一个或多个多边形覆盖的栅格单元的一部分：有没有更快的方法来做到这一点（在 R 中）？

Question

图胜于言，请关注

我拥有的是

• 一个 RasterLayer 对象（此处填充随机值仅用于说明目的，实际值无关紧要）
• 一个包含大量多边形的 SpatialPolygons 对象

您可以使用以下代码重新创建我用于图像的示例数据：

library(sp)
library(raster)
library(rgeos)

# create example raster
r <- raster(nrows=10, ncol=15, xmn=0, ymn=0)
values(r) <- sample(x=1:1000, size=150)

# create example (Spatial) Polygons
p1 <- Polygon(coords=matrix(c(50, 100, 100, 50, 50, 15, 15, 35, 35, 15), nrow=5, ncol=2), hole=FALSE)
p2 <- Polygon(coords=matrix(c(77, 123, 111, 77, 43, 57, 66, 43), nrow=4, ncol=2), hole=FALSE)
p3 <- Polygon(coords=matrix(c(110, 125, 125, 110, 67, 75, 80, 67), nrow=4, ncol=2), hole=FALSE)

lots.of.polygons <- SpatialPolygons(list(Polygons(list(p1, p2, p3), 1)))
crs(lots.of.polygons) <- crs(r) # copy crs from raster to polygons (please ignore any potential problems related to projections etc. for now)


# plot both
plot(r) #values in this raster for illustration purposes only
plot(lots.of.polygons, add=TRUE)

对于栅格中的每个像元，我想知道其中有多少被一个或多个多边形覆盖。或者实际上：栅格单元内所有多边形的面积，没有问题单元之外的区域。如果有多个多边形与一个单元格重叠，我只需要它们的组合区域。

以下代码可以满足我的要求，但需要一个多星期才能运行实际数据集：

# empty the example raster (don't need the values):
values(r) <- NA

# copy of r that will hold the results
r.results <- r

for (i in 1:ncell(r)){
  r.cell <- r # fresh copy of the empty raster
  r.cell[i] <- 1 # set the ith cell to 1
  p <- rasterToPolygons(r.cell) # create a polygon that represents the i-th raster cell
  cropped.polygons <- gIntersection(p, lots.of.polygons) # intersection of i-th raster cell and all SpatialPolygons

  if (is.null(cropped.polygons)) {
    r.results[i] <- NA # if there's no polygon intersecting this raster cell, just return NA ...
  } else{
    r.results[i] <- gArea(cropped.polygons) # ... otherwise return the area
  }
}

plot(r.results)
plot(lots.of.polygons, add=TRUE)

我可以通过使用sapply 而不是for-loop 来加快速度，但瓶颈似乎在其他地方。整个方法感觉很尴尬，我想知道我是否遗漏了一些明显的东西。起初我认为rasterize() 应该能够轻松做到这一点，但我不知道在fun= 参数中放入什么。有任何想法吗？

Answer 1

正如您在问题中提到的，另一种方法是利用光栅化来加快速度。这将涉及创建两个栅格文件：一个具有与像元编号对应的值的“渔网”栅格，另一个具有与多边形 ID 对应的值。两者都需要“重新采样”到比单元格原始栅格更大的分辨率。然后您可以计算有多少具有相同像元编号的超采样渔网像元对应于具有有效（非零）id 的多边形栅格的像元。在实践中，这样的事情会起作用（请注意，我稍微改变了输入多边形的构建，使其具有SpatialPolygonsDataFrame。

library(sp)
library(raster)
library(rgeos)
library(data.table)
library(gdalUtils)

# create example raster
r <- raster(nrows=10, ncol=15, xmn=0, ymn=0)
values(r) <- sample(x=1:1000, size=150)

# create example (Spatial) Polygons --> Note that I changed it slightly
# to have a SpatialPolygonsDataFrame with IDs for the different polys

p1 <- Polygons(list(Polygon(coords=matrix(c(50, 100, 100, 50, 50, 15, 15, 35, 35, 15), nrow=5, ncol=2), hole=FALSE)), "1")
p2 <- Polygons(list(Polygon(coords=matrix(c(77, 123, 111, 77, 43, 57, 66, 43),         nrow=4, ncol=2), hole=FALSE)), "2")
p3 <- Polygons(list(Polygon(coords=matrix(c(110, 125, 125, 110, 67, 75, 80, 67),       nrow=4, ncol=2), hole=FALSE)), "3")
lots.of.polygons <- SpatialPolygons(list(p1, p2, p3), 1:3)
lots.of.polygons <- SpatialPolygonsDataFrame(lots.of.polygons, data = data.frame (id = c(1,2,3)))
crs(lots.of.polygons) <- crs(r) # copy crs from raster to polygons (please ignore any potential problems related to projections etc. for now)

# plot both
plot(r) #values in this raster for illustration purposes only
plot(lots.of.polygons, add = TRUE)


# Create a spatial grid dataframe and convert it to a "raster fishnet"
# Consider also that creating a SpatialGridDataFrame could be faster
# than using "rasterToPolygons" in your original approach !

cs <- res(r) # cell size.
cc <- c(extent(r)@xmin,extent(r)@ymin) + (cs/2)   # corner of the grid.
cd <- ceiling(c(((extent(r)@xmax - extent(r)@xmin)/cs[1]), # construct grid topology
                ((extent(r)@ymax - extent(r)@ymin)/cs[2]))) - 1
# Define grd characteristics
grd    <- GridTopology(cellcentre.offset = cc, cellsize = cs, cells.dim = cd)   
#transform to spatial grid dataframe. each cell has a sequential numeric id
sp_grd <- SpatialGridDataFrame(grd,
                               data = data.frame(id = seq(1,(prod(cd)),1)),  # ids are numbers between 1 and ns*nl
                               proj4string = crs(r) )

# Save the "raster fishnet"
out_raster   <- raster(sp_grd) %>%
                setValues(sp_grd@data$id)
temprast     <- tempfile(tmpdir = tempdir(), fileext = ".tif")
writeRaster(out_raster, temprast, overwrite = TRUE)

# "supersample" the raster of the cell numbers

ss_factor = 20  # this indicates how much you increase resolution of the "cells" raster
                # the higher this is, the lower the error in computed percentages

temprast_hr  <- tempfile(tmpdir = tempdir(), fileext = ".tif")
super_raster <- gdalwarp(temprast, temprast_hr, tr = res(r)/ss_factor, output_Raster = TRUE, overwrite = TRUE)

# Now rasterize the input polygons with same extent and resolution of super_raster

tempshapefile <- writeOGR(obj = lots.of.polygons, dsn="tempdir", layer="tempshape", driver="ESRI Shapefile") 
temprastpoly <- tempfile(tmpdir = tempdir(), fileext = ".tif")
rastpoly <- gdal_rasterize(tempshapefile, temprastpoly, tr = raster::res(super_raster),
                           te = extent(super_raster)[c(1,3,2,4)], a = 'id', output_Raster = TRUE)

# Compute Zonal statistics: for each "value" of the  supersampled fishnet raster,
# compute the number of cells which  have a non-zero value  in the supersampled  
# polygons raster (i.e., they belong to one polygon), and divide by the maximum
# possible of cells (equal to ss_factor^2)

cell_nos <- getValues(super_raster)
polyid   <- getValues(rastpoly)
rDT <- data.table(polyid_fc = as.numeric(polyid), cell_nos = as.numeric(cell_nos))
setkey(rDT, cell_nos)

# Use data.table to quickly summarize over cell numbers
count <- rDT[, lapply(.SD, FUN = function(x, na.rm = TRUE) {
                                        100*length(which(x > 0))/(ss_factor^2)
                                          },
                            na.rm = na.rm),
             by = cell_nos]

# Put the results back in the SpatialGridDataFrame and plot
sp_grd@data <- data.frame(count)
sp_grd$polyid_fc[sp_grd$polyid_fc == 0] <- NA
spplot(sp_grd, zcol = 'polyid_fc')

这应该非常快，并且随着多边形数量的增加也可以很好地缩放。

需要注意的是，您必须处理计算百分比中的近似值！所犯的错误取决于您对栅格的“超采样”程度（此处由ss_factor 变量设置为20）。更高的超级采样因子会导致更低的错误，但需要更大的内存和处理时间。

我还认为加快“基于矢量”方法的一种方法可能是对栅格单元和不同多边形之间的距离进行先验分析，这样您就可以只寻找它们之间的交叉点单元格和“附近”多边形。也许你可以使用多边形的 bbox 来寻找有趣的单元格......

HTH，

洛伦佐

Answer 2

[编辑]

也许 gIntersection(..., byid = T) 和 gUnaryUnion(lots.of.polygons)（它们使您能够一次处理所有单元格）比 for 循环更快（如果 gUnaryUnion() 花费太多时间，这是个坏主意）。

r <- raster(nrows=10, ncol=15, xmn=0, ymn=0)
set.seed(1); values(r) <- sample(x=1:1000, size=150)
rr <- rasterToPolygons(r)

# joining intersecting polys and put all polys into single SpatialPolygons
lots.of.polygons <- gUnaryUnion(lots.of.polygons)   # in this example, it is unnecessary

gi <- gIntersection(rr, lots.of.polygons, byid = T)

ind <- as.numeric(do.call(rbind, strsplit(names(gi), " "))[,1])   # getting intersected rr's id
r[] <- NA
r[ind] <- sapply(gi@polygons, function(x) slot(x, 'area'))  # a bit faster than gArea(gi, byid = T)

plot(r)
plot(lots.of.polygons, add=TRUE)

Answer 3

您可以使用 doSNOW 和 foreach 包并行化您的循环。这将通过您的 CPU 数量加快计算速度

library(doSNOW)
library(foreach)

cl <- makeCluster(4) 
# 4 is the number of CPUs used. You can change that according 
# to the number of processors you have 
registerDoSNOW(cl)

values(r.results) <- foreach(i = 1:ncell(r), .packages = c("raster", "sp", "rgeos"), .combine = c) %dopar% {
  r.cell <- r # fresh copy of the empty raster
  r.cell[i] <- 1 # set the ith cell to 1
  p <- rasterToPolygons(r.cell) # create a polygon that represents the i-th raster cell
  cropped.polygons <- gIntersection(p, lots.of.polygons) # intersection of i-th raster cell and all SpatialPolygons

  if (is.null(cropped.polygons)) {
    NA # if there's no polygon intersecting this raster cell, just return NA ...
  } else{
    gArea(cropped.polygons) # ... otherwise return the area
  }
}

plot(r.results)
plot(lots.of.polygons, add=TRUE)