focal: Focal values

Description

Calculate focal ("moving window") values for the neighborhood of focal cells using a matrix of weights, perhaps in combination with a function.

Usage

# S4 method for RasterLayer
focal(x, w, fun, filename='', na.rm=FALSE, pad=FALSE, padValue=NA, NAonly=FALSE, ...)

Value

RasterLayer

Arguments

x: RasterLayer
w: matrix of weights (the moving window), e.g. a 3 by 3 matrix with values 1; see Details. The matrix does not need to be square, but the sides must be odd numbers. If you need even sides, you can add a column or row with weights of zero or NA
fun: function (optional). The function fun should take multiple numbers, and return a single number. For example mean, modal, min or max. It should also accept a na.rm argument (or ignore it, e.g. as one of the 'dots' arguments. For example, length will fail, but function(x, ...){na.omit(length(x))} works.
filename: character. Filename for a new raster (optional)
na.rm: logical. If TRUE, NA will be removed from focal computations. The result will only be NA if all focal cells are NA. Except for some special cases (weights of 1, functions like min, max, mean), using na.rm=TRUE may not be a good idea in this function because it can unbalance the effect of the weights
pad: logical. If TRUE, additional 'virtual' rows and columns are padded to x such that there are no edge effects. This can be useful when a function needs to have access to the central cell of the filter
padValue: numeric. The value of the cells of the padded rows and columns
NAonly: logical. If TRUE, only cell values that are NA are replaced with the computed focal values
...: Additional arguments as for writeRaster

Details

focal uses a matrix of weights for the neighborhood of the focal cells. The default function is sum. It is computationally much more efficient to adjust the weights-matrix than to use another function through the fun argument. Thus while the following two statements are equivalent (if there are no NA values), the first one is faster than the second one:

a <- focal(x, w=matrix(1/9, nc=3, nr=3))

b <- focal(x, w=matrix(1,3,3), fun=mean)

There is, however, a difference if NA values are considered. One can use the na.rm=TRUE option which may make sense when using a function like mean. However, the results would be wrong when using a weights matrix.

Laplacian filter: filter=matrix(c(0,1,0,1,-4,1,0,1,0), nrow=3)

Sobel filters: fx=matrix(c(-1,-2,-1,0,0,0,1,2,1) / 4, nrow=3) and fy=matrix(c(1,0,-1,2,0,-2,1,0,-1)/4, nrow=3)

see the focalWeight function to create distance based circular, rectangular, or Gaussian filters.

Note that there is a difference between 0 and NA in the weights matrix. A zero weight cell is included in the computation, whereas a NA weight cell is excluded. This does not matter for "sum", nor for "mean" (zeros are removed), but it affects many other functions such as "var" as you could be adding a lot of zeros that should not be there.

Examples

Run this code

r <- raster(ncols=36, nrows=18, xmn=0)
values(r) <- runif(ncell(r)) 

# 3x3 mean filter
r3 <- focal(r, w=matrix(1/9,nrow=3,ncol=3)) 

# 5x5 mean filter
r5 <- focal(r, w=matrix(1/25,nrow=5,ncol=5)) 

# Gaussian filter
gf <- focalWeight(r, 2, "Gauss")
rg <- focal(r, w=gf)

# The max value for the lower-rigth corner of a 3x3 matrix around a focal cell
f = matrix(c(0,0,0,0,1,1,0,1,1), nrow=3)
f
rm <- focal(r, w=f, fun=max)

# global lon/lat data: no 'edge effect' for the columns
xmin(r) <- -180
r3g <- focal(r, w=matrix(1/9,nrow=3,ncol=3)) 


if (FALSE) {
## focal can be used to create a cellular automaton

# Conway's Game of Life 
w <- matrix(c(1,1,1,1,0,1,1,1,1), nr=3,nc=3)
gameOfLife <- function(x) {
	f <- focal(x, w=w, pad=TRUE, padValue=0)
	# cells with less than two or more than three live neighbours die
	x[f<2 | f>3] <- 0
	# cells with three live neighbours become alive
	x[f==3] <- 1
	x
}

# simulation function
sim <- function(x, fun, n=100, pause=0.25) {
	for (i in 1:n) {
		x <- fun(x)
		plot(x, legend=FALSE, asp=NA, main=i)
		dev.flush()
		Sys.sleep(pause)
	}
	invisible(x)
}

# Gosper glider gun
m <- matrix(0, nc=48, nr=34)
m[c(40, 41, 74, 75, 380, 381, 382, 413, 417, 446, 452, 480, 
  486, 517, 549, 553, 584, 585, 586, 619, 718, 719, 720, 752, 
  753, 754, 785, 789, 852, 853, 857, 858, 1194, 1195, 1228, 1229)] <- 1
init <- raster(m)

# run the model
sim(init, gameOfLife, n=150, pause=0.05)

## Implementation of Sobel edge-detection filter
## for RasterLayer r
sobel <- function(r) {
	fy <- matrix(c(1,0,-1,2,0,-2,1,0,-1), nrow=3)
	fx <- matrix(c(-1,-2,-1,0,0,0,1,2,1) , nrow=3)
	rx <- focal(r, fx)
	ry <- focal(r, fy)
	sqrt(rx^2 + ry^2)
}
}