DispField: Displacement fields based on 2D cross-covariance

In ICvectorfields: Vector Fields from Spatial Time Series of Population Abundance

Displacement fields based on 2D cross-covariance

Description

Calculates a displacement field based on the cross-covariance of two input rasters presumably representing spatial population abundance or density at two different instances of time.

Usage

DispField(inputrast1, inputrast2, factv1, facth1, restricted = FALSE)

Arguments

inputrast1	a raster as produced by terra::rast
inputrast2	a raster of equivalent dimension to inputrast1 as produced by terra::rast
factv1	an odd integer for the vertical dimension of sub-grids
facth1	an odd integer for the horizontal dimension of sub-grids
restricted	logical (TRUE or FALSE)

Details

The input rasters are first converted to equivalent matrices. The function then divides the domain up into sub-grids of size factv1 X facth1, which are vertical and horizontal sub-grid dimensions.

If restricted is set to FALSE (the default), the function computes cross-covariance between each sub-grid of the first input raster and the entirety of the second input raster and then uses the location of maximum cross-covariance to estimate displacement in the vertical and horizontal directions from the centre of each sub-grid.

If restricted is set to TRUE, the function uses cross-covariance between each sub-grid in the first input raster and the equivalent sub-grid in the second input raster to estimate vertical and horizontal displacement.

Reference coordinates and cell size are extracted from the first input raster such that the locations from whence displacement is estimated as well as displacement estimates can be expressed in the units of the projected coordinates.

The coordinates are assumed to increase vertically and horizontally from the lower left corner of the two-dimensional domain.

Caution is warranted when defining the sub-grid dimensions because the function can produce erroneous results when sub-grids are too small.

Value

A data frame is returned with the following column names: rowcent, colcent, frowmin, frowmax, fcolmin, fcolmax, centx, centy, dispx, and dispy. The rowcent and colcent column names are the row and column indices for the center of each sub-grid; frowmin and frowmax are the sub-grid minimum and maximum row indices; fcolmin and fcolmax are the sub-grid minimum and maximum column indices; centx and centy are the projected coordinates of the centre of the subgrid derived from the raster input files; dispx and dispy are the displacement in the horizontal and vertical directions in the same units as the projected coordinates of the raster input files.

See Also

DispFieldbb for a similar function using a bounding box to define a focal region, DispFieldST for a version designed to quantify persistent directional movement when the time series features more than two time instances, DispFieldSTall for a version designed to quantify persistent directional movement when velocity is variable in space, and Xcov2D for demonstration of how two-dimensional cross-covariance is used to determine displacement (see examples of Xcov2D function documentation).

Examples

(Mat1 <- matrix(rep(c(1:5, 0, 0, 0, 0), 9), nrow = 9, byrow = TRUE))
(Mat2 <- matrix(rep(c(0, 1:5, 0, 0, 0), 9), nrow = 9, byrow = TRUE))

# rasterizing
rast1 <- terra::rast(Mat1)
terra::plot(rast1)
rast2 <- terra::rast(Mat2)
terra::plot(rast2)

(VFdf1 <- DispField(rast1, rast2, factv1 = 9, facth1 = 9))
# The second raster is shifted right by 1 unit relative to the first raster
# dispx = 1

ICvectorfields documentation built on March 18, 2022, 7:34 p.m.