up)
   at 8,000 x 4,000 it will run for about 2 hours (I go and cook and
   serve dinner)
   when it gets to 12,000 x 6,000 (I set it running before I go to bed
   and check before breakfast in the morning  - either we have a good
   final image or an error report) when I check the file creation times
   it will have run for 6 or 7 hours!

That's more than linear, but not by much -- N*sqrt(N).

 5000x2500   =   12.5 MP, 0.5 hr  = 25 MP/hr
 8000x4000   =   32.0 MP, 2.0 hr  = 16 MP/hr
12000x6000   =   72.0 MP, 6.0 hr  =  8 MP/hr

Or, based on the time for 12.5 MP, you'd expect the 8Kx4K to take 1.3
hours and the 72 MP to take about 3 hours if it were linear.  If it
were N^2, you'd expect 32 MP to take about 3~3.5 hours and 72 MP to
take about 15 hours.  If it were N*sqrt(N), the 32 MP should take
about 2.0 hours and the 72 MP about 6.5~7 hours -- exactly what you're
seeing.  The 2 MP image should take about 0.064 hours, or 4 minutes.
You're seeing consistent behavior all the way up.  That's not usually
a signature of memory thrashing -- usually when that happens you hit a
wall, where above that point the time may well increase by orders of
magnitude.

   So my intuition is that there is a square or possibly cubic
   progression in the processing time as the final image size
   increases.  The processing time is proportional to something like
   n^3 where n is width of the image.  It is NOT proportional to n^4 -
   so it is NOT the square of the area.

Proportional to the cube of the width (linear dimension) appears to be
correct based on these 3 or 4 data points, but since each pixel has to
be processed I'd expect to calculate complexity based on the pixel
area.  Thus, N * sqrt(N).  Perhaps the developers can explain why it's
more than linear, but it's certainly not quadratic.

-- 
Robert Krawitz                                     <r...@alum.mit.edu>

Tall Clubs International  --  http://www.tall.org/ or 1-888-IM-TALL-2
Member of the League for Programming Freedom  --  http://ProgFree.org
Project lead for Gutenprint   --    http://gimp-print.sourceforge.net

"Linux doesn't dictate how I work, I dictate how Linux works."
--Eric Crampton

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