R - FFT Fourier Spectrum of Image

Question

I am using R Studio in sake of doing my tasks in Image Processing. I am currently using the 'EBImage, fftw, ...' libraries. I have a question about fourier analysis and power spectrum.

1) I have 2D matrix, which is an image. This image consist on horizontal lines, black and white. I want to make Fourier Transformation and show its magnitude by ploting. Since the black lines in image are horizontal, the power spectrum will have an vertical line. I couldn't find a way to achieve it.

Now I am using this image for test: Square

When it is true, this image has some periodic frequencies on both horizontal and vertical axis. Then. the FFT Spectrum should look like a "+". But what I found is something way different.

Here is my code:

setwd(".../Project/R/Workspace/Task1")
library("EBImage"  , lib.loc="~/R/win-library/3.2")
library("fftwtools", lib.loc="~/R/win-library/3.2")
library("fftw", lib.loc="~/R/win-library/3.2")

# Image Acquisition
img <- readImage(".../Project/Beispielbilder/drmcircle.jpg")
display(img, title='Image')

# Grayscaled
img_gray<-channel(img,"gray")

# FFT
img_ff <- fft(img_gray)    #fftw2d

magntd <- sqrt(Re(img_ff)^2+Im(img_ff)^2)
phase  <- atan(Im(img_ff)/Re(img_ff))

plot(log(magntd),main="FFT")

As a result, this is what I have: FFT Spectrum

Here are my questoions:

1) How can I get a correct spectrum image? 2) How can I see it as an image, not a plot? (See Example Link on top.)

Thank you for your help in advance.

Can you provide us a small reproducible example (e.g. a sample 2D matrix together with your code)?stackoverflow.com/questions/5963269/… — Eugen
Hello @Eugen, I have corrected my question for clear definition. Here is the example link, what I want to reach. [matlabgeeks.com/tips-tutorials/… — EMI

EMI EMI · Accepted Answer · 2016-11-03T09:14:57

I solved it. Here I am adding the code. Please see that, fftshift functions were taken from: [How to write fftshift and ifftshift in R?

setwd(".../Project/R/Workspace/Task1")
library("EBImage"  , lib.loc="~/R/win-library/3.2")

# Image
img <- readImage(".../Project/Beispielbilder/drmtri.jpg")
display(img, title='Image')

# Grayscaled
img_gray<-channel(img,"gray")

# FFT
img_ff <- fft(img_gray) #fftw2d


###################################################
###################################################
# FFT SHIFT
fftshift <- function(img_ff, dim = -1) {

  rows <- dim(img_ff)[1]    
  cols <- dim(img_ff)[2]    

  swap_up_down <- function(img_ff) {
    rows_half <- ceiling(rows/2)
    return(rbind(img_ff[((rows_half+1):rows), (1:cols)], img_ff[(1:rows_half), (1:cols)]))
  }

  swap_left_right <- function(img_ff) {
    cols_half <- ceiling(cols/2)
    return(cbind(img_ff[1:rows, ((cols_half+1):cols)], img_ff[1:rows, 1:cols_half]))
  }

  if (dim == -1) {
    img_ff <- swap_up_down(img_ff)
    return(swap_left_right(img_ff))
  }
  else if (dim == 1) {
    return(swap_up_down(img_ff))
  }
  else if (dim == 2) {
    return(swap_left_right(img_ff))
  }
  else {
    stop("Invalid dimension parameter")
  }
}

ifftshift <- function(img_ff, dim = -1) {

  rows <- dim(img_ff)[1]    
  cols <- dim(img_ff)[2]    

  swap_up_down <- function(img_ff) {
    rows_half <- floor(rows/2)
    return(rbind(img_ff[((rows_half+1):rows), (1:cols)], img_ff[(1:rows_half), (1:cols)]))
  }

  swap_left_right <- function(img_ff) {
    cols_half <- floor(cols/2)
    return(cbind(img_ff[1:rows, ((cols_half+1):cols)], img_ff[1:rows, 1:cols_half]))
  }

  if (dim == -1) {
    img_ff <- swap_left_right(img_ff)
    return(swap_up_down(img_ff))
  }
  else if (dim == 1) {
    return(swap_up_down(img_ff))
  }
  else if (dim == 2) {
    return(swap_left_right(img_ff))
  }
  else {
    stop("Invalid dimension parameter")
  }
}
###################################################
###################################################
# FFT SHIFT


# Magnitude and Phase
magntd <- sqrt(Re(img_ff)^2+Im(img_ff)^2)
phase  <- atan(Im(img_ff)/Re(img_ff))

img_fftsh <- fftshift(magntd)

display(log(img_fftsh),title="FFT")

R - FFT Fourier Spectrum of Image

1 Answers