tortuosity {SoPhy}R Documentation

Variability of the tortuosity

Description

The function estimates the ratio between the mean tortuosity and the smallest tortuosity from profiles of Brilliant Blue tracer experiments

Usage

  tortuosity(depth, freq,range.depth, range.xi, len.xi=100,
             lower.bound.m = 1.005, tolerance.m=0.01, PrintLevel=0) 

Arguments

depth depth in pixels
freq number of stained pixels found in depth depth
range.depth range of depths for which 1-H^* is fitted
range.xi range of values of xi for which 1-H^* is fitted
len.xi range.xi and len.xi define the grid seq(min(range.xi), max(range.xi), len=len.xi) for which 1-H^* is fitted.
lower.bound.m lower bound for m used in the numerical optimisation
tolerance.m non-negative value. If tolerance.m=0 only the optimal xi is used to estimate m. If tolerance.m>0 then all estimated m(D, xi) are considered for which the span of m is less than or equal to (1 + tolerance.m) times the minimal span value.
PrintLevel integer. If the value is greater than 1 then tracing information is given

Value

tortuosity returns a list of the following elements:

xi vector of length len.xi. It contains the values of xi used in the algorithm
raw.m matrix with len.xi rows. The number of colums equals the number of depth values that are between the given bounds range.depth. It contains the fitted values of m
span.xi vector of length len.xi contains span of all raw.m values for the respective value of xi
span.m vector of length len.xi. It contains the difference between the largest and the smallest value of raw.m for given xi
opt list of the optimal values: xi, m, s, mspan (the span.xi found at xi) and D (threshold depth)
input list of two vectors: freq and depth
fitted list of two vectors that give the best fitted curve: depth and p; the latter cannot be given if tolerance.m>0

Author(s)

Martin Schlather, martin.schlather@math.uni-goettingen.de http://www.stochastik.math.uni-goettingen.de/institute

References

Schlather, M. and Huwe, B. (2005) A characteristic for the variability of tortuosity. Submitted.

Examples

data(F04)
path <- paste(system.file(package='SoPhy'),"tracer", sep="/")
F04$name <- paste(path, "F04.G.tif", sep="/")
m <- analyse.profile(F04, estimate.all=FALSE, method="fix.m",
                     selected.rate=c(0, 0), selected.dist=NULL,
                     interactive=FALSE, Print=0)
stained <- m$fct(m$picture, m$param)
freq <- m$absfr
truedepth <- m$r.i$data[, 1] + ncol(stained) - m$loc[[1]]$y[2]
tol = 0

mt <- tortuosity(truedepth, freq,  range.depth=c(85, 97),
                 range.xi=c(-2.5, -0.6), Print=2, tol=tol)
str(mt$opt)

# fig. 3A in Schlather and Huwe (2005)
matplot(mt$xi, mt$raw.m, xlab=expression(xi), ylab="m",
        type="l", col=1, lty=1)     

# fig. 3B in Schlather and Huwe (2005)
plot(mt$xi, mt$span.m, xlab=expression(xi), ylab="span m",
     type="l", col=1, lty=1)
for (cex in c(9, 9.5, 10))
  points(mt$opt$x, mt$opt$mspan, cex=cex, col="darkgrey")

# fig. 2 in Schlather and Huwe (2005)
plot(mt$input$depth, mt$input$freq, xaxs="i", yaxs="i",
     pch=16, ylab="stained pixels", xlab="depth [pixels]",
     col="blue", cex=2)
lines(mt$fitted$depth, mt$fitted$p, lwd=3, col=2)

[Package SoPhy version 1.0.34 Index]