Re: particle analysis-Feret diameter

Gabriel Landini wrote:
> On Sunday 27 November 2005 08:57, K. Kachrimanis wrote:
>
> > If this is the maximum Feret and it is selected from all Ferets measured,
> > then the only thing missing is to report the minimum and a mean Feret also.
>
>
> My plugin Particles8_Plus at
> http://www.dentistry.bham.ac.uk/landinig/software/software.html
>
> does most of the descriptors mentioned and includes the angle of the maximum 
> feret diameter. It also calculates the Breadth, which I think is a better 
> parameter than the minimum feret, but it uses a different way to estimate 
> perimeter (it uses Freeman's algorithm) so sometimes the results are not 
> exactly the same as the built-in analyser.
>
> How do you propose to place the other feret diameters at n angles?
> Is this based on the image frame of reference or angles offset from the 
> direction of the largest one?

No, you just calculate Feret diameter for each angle. You have a vector 
of Feret diameters. Maximum is the max value in this vector. Minimum is 
min value. Mean is the average of all values. This is how Matrox Imaging 
Library calculates the three values. According to MIL, breadth is max 
Feret/min Feret. So, no mather if you have max and min Feret or max 
feret and Breadth... you can calculate the third parameter easily. May 
be do you calculate breadth in a different way?

> And what should one use, the centroid or the centre of mass of the particle? 
> Note that when using the centre of mass, holes in the particle make it 
> difficult to standardise the measurements (the same particle filled and with 
> holes has different feret legths because the "centre" is in a different 
> location.

Sorry, but I don't understand how this affects calculation of Feret 
diameter. Obviously, choosing a different centre for rotation affects 
the way the rotated particle is represented (well, just a translation 
depending on the choosen centre). However, as far as I know, Feret 
diameter is not constrained to pass by a given centre. So, no mather 
which centre you use for the rotation, once your particle is rotated, 
you should get the same Feret diameter. This is true also for holes: 
Feret is calculated on the outline of the particle. So, holes have no 
effect on it.

> > a "microshape" descriptor is also available (fractal dimension), 
>
>
> Fractal dimension is not a microshape descriptor, but a global one which has 
> no scale (and therefore is not micro, meso or macro). However I have been 
> always suspicious of other commercial programs that "estimate" the f dim of 
> particles, for two reasons:
> 1."particles" I guess are image objects that are most of the time not large 
> enough to satisfy the requirement of an order of magnitude in the range of 
> scales analysed.

I agree totally! Even something simple like circularity is measured with 
a large error, due to pixellisation of the particle outline and other 
systematic errors introduced in the image, like shadows (just try to 
digitize spherical objects and analyze them... you would be surprised of 
the results: sometimes circularity is very far from one!)

> 2. fractal dimension is a bit of a statistical measure, it depends of a 
> goodness of fit to a particular model, so the "goodness" of the result needs 
> to be monitored by some other means (for instance the r-squared of a log-log 
> plot linear fit). When particles are all different sizes, these goodness of 
> fit are not comparable (it is not the same to look at a 30 pixel particle 
> than to a 30000 pixel one, in the latter there will be much larger scales 
> that are not present in the former, and so one is not measuring the same 
> property unless we already know that the objects are strictly fractal). I do 
> not think that it is a good idea to do this blindly.
> I think that if f dim is incorporated in the Particle Analyzer, it is going to 
> be misused extensively. If there were a vote I would go for "no".

Same to me!

Best,

Philippe Grosjean

> Cheers,
>
> Gabriel