[GIS] Conditional assignment of values to adjacent raster cells

adjacencyrraster

I have a value raster:

m <- matrix(c(2,4,5,5,2,8,7,3,1,6,
         5,7,5,7,1,6,7,2,6,3,
         4,7,3,4,5,3,7,9,3,8,
         9,3,6,8,3,4,7,3,7,8,
         3,3,7,7,5,3,2,8,9,8,
         7,6,2,6,5,2,2,7,7,7,
         4,7,2,5,7,7,7,3,3,5,
         7,6,7,5,9,6,5,2,3,2,
         4,9,2,5,5,8,3,3,1,2,
         5,2,6,5,1,5,3,7,7,2),nrow=10, ncol=10, byrow = T)
r <- raster(m)
extent(r) <- matrix(c(0, 0, 10, 10), nrow=2)
plot(r)
text(r)

From this raster, how can I assign values (or change values) to the 8 adjacent cells of the current cell according to this illustration ? I placed a red point within the current cell from this code line:

points(xFromCol(r, col=5), yFromRow(r, row=5),col="red",pch=16)

Here, the expected result will be:

where the value of the current cell (i.e, 5 in the value raster) is replaced with 0.

Overall, the new values for the 8 adjacent cells must be calculated as follows:

New value = average of cell values contained in the red rectangle * distance between the current cell (red point) and the adjacent cell (i.e., sqrt(2) for diagonally adjacent cells or 1 otherwise)

Update

When bounds for the adjacent cells are out of the raster limits, I need to calculate new values for the adjacent cells which respect the conditions. The adjacent cells which don't respect the conditions will equal to "NA".

For example, if the reference position is c(1,1) instead of c(5,5) by using [row, col] notation, only the new value at the bottom-right corner can be calculated. Thus, the expected result will be:

     [,1] [,2] [,3]       
[1,] NA   NA   NA         
[2,] NA   0    NA         
[3,] NA   NA   New_value

For example, if the reference position is c(3,1), only the new values at the top-right, right and bottom-right corners can be calculated. Thus, the expected result will be:

     [,1] [,2] [,3]       
[1,] NA   NA   New_value         
[2,] NA   0    New_value         
[3,] NA   NA   New_value

Here is my first attempt at this by using the function focal but I have some difficulty to make an automatic code.

Select adjacent cells

mat_perc <- matrix(c(1,1,1,1,1,
                     1,1,1,1,1,
                     1,1,0,1,1,
                     1,1,1,1,1,
                     1,1,1,1,1), nrow=5, ncol=5, byrow = T)
cell_perc <- adjacent(r, cellFromRowCol(r, 5, 5), directions=mat_perc, pairs=FALSE, sorted=TRUE, include=TRUE)
r_perc <- rasterFromCells(r, cell_perc)
r_perc <- setValues(r_perc,extract(r, cell_perc))
plot(r_perc)
text(r_perc)

if the adjacent cell is located at the upper-left corner of the current cell

focal_m <- matrix(c(1,1,NA,1,1,NA,NA,NA,NA), nrow=3, ncol=3, byrow = T)
focal_function <- function(x) mean(x,na.rm=T)*sqrt(2)
test <- as.matrix(focal(r_perc, focal_m, focal_function))

if the adjacent cell is located at the upper-middle corner of the current cell

focal_m <- matrix(c(1,1,1,1,1,1,NA,NA,NA), nrow=3, ncol=3, byrow = T)
focal_function <- function(x) mean(x,na.rm=T)
test <- as.matrix(focal(r_perc, focal_m, focal_function))

if the adjacent cell is located at the upper-left corner of the current cell

focal_m <- matrix(c(NA,1,1,NA,1,1,NA,NA,NA), nrow=3, ncol=3, byrow = T)
focal_function <- function(x) mean(x,na.rm=T)*sqrt(2)
test <- as.matrix(focal(r_perc, focal_m, focal_function))

if the adjacent cell is located at the left corner of the current cell

focal_m <- matrix(c(1,1,NA,1,1,NA,1,1,NA), nrow=3, ncol=3, byrow = T)
focal_function <- function(x) mean(x,na.rm=T)
test <- as.matrix(focal(r_perc, focal_m, focal_function))

if the adjacent cell is located at the right corner of the current cell

focal_m <- matrix(c(NA,1,1,NA,1,1,NA,1,1), nrow=3, ncol=3, byrow = T)
focal_function <- function(x) mean(x,na.rm=T)
test <- as.matrix(focal(r_perc, focal_m, focal_function))

if the adjacent cell is located at the bottom-left corner of the current cell

focal_m <- matrix(c(NA,NA,NA,1,1,NA,1,1,NA), nrow=3, ncol=3, byrow = T)
focal_function <- function(x) mean(x,na.rm=T)*sqrt(2)
test <- as.matrix(focal(r_perc, focal_m, focal_function))

if the adjacent cell is located at the bottom-middle corner of the current cell

focal_m <- matrix(c(NA,NA,NA,1,1,1,1,1,1), nrow=3, ncol=3, byrow = T)
focal_function <- function(x) mean(x,na.rm=T)
test <- as.matrix(focal(r_perc, focal_m, focal_function))

if the adjacent cell is located at the bottom-right corner of the current cell

focal_m <- matrix(c(NA,NA,NA,NA,1,1,NA,1,1), nrow=3, ncol=3, byrow = T)
focal_function <- function(x) mean(x,na.rm=T)*sqrt(2)
test <- as.matrix(focal(r_perc, focal_m, focal_function))

Best Answer

The function AssignValuesToAdjacentRasterCells below returns a new RasterLayer object with the desired values assigned from the original raster input. The function check if the adjacent cells from the reference position are inside raster limits. It also display messages if some bound is out. If yo need to move the reference position you can simply write an iteration changing input position to c(i,j).

Data input

# Load packages
library("raster")

# Load matrix data
m <- matrix(c(2,4,5,5,2,8,7,3,1,6,
              5,7,5,7,1,6,7,2,6,3,
              4,7,3,4,5,3,7,9,3,8,
              9,3,6,8,3,4,7,3,7,8,
              3,3,7,7,5,3,2,8,9,8,
              7,6,2,6,5,2,2,7,7,7,
              4,7,2,5,7,7,7,3,3,5,
              7,6,7,5,9,6,5,2,3,2,
              4,9,2,5,5,8,3,3,1,2,
              5,2,6,5,1,5,3,7,7,2), nrow=10, ncol=10, byrow = TRUE)

# Convert matrix to RasterLayer object
r <- raster(m)

# Assign extent to raster
extent(r) <- matrix(c(0, 0, 10, 10), nrow=2)

# Plot original raster
plot(r)
text(r)
points(xFromCol(r, col=5), yFromRow(r, row=5), col="red", pch=16)

Function

# Function to assigning values to the adjacent raster cells based on conditions
# Input raster: RasterLayer object
# Input position: two-dimension vector (e.g. c(5,5))

AssignValuesToAdjacentRasterCells <- function(raster, position) {

  # Reference position
  rowPosition = position[1]
  colPosition = position[2]

  # Adjacent cells positions
  adjacentBelow1 = rowPosition + 1
  adjacentBelow2 = rowPosition + 2
  adjacentUpper1 = rowPosition - 1
  adjacentUpper2 = rowPosition - 2
  adjacentLeft1 = colPosition - 1 
  adjacentLeft2 = colPosition - 2 
  adjacentRight1 = colPosition + 1
  adjacentRight2 = colPosition + 2

  # Check if adjacent cells positions are out of raster positions limits
  belowBound1 = adjacentBelow1 <= nrow(raster)
  belowBound2 = adjacentBelow2 <= nrow(raster)
  upperBound1 = adjacentUpper1 > 0
  upperBound2 = adjacentUpper2 > 0
  leftBound1 = adjacentLeft1 > 0 
  leftBound2 = adjacentLeft2 > 0 
  rightBound1 = adjacentRight1 <= ncol(raster)
  rightBound2 = adjacentRight2 <= ncol(raster) 

  if(upperBound2 & leftBound2) {

    val1 = mean(r[adjacentUpper2:adjacentUpper1, adjacentLeft2:adjacentLeft1]) * sqrt(2)

  } else {

    val1 = NA

  }

  if(upperBound2 & leftBound1 & rightBound1) {

    val2 = mean(r[adjacentUpper1:adjacentUpper2, adjacentLeft1:adjacentRight1])

  } else {

    val2 = NA

  }

  if(upperBound2 & rightBound2) {

    val3 = mean(r[adjacentUpper2:adjacentUpper1, adjacentRight1:adjacentRight2]) * sqrt(2)

  } else {

    val3 = NA

  }

  if(upperBound1 & belowBound1 & leftBound2) {

    val4 = mean(r[adjacentUpper1:adjacentBelow1, adjacentLeft2:adjacentLeft1])

  } else {

    val4 = NA

  }

  val5 = 0

  if(upperBound1 & belowBound1 & rightBound2) {

    val6 = mean(r[adjacentUpper1:adjacentBelow1, adjacentRight1:adjacentRight2])

  } else {

    val6 = NA

  }

  if(belowBound2 & leftBound2) {

    val7 = mean(r[adjacentBelow1:adjacentBelow2, adjacentLeft2:adjacentLeft1]) * sqrt(2)

  } else {

    val7 = NA

  }

  if(belowBound2 & leftBound1 & rightBound1) {

    val8 = mean(r[adjacentBelow1:adjacentBelow2, adjacentLeft1:adjacentRight1])

  } else {

    val8 = NA

  }

  if(belowBound2 & rightBound2) {

    val9 = mean(r[adjacentBelow1:adjacentBelow2, adjacentRight1:adjacentRight2]) * sqrt(2)

  } else {

    val9 = NA

  }

  # Build matrix
  mValues = matrix(data = c(val1, val2, val3,
                            val4, val5, val6,
                            val7, val8, val9), nrow = 3, ncol = 3, byrow = TRUE)    

  if(upperBound1) {

    a = adjacentUpper1

  } else {

    # Warning message
    cat(paste("\n Upper bound out of raster limits!"))
    a = rowPosition
    mValues <- mValues[-1,]

  }

  if(belowBound1) {

    b = adjacentBelow1

  } else {

    # Warning message
    cat(paste("\n Below bound out of raster limits!"))
    b = rowPosition
    mValues <- mValues[-3,]

  }

  if(leftBound1) {

    c = adjacentLeft1

  } else {

    # Warning message
    cat(paste("\n Left bound out of raster limits!"))
    c = colPosition
    mValues <- mValues[,-1]

  }

  if(rightBound1) {

    d = adjacentRight1

  } else {

    # Warning
    cat(paste("\n Right bound out of raster limits!"))
    d = colPosition
    mValues <- mValues[,-3]

  }

  # Convert matrix to RasterLayer object
  rValues = raster(mValues)

  # Assign values to raster
  raster[a:b, c:d] = rValues[,]  

  # Assign extent to raster
  extent(raster) <- matrix(c(0, 0, 10, 10), nrow = 2)

  # Return raster with assigned values
  return(raster)      

}

Run examples

# Run function AssignValuesToAdjacentRasterCells

# reference position (1,1)
example1 <- AssignValuesToAdjacentRasterCells(raster = r, position = c(1,1))

# reference position (1,5)
example2 <- AssignValuesToAdjacentRasterCells(raster = r, position = c(1,5))

# reference position (1,10)
example3 <- AssignValuesToAdjacentRasterCells(raster = r, position = c(1,10))

# reference position (5,1)
example4 <- AssignValuesToAdjacentRasterCells(raster = r, position = c(5,1))

# reference position (5,5)
example5 <- AssignValuesToAdjacentRasterCells(raster = r, position = c(5,5))

# reference position (5,10)
example6 <- AssignValuesToAdjacentRasterCells(raster = r, position = c(5,10))

# reference position (10,1)
example7 <- AssignValuesToAdjacentRasterCells(raster = r, position = c(10,1))

# reference position (10,5)
example8 <- AssignValuesToAdjacentRasterCells(raster = r, position = c(10,5))

# reference position (10,10)
example9 <- AssignValuesToAdjacentRasterCells(raster = r, position = c(10,10))

Plot examples

# Plot examples
par(mfrow=(c(3,3)))

plot(example1, main = "Position ref. (1,1)")
text(example1)
points(xFromCol(example1, col=1), yFromRow(example1, row=1), col="red", cex=2.5, lwd=2.5)

plot(example2, main = "Position ref. (1,5)")
text(example2)
points(xFromCol(example2, col=5), yFromRow(example2, row=1), col="red", cex=2.5, lwd=2.5)

plot(example3, main = "Position ref. (1,10)")
text(example3)
points(xFromCol(example3, col=10), yFromRow(example3, row=1), col="red", cex=2.5, lwd=2.5)

plot(example4, main = "Position ref. (5,1)")
text(example4)
points(xFromCol(example4, col=1), yFromRow(example4, row=5), col="red", cex=2.5, lwd=2.5)

plot(example5, main = "Position ref. (5,5)")
text(example5)
points(xFromCol(example5, col=5), yFromRow(example5, row=5), col="red", cex=2.5, lwd=2.5)

plot(example6, main = "Position ref. (5,10)")
text(example6)
points(xFromCol(example6, col=10), yFromRow(example6, row=5), col="red", cex=2.5, lwd=2.5)

plot(example7, main = "Position ref. (10,1)")
text(example7)
points(xFromCol(example7, col=1), yFromRow(example7, row=10), col="red", cex=2.5, lwd=2.5)

plot(example8, main = "Position ref. (10,5)")
text(example8)
points(xFromCol(example8, col=5), yFromRow(example8, row=10), col="red", cex=2.5, lwd=2.5)

plot(example9, main = "Position ref. (10,10)")
text(example9)
points(xFromCol(example9, col=10), yFromRow(example9, row=10), col="red", cex=2.5, lwd=2.5)

Figure example

Note: white cells mean NA values

Related Solutions

[GIS] Handling NA values from analysis in R with Raster

I really do not follow the logic of what you are attempting with "freq". The DEM values should be continuous and using freq just does not make sense to me but, you may have an unstated reason for doing so.

I would follow @Thomas advice and use extract. You will then have a list object with a vector of raster values for each sample site. You can use lapply to calculate moments to compare to a random sample of the entire raster.

Here is a quick example of one way to approach your problem.

require(raster)
require(sp)

# Create some example data
r <- raster(ncol=500, nrow=500)
  r[] <- runif(ncell(r),0,1)
cds1 <- rbind(c(-180,-20), c(-160,5), c(-60, 0), c(-160,-60), c(-180,-20))
cds2 <- rbind(c(80,0), c(100,60), c(120,0), c(120,-55), c(80,0))
polys <- SpatialPolygons(list(Polygons(list(Polygon(cds1)), 1), 
                              Polygons(list(Polygon(cds2)), 2)))

plot(r)
  plot(polys, add=TRUE)                           

# Create a vector of raster values within polygons,
#   here I collapse the list into a vector
v <- unlist(extract(r, polys))

# Create random sample of raster
rs <- sampleRandom(r, length(v), na.rm=TRUE)

# Evaluate moments of each distribution
summary(v)
summary(rs)

# Test distributional equlaity using Kolmogorov-Smirnov Test
ks.test(v, rs, alternative="two.sided", exact=FALSE)  

# Plot distributions for visual comparison 
rast.den <- density(rs)
samp.den <- density(v)
rast.den$y <- rast.den$y / max(c(rast.den$y, samp.den$y)) 
samp.den$y <- samp.den$y / max(c(rast.den$y, samp.den$y)) 
plot(rast.den, type="n", main="", 
  xlim=c(min(c(rast.den$x, samp.den$x)), max(c(rast.den$x, samp.den$x))), 
  ylim=c(min(c(rast.den$y, samp.den$y)), max(c(rast.den$y, samp.den$y))) )     
        polygon(rast.den, col=rgb(1,0,0,0.5))
        polygon(samp.den, col=rgb(0,0,1,0.5))
     legend("topright", legend=c("Raster","Sample"), 
            fill=c(rgb(1,0,0,0.5),rgb(0,0,1,0.5))  )


# FYI, here is how you apply a function on the results of extract,
#   accounting for NA's  
v <- extract(r, polys)
unlist(lapply(v, function(x) if (!is.null(x)) mean(x, na.rm=TRUE) else NA ))

[GIS] R: aggregate raster with ‘mode’ function – how does it work

Ideally, when reducing by a factor, if there is a multimodal result I'd like aggregate to randomly assign the new cell one of the modal values and not always choose the same (if that's indeed what it does).

That is not what it does. See ?modal and the ties argument.

Your question is really about the modal function which you pass on to aggregate (both in package raster). So read the help file of modal and pick the arguments you like to make it behave how you want it to. If you cannot do that, find a better one elsewhere, or write your own.

The default behavior of modal is to break ties randomly, as illustrated here:

set.seed(9)
table(sapply(1:1000, function(i) modal(c(1,1,2,2))))

#  1   2 
#507 493

You have a further question about na.rm stating that

in the top right of the data, that new cell should really be NA as it has 3 smaller NA values.

I suppose you mean is that there are 3 NAs and 1 1 such that NA should be the mode. Perhaps that should be allowed as an option, but currently NA itself cannot be the modal value. The workaround you propose should be OK.