Which graphic?

[Jelena Vasiljevic]

Dear Audrey,

 

Thank you very much for your thorough explanation. That was very useful, but I also need an information about next issue: which one of several graphics that I get for each parametar should I choose to put into further statistical analysys? For example, when I analize one picture (precisely, region of the picture), I get several graphics for F vs Alpha (the same case is for D vs Q, etc). Because I need only one graphic for each parametar, which one (and I need only one) of those graphics should I use. Should I, perhaps, use mean values of given extremes? Please, help me with this :)

 

Sincerely,

Jelena Andjelkovic

 

 

 

 

 

----- Original Message -----
From: "audrey karperien" <[hidden email]>
To: <[hidden email]>
Sent: Friday, February 17, 2006 6:23 PM
Subject: Re: SOS What graphic should I use?

>I forgot to mention to include images of known mono-and multi-fractals and
>euclidean forms of similar size and foreground pixels to compare to your
>data images.
>
> audrey karperien <[hidden email]> wrote:  Hello.
> 1. It is likely that you can set it to 1 scan location. The number of
> scans depends on the sampling you need. FracLac 1) randomly samples parts
> of an image then reconstructs the distribution, and more effectively, 2)
> samples the entire image multiple times after partitioning it in different
> ways. Bottom line: 1 will probably be good, but if there is a big
> difference in the graphs when you set it to 4, then you need to consider
> more data.
> 2. Use DQ vs Q plots graphics and for statistical analysis, use the slope
> of DQ vs. Q and the coefficient of variation. The plot is usually either
> essentially unchanging or decreasing. For simple monofractals, DQ is
> usually essentially unchanged, with low dispersion, over Q so the DQ vs. Q
> plot is stable and generally non-decreasing. For multifractals, in
> contrast, DQ typically decreases with Q, being sigmoidal around Q=0.The
> coefficient of variation is one way to measure the variation (CV =
> standard deviation over the mean). The CV for the graph of DQ vs. Q is
> generally greater for multifractals than monofractals.
> 3. Also use f(alpha) vs alpha plots, converging = not multifractal;
> broadly humped = multifractal. The graph of a monofractal for f(alpha) vs
> alpha is typically converging (especially for Q>0) but for multifractals
> f(alpha) rises and falls over a broad hump with alpha.
> 4. Use the default minimum pixel ratio. That setting is important for
> excluding nonrepresentative image samples.
> 5. Strengthen your argument using sliding lacunarity which adds
> information for understanding scaling of patterns in digital images:
> multifractal patterns are characterized by negative Dq vs Q, with high
> CVs, diverging humped f(alpha) spectra and a typically humped then
> decreasing lacunarity plot; monofractals converge in the f(alpha) plot
> (Q>0) and generally increase in lacunarity; non fractals converge over the
> f(alpha) vs alpha plot and for simple forms usually show low, stable
> lacunarity.
>
> Jelena Vasiljevic wrote:
>
> Hi
>
> I am doing my thesis on multifractal analysys of medical images, and need
> any kind of help I can get. When I've analyzed images with ImageJ , for
> every analized image I've got several graphics with different values of F
> vs Alpha, Q, F vs Q, Alpha vs Q, etc. Should I use mean values of each of
> those variables for statistical analysys, or the last one made graphic or
> something else? I do that analysys on images of three groups of cells, and
> my aim is to find some statisticaly important diferences between those
> groups (regarding Alpha, Q, FvsAlpha...). I am not sure which values for
> "Minimum pixel ratio to accept in samples" and "Number of global scan
> positions" should I set. Could you please give me some suggestions, it is
> very urgent?
>
> Thank you in advance!
>
> Sincerely,
>
> Jelena Andjelkovic

[Leonardo Bocchi]

Jelena Vasiljevic wrote:

> Dear Audrey,
>
>  
>
> Thank you very much for your thorough explanation. That was very useful, but I also need an information about next issue: which one of several graphics that I get for each parametar should I choose to put into further statistical analysys? For example, when I analize one picture (precisely, region of the picture), I get several graphics for F vs Alpha (the same case is for D vs Q, etc). Because I need only one graphic for each parametar, which one (and I need only one) of those graphics should I use. Should I, perhaps, use mean values of given extremes? Please, help me with this :)
>
>  
>
> Sincerely,
>
> Jelena Andjelkovic

In my work, I use the parameter 'average of (slope of the curve)'.

In my images, there is a part of the curve which is approximately linear
for all images. Therefore, I resorted to evaluate the slope of each
curve over the linear tract, and average it for all curves belonging to
the image.
But I think it mainly depend on the problem...

Leonardo Bocchi


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