edge.Trans {spatstat.explore} | R Documentation |
Translation Edge Correction
Description
Computes Ohser and Stoyan's translation edge correction weights for a point pattern.
Usage
edge.Trans(X, Y = X, W = Window(X),
exact = FALSE, paired = FALSE,
...,
trim = spatstat.options("maxedgewt"),
dx=NULL, dy=NULL,
give.rmax=FALSE, gW=NULL)
rmax.Trans(W, g=setcov(W))
Arguments
X , Y |
Point patterns (objects of class |
W |
Window for which the edge correction is required. |
exact |
Logical. If |
paired |
Logical value indicating whether |
... |
Ignored. |
trim |
Maximum permitted value of the edge correction weight. |
dx , dy |
Alternative data giving the |
give.rmax |
Logical. If |
g , gW |
Optional. Set covariance of |
Details
The function edge.Trans
computes Ohser and Stoyan's translation edge correction
weight, which is used in estimating the K
function and in many
other contexts.
The function rmax.Trans
computes the maximum value of
distance r
for which the translation edge correction
estimate of K(r)
is valid.
For a pair of points x
and y
in a window W
,
the translation edge correction weight
is
e(u, r) = \frac{\mbox{area}(W)}{\mbox{area}(W \cap (W + y - x))}
where W + y - x
is the result of shifting the window W
by the vector y - x
. The denominator is the area of the overlap between
this shifted window and the original window.
The function edge.Trans
computes this edge correction weight.
If paired=TRUE
, then X
and Y
should contain the
same number of points. The result is a vector containing the
edge correction weights e(X[i], Y[i])
for each i
.
If paired=FALSE
,
then the result is a matrix whose i,j
entry gives the
edge correction weight e(X[i], Y[j])
.
Computation is exact if the window is a rectangle. Otherwise,
if
exact=TRUE
, the edge correction weights are computed exactly usingoverlap.owin
, which can be quite slow.if
exact=FALSE
(the default), the weights are computed rapidly by evaluating the set covariance functionsetcov
using the Fast Fourier Transform.
If any value of the edge correction weight exceeds trim
,
it is set to trim
.
The arguments dx
and dy
can be provided as
an alternative to X
and Y
.
If paired=TRUE
then dx,dy
should be vectors of equal length
such that the vector difference of the i
th pair is
c(dx[i], dy[i])
. If paired=FALSE
then
dx,dy
should be matrices of the same dimensions,
such that the vector difference between X[i]
and Y[j]
is
c(dx[i,j], dy[i,j])
. The argument W
is needed.
The value of rmax.Trans
is the shortest distance from the
origin (0,0)
to the boundary of the support of
the set covariance function of W
. It is computed by pixel
approximation using setcov
, unless W
is a
rectangle, when rmax.Trans(W)
is the length of the
shortest side of the rectangle.
Value
Numeric vector or matrix.
Author(s)
Adrian Baddeley Adrian.Baddeley@curtin.edu.au and Rolf Turner rolfturner@posteo.net.
References
Ohser, J. (1983) On estimators for the reduced second moment measure of point processes. Mathematische Operationsforschung und Statistik, series Statistics, 14, 63 – 71.
See Also
rmax.Trans
,
edge.Ripley
,
setcov
,
Kest
Examples
v <- edge.Trans(cells)
rmax.Trans(Window(cells))