Each scan is interpreted differently. Click below to learn how to interpret the different results.

Interpreting Results with FracLac

Type of Result

This page is a central index for interpreting results files from your scans.

It covers regular box counting scans and links you to other types of scans. Click a link below or search for a term using your browser's "Find" function. You can find further details in the Standard Box Counting tutorial, Background Section, glossary, JavaDoc, and source code.

The FracLac Box Counting Results File

  1. This is the default results file generated automatically with a box counting scan.
  2. General headings repeated in multiple places are statistics for the parameter that comes in the column before it (e.g., if you see a column labelled "Mean DB" with a column beside it labeled "CV", then the second column is the CV for all of the DBs):
    1. CV=standard deviation/mean=Coefficient of Variation
    2. r2= coefficient of determination for the value preceding this in the results file
    3. Standard Error (SE)= standard error for the value preceding this in the results file
  3. Specific column headings are described in the scrolling window below.
  4. Mean. Some columns in the file have the word "mean" listed for some value, V, referring to the average over multiple grids. If a series of grid sizes was reapplied over multiple orientations (an option set in the options panel), then the column contains
    V =GridsΣg=1(Vg)/Grids
    where the coordinates of each grid orientation are available in the data file; otherwise, the column contains V at the grid orientation given in the filename column.

FracLac 2.5 Release 1b5k: file/slice/roi

The first column in the results file is a description of the part of the image scanned.

  • The first part of the entry is the image file name followed by "roi" if there was an roi selected, then "S" and the slice number (e.g., "yourimageS1" if there was no roi selected and this was the first or only slice in the image).
  • The numbers that follow in parentheses are the x,y coordinates then width × height of the rectangle scanned.
  • the last part is the least x,y--greatest x,y coordinates of the grid.
  • If there was an roi, the grid's coordinates are relative to the roi, so start at 0,0.
  • If there was more than one grid orientation, only the first is reported here but all are reported in the Data file.
DB for each grid orientation
more on this in the tutorial

Foreground pixels

The number of pixels deemed foreground. You may want to compare this number and the value for density to the values for complexity and heterogeneity.more on this in the tutorial

Total pixels

The total pixels in the image or roi scanned that were the foreground colour or the background colour. This value will be over a rectangular area; compare it to area of the convex hull. more on this in the tutorial

Mean DB

The box counting dimension (DB) or its average (DB).*UNDERSTANDING MEANS
DB for each grid orientation

Mean ΛD

The lacunarity based box counting dimension (ΛDB) or its average.*UNDERSTANDING MEANS.

r2

Standard Error (SE)

Mean Smoothed (Biggest) D

A filtered value for reference; the smoothed box counting dimension (DB(biggest)) or its average (DB(biggest)) UNDERSTANDING MEANS.

Mean Smoothed (Smallest) D

the smoothed box counting dimension (DB(small)) or its average (DB(small)); this is a relatively stable, filtered value that corrects for inappropriate box sizes *UNDERSTANDING MEANS.

Minimum Cover D

The DB calculated from a most efficient grid covering.

Minimum Cover Smoothed (Biggest) D

The DB(biggest) filtered for the minimum cover if there was more than 1 grid position; otherwise the same value reported as DB(biggest)

Minimum Cover Smoothed (Smallest) D

The DB(small) filtered for the minimum cover if there was more than 1 grid position; otherwise the same value reported as DB(small)

Maximum Cover D

A reference provided for data checking only; see the Glossary for more information

Maximum Cover Smoothed (Biggest) D

A reference provided for data checking only; see the Glossary for more information

Maximum Cover Smoothed (Smallest) D

A reference provided for data checking only; see the Glossary for more information

Mean Y-intercept for D

the y-intercept or its mean from the regression line of count vs. ε that was used for calculating the DB*Understanding Means
the prefactor

Λ Mean Y-intercept Prefactor for D (Count vs Mass)

PΛ is a measure of heterogeneity based on the y-intercept for the regression lines from all grid locations; it depends on ε and the number of grids; as explained in the calculations, PΛ = 0 if there is only 1 grid positionthe calculations Two values separated by a "/" are presented; they are calculated by essentially the same method, but the first uses counts (the number of boxes containing pixels at ε), and the second masses (stats for the pixels per box at ε).

σ/μ for Y-Intercepts for D

the CV for variation in the equations used to calculate the DB; tells how much variation there was in the absolute position, the y-intercept, according to grid orientation; is 0 if there was only 1 position used

Coefficient of Variation

Lacunarity =L(F (foreground mass))=(Σ[FΛ])/Grids

lacunarity based on the variation in pixels per box summarized over all grid orientations for an image; "F" refers to foreground pixels per box; To interpret the value reported here, refer to Interpreting Lacunarity: Λ.

σ/μ for L(F)

Lacunarity =L(E (foreground and empty space))=(Σ[EΛ])/GRIDS

A type of lacunarity based on the image count

σ/μ for L(E)

Coefficient of Variation

Lacunarity =L(binned probability distribution for foreground)=(Σ[FBPDΛ])/GRIDS

Lacunarity based on foreground pixels using a binned probability distribution. See Fλ and BPD

σ/μ for L(FBPD)

Lacunarity =L(EBPD (foreground and empty boxes))=(Σ[EBPDΛ])/GRIDS

Lacunarity based on the empties count using a binned probability distribution. See Fλ and BPD

σ/μ for L(EBPD)

Variation in Count=Σ(Count σ/μ)/GRIDS

The relative variation in the number of boxes it took to cover an image for the mean DB over all grid orientations

Σ(Foreground Count CV/Image Count CV)/GRIDS

See explanation

Box Sizes for D

actual number of sizes used to calculate the DB; see settings also

Box Sizes for Smoothed D (Biggest)

The number of box sizes the original series was filtered to for calculating the smoothed DB(big)

Box Sizes for Smoothed D (Smallest)

The number of box sizes the original series was filtered to for calculating the smoothed DB(small)

GRIDS = Number of origins

The number of times a complete scan was done, each at a different randomly generated grid position, as specified in the box counting options. The x,y coordinates of the starting grid are specified in the filename columns for the results and data files.

Mean Max box size for D

The average from the maximum box size used at each grid orientation

Mean Min box size for D

The average from the minimum box size used at each grid orientation