SOS What grafic should I use?

[Jelena Vasiljevic]

 
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 grafic 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

elektrotehnical ing.

Institute " Mihajlo Pupin"

Belgrade

[audrey karperien]

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 <[hidden email]> 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 grafic 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

elektrotehnical ing.

Institute " Mihajlo Pupin"

Belgrade
 

[audrey karperien]

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 grafic 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

elektrotehnical ing.

Institute " Mihajlo Pupin"

Belgrade