Erosion of a Hexagon Count Image

This erosion algorithm removes counts from hexagon cells at a rate proportional to the cells' exposed surface area. When a cell becomes empty, algorithm removes the emptied cell and notes the removal order. Cell removal increases the exposure of any neighboring cells. The last cell removed is a type of bivariate median.

erode(hbin, cdfcut = 0.5)
erode.hexbin(hbin, cdfcut = 0.5)

Arguments

hbin

an object of class hexbin.

cdfcut

number in (0,1) indicating the confidence level for the limits.

Value

An "erodebin" object (with all the slots from hbin) and additionally with high count cells and a component erode that gives the erosion order.

Details

The algorithm extracts high count cells with containing a given fraction (cdfcut) of the total counts. The algorithm extracts all cells if cdfcut=0. The algorithm performs gray-level erosion on the extracted cells. Each erosion cycle removes counts from cells. The counts removed for each cell are a multiple of the cell's exposed-face count. The algorithm choses the multiple so at least one cell will be empty or have a count deficit on each erosion cycle. The erode vector contain an erosion number for each cell. The value of erode is

6*erosion_cycle_at_cell_removal - cell_deficit_at_removal

Cells with low values are eroded first. The cell with the highest erosion number is a candidate bivariate median. A few ties in erode are common.

Examples

set.seed(153)
x <- rnorm(10000)
y <- rnorm(10000)
bin <- hexbin(x,y)

smbin  <- smooth.hexbin(bin)
erodebin <- erode.hexbin(smbin, cdfcut=.5)
plot(erodebin)


## bivariate boxplot
hboxplot(erodebin, main = "hboxplot(erodebin)")




# show erosion order
plot(bin,style= "lat", minarea=1, maxarea=1,
     legend=FALSE, border=gray(.7))


grid.hexagons(erodebin,style= "lat", minarea=1, maxarea=1,pen="green")
xy <- hcell2xy(erodebin)
library("grid")
grid.text(lab = as.character(erodebin@erode), xy$x, xy$y,
          gp = gpar(col="white", cex=0.65))