This week, I wanted to get information I found on the nice map, below. I could not get access to the original dataset, per zip code… and I was wondering, if (assuming that the map was with high resolution) it was actually possible to extract information, using a simple R function…

As we can see, there is red, and green on the map, and I would love to know which are the green and the red cities, in France. One important issue is actually the background. Here it’s nice, it white… but white is a strange color, achromatic and very light. More specifically, if I search red areas, the background is very red. And very green, too. So, to avoid those issues, I did use gimp to change the background, into black. On the opposite, where it’s black, it’s neither red, nor green !

Let us get the map, and extract information from the file

url="https://freakonometrics.hypotheses.org/files/2018/12/inondation3.png"
download.file(url,"inondation3.png")
image="inondation3.png"
library(pixmap)
library(png)
IMG=readPNG(image)

Information is stored in several matrices – or in arrays.  Dimension 1 is the height of the picture (in pixels), dimension 2 is the width, and the third one is either 1 (red), 2 (green) or 3 (blue), based on the rgb decomposition of each pixel. Then, I try to find the border of the map

nl=dim(IMG)[1]
nc=dim(IMG)[2]
MAT=(IMG[,,1]+IMG[,,2])/2
x=apply(MAT,2,max)
plot(x,type="l")

When it’s null, it means no color on the line of the matrix, i.e. completly black (initially, I used the mean function, but the maximum really behaves like a step function)

y=apply(MAT,1,max)
plot(y,type="l")

Let us find cutoff values, on the left and on the right, on top and on the bottom

image(1:nc,1:nl,t(MAT))
abline(v=min(which(x>.2)),col="blue")
abline(v=max(which(x>.2)),col="blue")
abline(h=min(which(y>.2)),col="blue")
abline(h=max(which(y>.2)),col="blue")

We obtain the following (forget about the fact that – somehow – France is upside-down)

We can zoom-in, just to make sure that our border are fine

par(mfrow=c(1,2))
image(min(which(x>.2))+(-5):5,1:nl,t(MAT)[min(which(x>.2))+(-5):5,])
abline(v=min(which(x>.2))+(-5):5,col="white")
abline(v=min(which(x>.2)),col="blue")
x1=min(which(x>.2))-1

and on the vertical range

image(max(which(x>.2))+(-5):5,1:nl,t(MAT)[max(which(x>.2))+(-5):5,])
abline(v=max(which(x>.2))+(-5):5,col="white")
abline(v=max(which(x>.2)),col="blue")
x2=max(which(x>.2))+1

So far so good. Let us keep the subpart of the picture,

image(x1:x2,y1:y2,t(MAT)[x1:x2,y1:y2])

Now, let us focus on the red part / component of that picture

ROUGE=t(IMG[,,1])[x1:x2,]
ROUGE=ROUGE[,y2:y1]
library(scales)
image(x1:x2,y1:y2,ROUGE,col=alpha(colour=rgb(1,0,0,1), alpha = seq(0,1,by=.01))

That’s not bad, isn’t it ? And get can have a similar graph for the green part

VERT=t(IMG[,,2])[x1:x2,]
VERT=VERT[,y2:y1]
image(x1:x2,y1:y2,VERT,col=alpha(colour=rgb(0,1,0,1), alpha = seq(0,1,by=.01)))

Now, I wanted to ajust a map of France on that one. Using shapefiles of administrative regions, it would be possible to get the proportion of red and green parts (départements, cantons, etc). As a starting point (before going to ‘départements’), let us use a standard shapefile for France

library(maptools)
library(PBSmapping)
url="http://biogeo.ucdavis.edu/data/gadm2.8/rds/FRA_adm0.rds"
download.file(url,"FRA_adm0.rds")
FR=readRDS("FRA_adm0.rds")
library(maptools)
PP = SpatialPolygons2PolySet(FR)
PP=PP[(PP$X<=8.25)&(PP$Y>=42.2),]
u=(x1:x2)-x1
v=(y1:y2)-y1
ax=min(PP$X)
bx=max(PP$X)-min(PP$X)
ay=min(PP$Y)
by=max(PP$Y)-min(PP$Y)
PP$X=(PP$X-ax)/bx*max(u)
PP$Y=(PP$Y-ay)/by*max(v)
image(u,v,ROUGE,col=alpha(colour=rgb(1,0,0,1), alpha = seq(0,1,by=.01)))
points(PP$X,PP$Y)

We try here to rescale it. The left part should be on the left part of the picture as well as the right part. And the same holds for the top, and the bottom,

Unfortunately, even if we change the projection technique, I could not match perfectly the contour of France. I am quite sure that it’s a projection problem ! But I did try a dozen popular ones, with no success… so if anyone has a clever idea…

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