R中的极化变换图像

Question

我试图将R中的图像(表示为矩阵)转换为极坐标空间,原点为0,0(左上角).鉴于215x215矩阵x看起来像:

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)

但是,xn看起来像:

当我期待这个:

知道我做错了什么吗？

Answer 1

角度有问题:atan以弧度返回角度.如果你围绕它,没有太多的信息.​​..

试试:

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

它不是你期望的图像,它显然是逆变换,中心位于图像的中间.

# 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))