# Extracting information from a picture, round 2

Yesterday, I published a post on extracting information from a picture, but it did not work as expected. I claimed that it was because of the original graph I had. More precisely, the was based on some weird projection, and I could not reconcile. So I decide to cheat a little bit, by creating my own map, Colors are ugly, I know. But I got them using

```u = seq(0,1,length=30) couleurs = rgb(u,rev(u),0,1)```

The picture is

```url = "https://freakonometrics.hypotheses.org/files/2018/12/chomage3.png" library(pixmap) library(png) IMG = readPNG(url)```

I used those colors because it would make things easy when extracting reds and greens…

```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))) 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)))``` Let us see if the contour of France can be overlaid

```library(maptools) library(PBSmapping) download.file("http://biogeo.ucdavis.edu/data/gadm2.8/rds/FRA_adm0.rds","FRA_adm0.rds") FR=readRDS("FRA_adm0.rds") library(maptools) PP = SpatialPolygons2PolySet(FR) par(mfrow=c(1,1)) PP=PP[(PP\$X&lt;=8.25)&amp;(PP\$Y&gt;=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 have a perfect match, don’t we…? Let us now use a shapefile based on départements,

```download.file("http://biogeo.ucdavis.edu/data/gadm2.8/rds/FRA_adm2.rds","FRA_adm2.rds") FR2=readRDS("FRA_adm2.rds") library(maptools) PP = SpatialPolygons2PolySet(FR2) image(u,v,ROUGE,col=alpha(colour=rgb(1,0,0,1), alpha = seq(0,1,by=.01))) k=35 pX=(PP\$X[PP\$PID==k]-ax)/bx*max(u) pY=(PP\$Y[PP\$PID==k]-ay)/by*max(v) points(pX,pY)nge(pX)```

For instance, the thirty-fifth polygon is the following Let us extract the color inside that polygon

```u=1:nrow(ROUGE) v=1:ncol(ROUGE)```

The code would be

```pX=(PP\$X[PP\$PID==k]-ax)/bx*max(u) pY=(PP\$Y[PP\$PID==k]-ay)/by*max(v) E=expand.grid(u,v) M=matrix(point.in.polygon(E[,1],E[,2],pX,pY)&gt;0,length(u),length(v)) image(u,v,ROUGE*M,col=alpha(colour=rgb(1,0,0,1), alpha = seq(0,1,by=.01))) points(pX,pY)``` Now, for each département, I extract the average value of red, and the average value of green,

```extract_info = function(k){ pX=(PP\$X[PP\$PID==k]-ax)/bx*max(u) pY=(PP\$Y[PP\$PID==k]-ay)/by*max(v) E=expand.grid(u,v) M=matrix(point.in.polygon(E[,1],E[,2],pX,pY)&gt;0,length(u),length(v)) nom=FR2[FR2\$OBJECTID ==k,c("NAME_2","CCA_2")] return(c(as.numeric(nom\$CCA_2),sum(ROUGE[M==1])/sum(M),sum(VERT[M==1])/sum(M))) } donnees = Vectorize(extract_info)(1:95) x2=donnees[1,] y2=donnees[2,]/(donnees[2,]+donnees[3,]) df2=data.frame(dpt=x2,extract=y2) x1=as.numeric(as.character(baseChomage\$no)) y1=baseChomage\$chomagePremierTrimestre2017 df1=data.frame(dpt=x1,obs=y1) df=merge(df1,df2) plot(df\$obs,df\$extract)```

On the graph below, we have the original values on the x-axis (unemployement, in percent) and the “average value of red”.  Note that points are almost perfectly correlated… The accumulation can be explained because on the original map, different values could have the same color So far, I can claim that we’ve been able to extract useful information from the original picture.

Consider the case now that the original map was the following one ```url = "https://freakonometrics.hypotheses.org/files/2018/12/chomage5.png" library(pixmap) library(png) IMG = readPNG(url)```

Here, the colors are obtained from a standard palette,

```library(pals) couleurs = rev(brewer.rdylgn(30))```

Here again, we use our previous code to extract reds and greens And if we use our function

```extract_info = function(k){ pX=(PP\$X[PP\$PID==k]-ax)/bx*max(u) pY=(PP\$Y[PP\$PID==k]-ay)/by*max(v) E=expand.grid(u,v) M=matrix(point.in.polygon(E[,1],E[,2],pX,pY)&gt;0,length(u),length(v)) nom=FR2[FR2\$OBJECTID ==k,c("NAME_2","CCA_2")] return(c(as.numeric(nom\$CCA_2),sum(ROUGE[M==1])/sum(M),sum(VERT[M==1])/sum(M))) } donnees = Vectorize(extract_info)(1:95) x2=donnees[1,] y2=donnees[2,]/(donnees[2,]+donnees[3,]) df2=data.frame(dpt=x2,extract=y2) x1=as.numeric(as.character(baseChomage\$no)) y1=baseChomage\$chomagePremierTrimestre2017 df1=data.frame(dpt=x1,obs=y1) df=merge(df1,df2) plot(df\$obs,df\$extract)```

we obtain the following graph Here again, we have a strong correlation, not to say comonotonic variables (in the sense that ranks are identical). Nice, isn’t it ?