Hough transform R PET package detecting a line - r

Question

I have image as below and i want to detect the line in the image using PET package's hough tranform. I need help to understand how to get the line from that image.
library("PET", lib.loc="~/R/win-library/3.1")
library("raster", lib.loc="~/R/win-library/3.1")
p=matrix(diag(100), 100)
library(raster)
r <- raster(p)
plot(r)
abc=hough(p)
viewData(list(p, abc$hData), list("Phantom", "Hough transformed phantom"))
I applied hough transformation as above. The original image and image that i get after running the last line are as below
any inputs on how to get line's coordinates (from original image)? I understand that white point from the second image right side pane represents the line. That line is plotted using Polar Cordinate system. But i dont know how to use the second image to get coordinate of the original line
I looked at PET package's documentation but found it hard to understand :( I ran their sample code but i didn't understand it
==============================================================================
I followed advice given in comments by user NicE and updated my code as below
library("PET", lib.loc="~/R/win-library/3.1")
library("raster", lib.loc="~/R/win-library/3.1")
#p=matrix(diag(1000), 1000)
p=matrix(rep(0,10000), 100, 100)
# for (i in 1:100)
# {p[i,100-i+1]=1
# }
for (i in 1:100)
{p[i,50]=1
}
# library(raster)
# r <- raster(p)
# plot(r)
abc=hough(p)
maxPoint<-which(abc$hData==max(abc$hData),arr.ind=T)
library(pracma)
a<-cot(maxPoint[1,"row"]*pi/180)
b<-maxPoint[1,"col"]/sin(maxPoint[1,"row"]*pi/180)
a
b
par(pty="s")
par(mfrow=c(1,2))
#image(r, main="org")
image(p,main="original")
image(abc$hData, main="Houghmatrix")
Are new values of a and b correct? I feel that b should be 50 (perpendicular distance of the original line from the (0,0)). What am I doing wrong?
I would also like to know why does abc$hData has 181 rows and 143 columns. I can imagine 181 rows has something to do with PI radians is 180 degrees. But I dont have any clue about 143 columns...
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update 2
If i update my original matrix as I feel that i get weird answers. I get a=-57.6 and b=1786.12.
p=matrix(rep(0,10000), 100, 100)
for (i in 1:100)
{p[80,i]=1
}

Answer 1

Once you have the Hough transformation of the data, find the indices of the max of the matrix (assuming you have only one line):
maxPoint<-which(abc$hData==max(abc$hData),arr.ind=T)
You can also take the average of all the maxPoitns if you know there is only one line. In your case, you get this:
row col
[1,] 137 72
You need the default parameters of the function as well
houghParam<-unlist(abc$Header)
These give you RhoMin, ThethaMin, and DeltaMin and DeltaRho, the increments of both variables. With these you can get rho and theta from the matrix coordinates.
theta=(maxPoint[1,"row"]-1)*houghParam["DeltaXY1"]+houghParam["XYmin1"]
rho=(maxPoint[1,"col"]-1)*houghParam["DeltaXY2"]+houghParam["XYmin2"]
If the equation of the line is y=ax+b, you can get a and b using:
library(pracma)
a<--cot(theta)
b<-(rho)/sin(theta)
Also, in the man page of hough they state that they take the center of the image as (0,0) points.
For the math explanation, look at the Wikipedia page of Hough Transform ...
Edit: changed a formula and removed some wrong info
The total code would be:
library(PET)
library(pracma)
a=matrix(rep(0,10000), 100, 100)
for (i in 1:100)
{a[i,60]=1
}
d=matrix(rep(0,10000), 100, 100)
for (i in 1:100)
{d[60,i]=1
}
e=matrix(diag(100), 100)
getLineHough<-function(p){
abc=hough(p)
#get the brightest point in the hough tranform
maxPoint<-which(abc$hData==max(abc$hData),arr.ind=T)
#if there is only one line, can average the results in case there are several brightest points
maxPoint<-apply(maxPoint,2,mean)
houghParam<-unlist(abc$Header)
theta=(maxPoint[1]-1)*houghParam["DeltaXY1"]+houghParam["XYmin1"]
rho=(maxPoint[2]-1)*houghParam["DeltaXY2"]+houghParam["XYmin2"]
a<--cot(theta)
b<-rho/sin(theta)
par(mfrow=c(1,2))
image(p,main="original")
#add the predicted lines, also have to change the slope and intercept because
#the origin of the plot function is not the center of the image the bottom left corner
if(theta==0){
abline(v=(rho+50)/100)
} else{
abline((b+50-a*50)/100,a)
}
image(abc$hData, main="Houghmatrix")
}
getLineHough(a)
getLineHough(d)
getLineHough(e)
Edit2: the documentation doesn't really say what the value of the first row of the matrix is. Since there are 181 rows it should start at 0 and not 1*houghParam["DeltaXY1"]. Changed the code accordingly
Edit3: made the code into a function and added the predicted line to the plot