Polar image conversion to R

Question

I am trying to convert an image (represented as a matrix) into R, in a polar coordinate space with a start equal to 0.0 (upper left corner). Given a 215x215 x matrix, which looks like this:

  x0 = as.vector (col (x))
 y0 = as.vector (row (x))

 r = sqrt ((x0 ^ 2) + (y0 ^ 2)) #x
 a = atan (y0 / x0) #y
 m = as.matrix (data.frame (y = a, x = r))

 m = round (m)
 m [m> 215] = NA
 m [m == 0] = NA

 xn = x [m]
 xn = matrix (xn, 215, 215)

However, xn looks simple:

When I expect this:

Any idea what I'm doing wrong?

Answer 1

There is a problem with the angle: atan returns the angle in radians. if you round it, there is little information left ...

Try:

 a = atan(y0/x0) * 215 / (pi/2) 

This is not the image you expect, it is apparently the inverse transformation, centered in the middle of the image.

 # Load the image library(png) library(RCurl) d <- readPNG( getBinaryURL( "http://i.stack.imgur.com/rMR3C.png" ) ) image(d, col=gray(0:255/255)) # Origin for the polar coordinates x0 <- ncol(d)/2 y0 <- nrow(d)/2 # The value of pixel (i,j) in the final image # comes from the pixel, in the original image, # with polar coordinates (r[i],theta[i]). # We need a grid for the values of r and theta. r <- 1:ceiling(sqrt( max(x0,nrow(d))^2 + max(y0,ncol(d))^2)) theta <- -pi/2 + seq(0,2*pi, length = 200) r_theta <- expand.grid(r=r, theta=theta) # Convert those polar coordinates to cartesian coordinates: x <- with( r_theta, x0 + r * cos(theta) ) y <- with( r_theta, y0 + r * sin(theta) ) # Truncate them x <- pmin( pmax( x, 1 ), ncol(d) ) y <- pmin( pmax( y, 1 ), nrow(d) ) # Build an empty matrix with the desired size and populate it r <- matrix(NA, nrow=length(r), ncol=length(theta)) r[] <- d[cbind(x,y)] image(r, col=gray(0:255/255))