FracLac options - Use Relative Sizes

[Valerian Ignatescu]

Can anyone help me to understand how "Relative box sizes" works when one
selects this kind of generating the box size series?
My feeling is that using this option the fractal dimension is more
accurate at least in some types of solid structures (even a rotated
square). On the other side the number of boxes as given in the result
window ranges only from 6 to 20 depending on the value of the largest grid
(not a monotonic dependence though). In addition, the option "box sizes
per scan" does not seem to do anything in this case. Even worse, "Sliding
Box Lacunarity Scan" does not work at all if I "Use Relative Sizes".
My guess is that "Use default box sizes" generates a linear series from
the smalles to the biggest grid by adding the smallest increment, but I
have no idea how "Use Relative Sizes" works considering that power series
and scaled series (exponential?) are separated options.
Thank you.

Vali

[audrey karperien]

Hi.  Sorry to be so long in responding.  I've been ill.  The "relative sizes" option makes a series of sizes relative to the largest box where all sizes smaller than are factors of the largest box.  For this option, box sizes per scan does not affect the series.  To see the actual box sizes used, you can print the data file.  Also, the sliding box bug is fixed in the latest FracLac.  For textures, relative sizes/block analyses are generally most appropriate.  "Power" and "Scaled" series are the same essentially; they are separate to make it easy for the user to specify the largest box to scale down from or an exponent to scale up with.  The default series is linear, with smoothing and minimizing in the output in the analysis.  
   
  I hope that explains it.  Let me know if you need a better explanation.
  Audrey
   
   

Valerian Ignatescu <[hidden email]> wrote:
  Can anyone help me to understand how "Relative box sizes" works when one
selects this kind of generating the box size series?
My feeling is that using this option the fractal dimension is more
accurate at least in some types of solid structures (even a rotated
square). On the other side the number of boxes as given in the result
window ranges only from 6 to 20 depending on the value of the largest grid
(not a monotonic dependence though). In addition, the option "box sizes
per scan" does not seem to do anything in this case. Even worse, "Sliding
Box Lacunarity Scan" does not work at all if I "Use Relative Sizes".
My guess is that "Use default box sizes" generates a linear series from
the smalles to the biggest grid by adding the smallest increment, but I
have no idea how "Use Relative Sizes" works considering that power series
and scaled series (exponential?) are separated options.
Thank you.

Vali

[Valerian Ignatescu]

Hello Audrey,

I hope that your health problems have been completely solved. Thank you
for your answer. It didn't come too late, as myself I have to deal with a
nasty car accident a week ago. I hit a dear at 60 mph and the car was so
badly damaged that I have to buy a new one (I did not have collision
included on my old car insurance). Fortunately no one was injured.
Switching to your message, you answered to my main question related to the
"relative sizes" option.
Could you please tell me what "cover dimension" means? You wrote in the
documentation that "FracLac calculates an unadjusted fractal dimension, an
average fractal dimension over multiple scans, a slope-corrected
dimension, and a most efficient covering dimension" and further down: "The
algorithm finds an average fractal dimension over all scans, as well as a
"most efficient" covering fractal dimension using these scans". In the
result file, there is a second "MIN DB w/o intervals" that I think is MIN
COVER DB w/o intervals, isn't it?
Unfortunately "sliding box scan" still does not work with relative box
sizes. I am using FracLac v.2.3k with ImageJ 1.36b. But this is not a
major problem.
Could you also send me a reference related to the relative size boxes
method to compute the fractal dimension? Again, please do not forget to
tell me how do you prefer to cite your plugin in my paper.

Best regards,
Vali

> Hi.  Sorry to be so long in responding.  I've been ill.  The "relative
> sizes" option makes a series of sizes relative to the largest box where
> all sizes smaller than are factors of the largest box.  For this option,
> box sizes per scan does not affect the series.  To see the actual box
> sizes used, you can print the data file.  Also, the sliding box bug is
> fixed in the latest FracLac.  For textures, relative sizes/block analyses
> are generally most appropriate.  "Power" and "Scaled" series are the same
> essentially; they are separate to make it easy for the user to specify the
> largest box to scale down from or an exponent to scale up with.  The
> default series is linear, with smoothing and minimizing in the output in
> the analysis.
>
>   I hope that explains it.  Let me know if you need a better explanation.
>   Audrey
>
>
>
> Valerian Ignatescu <[hidden email]> wrote:
>   Can anyone help me to understand how "Relative box sizes" works when one
> selects this kind of generating the box size series?
> My feeling is that using this option the fractal dimension is more
> accurate at least in some types of solid structures (even a rotated
> square). On the other side the number of boxes as given in the result
> window ranges only from 6 to 20 depending on the value of the largest grid
> (not a monotonic dependence though). In addition, the option "box sizes
> per scan" does not seem to do anything in this case. Even worse, "Sliding
> Box Lacunarity Scan" does not work at all if I "Use Relative Sizes".
> My guess is that "Use default box sizes" generates a linear series from
> the smalles to the biggest grid by adding the smallest increment, but I
> have no idea how "Use Relative Sizes" works considering that power series
> and scaled series (exponential?) are separated options.
> Thank you.
>
> Vali
>

[audrey karperien]

Oh deer (har har).  But seriously, that is just awful. I'm glad you're ok, and I hope the car expense is not too bad on you.
   
  "Cover" refers to "most efficient cover" or "minimum cover".  The concept is to use the least number of units required to cover the image.  For an image scanned from multiple locations, the minimum cover is a new series from those locations.  It is comprised of, for each box size, the count from the grid position with the lowest count.  
  The smoothed or horizontal slope removed Df is found by removing horizontal intervals from the data.  These are combined in the last dimension.  
   
  The SLAC bug is fixed now. Thanks for letting me know.
   
  For references, I wrote about the methods of FracLac in my masters thesis and published the following using it:
  2005 - “Fractal Analysis of Microglial Morphology”, Karperien, Lucas, Aurel, and Jelinek in Bourgine, Kepes, and Schoenauer (eds.), poster, Proceedings of the European Complex Systems Society – Towards A Science Of Complex Systems.
  2004 - “Fractal Analysis Quantitates Overt and Subtle Effects of Naloxone and Lipopolysaccharide on Cultured Rat Microglia”, Karperien, Jelinek, Bossomaier, in Proceedings of Complex 2004, the 7th Asia-Pacific Conference on Complex Systems, Cairns, Australia.
  2004 - “Differentiating Grades of Microglia Activation with Fractal Analysis”, Jelinek, Karperien, Bossomaier, and Buchan, in Proceedings of Complex 2004, the 7th Asia-Pacific Conference on Complex Systems, Cairns, Australia.
  2002 - "MicroMod - an L-systems Approach to Neuron Modelling". Jelinek, Karperien, Cornforth, Cesar, and Leandro, in Sarker, McKay, Gen and Namatame (eds.), Proceedings of the Sixth Australia-Japan Joint Workshop on Intelligent and Evolutionary Systems, Canberra, Australia.
       

Valerian Ignatescu <[hidden email]> wrote:

  Hello Audrey,

I hope that your health problems have been completely solved. Thank you
for your answer. It didn't come too late, as myself I have to deal with a
nasty car accident a week ago. I hit a dear at 60 mph and the car was so
badly damaged that I have to buy a new one (I did not have collision
included on my old car insurance). Fortunately no one was injured.
Switching to your message, you answered to my main question related to the
"relative sizes" option.
Could you please tell me what "cover dimension" means? You wrote in the
documentation that "FracLac calculates an unadjusted fractal dimension, an
average fractal dimension over multiple scans, a slope-corrected
dimension, and a most efficient covering dimension" and further down: "The
algorithm finds an average fractal dimension over all scans, as well as a
"most efficient" covering fractal dimension using these scans". In the
result file, there is a second "MIN DB w/o intervals" that I think is MIN
COVER DB w/o intervals, isn't it?
Unfortunately "sliding box scan" still does not work with relative box
sizes. I am using FracLac v.2.3k with ImageJ 1.36b. But this is not a
major problem.
Could you also send me a reference related to the relative size boxes
method to compute the fractal dimension? Again, please do not forget to
tell me how do you prefer to cite your plugin in my paper.

Best regards,
Vali

> Hi. Sorry to be so long in responding. I've been ill. The "relative
> sizes" option makes a series of sizes relative to the largest box where
> all sizes smaller than are factors of the largest box. For this option,
> box sizes per scan does not affect the series. To see the actual box
> sizes used, you can print the data file. Also, the sliding box bug is
> fixed in the latest FracLac. For textures, relative sizes/block analyses
> are generally most appropriate. "Power" and "Scaled" series are the same
> essentially; they are separate to make it easy for the user to specify the
> largest box to scale down from or an exponent to scale up with. The
> default series is linear, with smoothing and minimizing in the output in
> the analysis.
>
> I hope that explains it. Let me know if you need a better explanation.
> Audrey
>
>
>
> Valerian Ignatescu wrote:
> Can anyone help me to understand how "Relative box sizes" works when one
> selects this kind of generating the box size series?
> My feeling is that using this option the fractal dimension is more
> accurate at least in some types of solid structures (even a rotated
> square). On the other side the number of boxes as given in the result
> window ranges only from 6 to 20 depending on the value of the largest grid
> (not a monotonic dependence though). In addition, the option "box sizes
> per scan" does not seem to do anything in this case. Even worse, "Sliding
> Box Lacunarity Scan" does not work at all if I "Use Relative Sizes".
> My guess is that "Use default box sizes" generates a linear series from
> the smalles to the biggest grid by adding the smallest increment, but I
> have no idea how "Use Relative Sizes" works considering that power series
> and scaled series (exponential?) are separated options.
> Thank you.
>
> Vali
>