Translation Edge Correction
Computes Ohser and Stoyan's translation edge correction weights for a point pattern.
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))
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 x and y coordinates
of the vector differences between the points.
Incompatible with |
give.rmax |
Logical. If |
g, gW |
Optional. Set covariance of |
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) = area(W) / area(intersect(W, 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 using
overlap.owin
, which can be quite slow.
if exact=FALSE
(the default),
the weights are computed rapidly by evaluating the
set covariance function setcov
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 ith 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.
Numeric vector or matrix.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au and Rolf Turner r.turner@auckland.ac.nz.
Ohser, J. (1983) On estimators for the reduced second moment measure of point processes. Mathematische Operationsforschung und Statistik, series Statistics, 14, 63 – 71.
v <- edge.Trans(cells) rmax.Trans(Window(cells))
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