Re: Possible bug with perimeter calculation on composite selections

Posted by Gabriel Landini on Jan 27, 2009; 10:51am
URL: http://imagej.273.s1.nabble.com/Possible-bug-with-perimeter-calculation-on-composite-selections-tp3693924p3693926.html

On Tuesday 27 January 2009 04:28:17 Chris Bradhurst wrote:
> As far as whether perimeter will actually have any discriminating value
> remains to be seen, although I suspect it will likely be ineffective, in
> accord with your experience.

What Kenneth was talking about is a special type of geometrical object where
the perimeter length scales with observational scale (i.e. fractal and
asymptotic fractal boundaries).
Those are very common in nature and so comparing their perimeters is only good
for a single resolution (while is unlikely to be exactly the same across
different setups).
Many traditional shape descriptors use also the perimeter in the calculation
(like circularity, shape factor, etc) so those can be badly affected as well.

For complex/fractal particles with varying sizes, computing their fractal
dimension is much more robust and informative than other shape parameters.

The paper full reference is very much worth reading:

Mandelbrot B. How long is the coast of Britain? Statistical self-similarity
and fractional dimension. Science 1967;156:636-638.

And within the biological context everybody doing microscopy should read these
two (both way ahead of their time):

Paumgartner D, Losa G, Weibel ER. Resolution effect on the stereological
estimation of surface and volume and its interpretation in terms of fractal
dimensions. Journal of Microscopy 1981;121(1):51-63.

Rigaut JP. An empirical formulation relating boundary lengths to resolution in
specimens showing 'non-ideally fractal' dimensions. Journal of Microscopy
1984;133(1):41-54.

Cheers

Gabriel