Identify a linear feature on a raster map and return a linear shape object using R

Question

I would like to identify linear features, such as roads and rivers, on raster maps and convert them to a linear spatial object (SpatialLines class) using R.

<

Answer 1

Here's my effort. The plan is:

• densify the lines
• compute a delaunay triangulation
• take the midpoints, and take those points that are in the polygon
• build a distance-weighted minimum spanning tree
• find its graph diameter path

The densifying code for starters:

densify <- function(xy,n=5){
  ## densify a 2-col matrix
  cbind(dens(xy[,1],n=n),dens(xy[,2],n=n))
}

dens <- function(x,n=5){
  ## densify a vector
  out = rep(NA,1+(length(x)-1)*(n+1))
  ss = seq(1,length(out),by=(n+1))
  out[ss]=x
  for(s in 1:(length(x)-1)){
    out[(1+ss[s]):(ss[s+1]-1)]=seq(x[s],x[s+1],len=(n+2))[-c(1,n+2)]
  }
  out
}

And now the main course:

simplecentre <- function(xyP,dense){
require(deldir)
require(splancs)
require(igraph)
require(rgeos)

### optionally add extra points
if(!missing(dense)){
  xy = densify(xyP,dense)
} else {
  xy = xyP
}

### compute triangulation
d=deldir(xy[,1],xy[,2])

### find midpoints of triangle sides
mids=cbind((d$delsgs[,'x1']+d$delsgs[,'x2'])/2,
  (d$delsgs[,'y1']+d$delsgs[,'y2'])/2)

### get points that are inside the polygon 
sr = SpatialPolygons(list(Polygons(list(Polygon(xyP)),ID=1)))
ins = over(SpatialPoints(mids),sr)

### select the points
pts = mids[!is.na(ins),]

dPoly = gDistance(as(sr,"SpatialLines"),SpatialPoints(pts),byid=TRUE)
pts = pts[dPoly > max(dPoly/1.5),]

### now build a minimum spanning tree weighted on the distance
G = graph.adjacency(as.matrix(dist(pts)),weighted=TRUE,mode="upper")
T = minimum.spanning.tree(G,weighted=TRUE)

### get a diameter
path = get.diameter(T)

if(length(path)!=vcount(T)){
  stop("Path not linear - try increasing dens parameter")
}

### path should be the sequence of points in order
list(pts=pts[path+1,],tree=T)

}

Instead of the buffering of the earlier version I compute the distance from each midpoint to the line of the polygon, and only take points that are a) inside, and b) further from the edge than 1.5 of the distance of the inside point that is furthest from the edge.

Problems can arise if the polygon kinks back on itself, with long segments, and no densification. In this case the graph is a tree and the code reports it.

As a test, I digitized a line (s, SpatialLines object), buffered it (p), then computed the centreline and superimposed them:

 s = capture()
 p = gBuffer(s,width=0.2)
 plot(p,col="#cdeaff")
 plot(s,add=TRUE,lwd=3,col="red")
 scp = simplecentre(onering(p))
 lines(scp$pts,col="white")

The 'onering' function just gets the coordinates of one ring from a SpatialPolygons thing that should only be one ring:

onering=function(p){p@polygons[[1]]@Polygons[[1]]@coords}

Capture spatial lines features with the 'capture' function:

capture = function(){p=locator(type="l")
            SpatialLines(list(Lines(list(Line(cbind(p$x,p$y))),ID=1)))}