Head-bang smoothing

Smooths values at points or areal units (rates by area centroid, say) by Hansen's (1991) head-bang rule, which removes isolated peaks and troughs while keeping edges between regions of different level. For each unit i the rule takes its nn nearest neighbours and every pair (j, k) of them whose angle at i is at least ang degrees, so that i lies roughly between j and k (a triple); with ntrip > 0 only the ntrip triples whose ends are nearest (smallest |p_j - p_i| + |p_k - p_i|) are kept. Each triple gives a low value min(v_j, v_k) and a high value max(v_j, v_k); the low screen is the median of the lows, the high screen the median of the highs, and the new value is the median of the low screen, v_i and the high screen, so v_i moves only if it lies outside both. With weights w (populations at risk, say) the screens are weighted medians, each end weighted by its own unit's weight, after Mungiole, Pickle and Simonson (1999): the smallest value whose cumulative weight reaches half the total. A unit with no triple (on the outer edge of the points) keeps its value; Hansen's extrapolated end triples are not formed. Each of iter passes starts from the previous pass's values.

Usage

hdbang(
  x,
  y = NULL,
  v,
  w = NULL,
  nn = 8,
  ang = 135,
  ntrip = 0,
  iter = 1,
  lonlat = FALSE
)

Arguments

x, y

The points: x and y numeric vectors of equal length; or x a matrix or data frame with columns named x and y (or X and Y, as sf::st_coordinates() names them, or lon and lat with lonlat = TRUE) and y NULL; or x an sf or sfc object of POINT geometries, whose coordinate reference system must agree with lonlat. An unnamed two-column matrix is read as x then y; other columns are never taken by position. Vectors given separately (x, y, and w or t where a function takes them) are matched by name when every one is named and no name repeats, as elsewhere in the package; otherwise by position. No missing or infinite values.

v

The values to smooth: finite numbers, one per point.

w

NULL, or positive weights, one per point.

nn

The number of nearest neighbours searched: from 2 to the number of points less 1.

ang

The smallest angle at i of a triple, in degrees, from 90 to 180 (135 by convention).

ntrip

The most triples used per unit, nearest first; 0 for all.

iter

The number of passes: a whole number from 0.

lonlat

FALSE (the default) when x and y are planar coordinates in one length unit; TRUE when they are longitude and latitude in degrees, which are then projected to metres by eqproj() about their own centre, and centres are returned in degrees. It is never guessed.

Value

A numeric vector of smoothed values, one per point, in input order.

References

Hansen, K. M. (1991). Head-banging: robust smoothing in the plane. IEEE Transactions on Geoscience and Remote Sensing, 29(3), 369-378.

Mungiole, M., Pickle, L. W. and Simonson, K. H. (1999). Application of a weighted head-banging algorithm to mortality data maps. Statistics in Medicine, 18(23), 3201-3209.

Examples

g <- expand.grid(x = 1:6, y = 1:6)
v <- rep(1, 36)
v[15] <- 50
hdbang(g, v = v)[15]
#> [1] 1