fracdim: Calculation of Fractal Dimension of Lef Veins Based on the...

In biogeom: Biological Geometries

Calculation of Fractal Dimension of Lef Veins Based on the Box-Counting Method

Description

fracdim is used to calculate the fractal dimension of leaf veins based on the box-counting method.

Usage

fracdim(x, y, frac.fig = TRUE, denomi.range = seq(8, 30, by=1), 
        ratiox = 0.02, ratioy = 0.08, main = NULL)

Arguments

x	the x coordinates of leaf-vein pixels.
y	the y coordinates of leaf-vein pixels.
frac.fig	the option of drawing the results of the linear fitting.
denomi.range	the number of equidistant segments of the maximum range between the range of the x coordinates and that of the y coordinates.
ratiox	the the x coordinate of the location parameter for positioning the legend.
ratioy	the the y coordinate of the location parameter for positioning the legend.
main	the main title of the figure.

Details

The box-counting approach uses a group of boxes (squares for simplicity) with different sizes (\delta) to divide the leaf vein image into different parts. Let N represent the number of boxes that include at least one pixel of leaf vein. The maximum of the range of the x coordinates and the range of the y coordinates for leaf-vein pixels is defined as z. Let \delta represent the vector of z/denomi.range. Then, we used the following equation to calculate the fractal dimension of leaf veins:

\mathrm{ln } N = a + b\,\mathrm{ ln} \left({\delta}^{-1}\right),

where b is the theoretical value of the fractal dimension. We can use its estimate as the numerical value of the fractal dimension for a leaf venation network.

Value

a	the estimate of the intercept.
sd.a	the standard deviation of the estimated intercept.
lci.a	the lower bound of the 95% confidence interval of the estimated intercept.
uci.a	the upper bound of the 95% confidence interval of the estimated intercept.
b	the estimate of the slope.
sd.b	the standard deviation of the estimated slope.
lci.a	the lower bound of the 95% confidence interval of the estimated slope.
uci.a	the upper bound of the 95% confidence interval of the estimated slope.
r.sq	the coefficient of determination.
delta	the vector of box sizes.
N	the number of boxes that include at least one pixel of leaf vein.

Note

Here, x and y cannot be adjusted by the adjdata function because the leaf veins are not the leaf's boundary data.

Author(s)

Peijian Shi [e-mail], Johan Gielis [e-mail], Brady K. Quinn [e-mail].

References

Shi, P., Gielis, J., Quinn, B.K., Niklas, K.J., Ratkowsky, D.A., Schrader, J., Ruan, H., Wang, L., Niinemets, Ü. (2022) 'biogeom': An R package for simulating and fitting natural shapes. Annals of the New York Academy of Sciences 1516, 123-134. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/nyas.14862")}

Shi, P., Yu, K., Niinemets, Ü., Gielis, J. (2021) Can leaf shape be represented by the ratio of leaf width to length? Evidence from nine species of Magnolia and Michelia (Magnoliaceae). Forests 12, 41. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.3390/f12010041")}

Vico, P.G., Kyriacos, S., Heymans, O., Louryan, S., Cartilier, L. (1998) Dynamic study of the extraembryonic vascular network of the chick embryo by fractal analysis. Journal of Theoretical Biology 195, 525-532. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1006/jtbi.1998.0810")}

See Also

veins

Examples

data(veins)

dev.new()
plot(veins$x, veins$y, cex=0.01, asp=1, cex.lab=1.5, cex.axis=1.5, 
     xlab=expression(italic("x")), ylab=expression(italic("y")))

fracdim(veins$x, veins$y)

graphics.off()

biogeom documentation built on May 29, 2024, 8:52 a.m.