I am trying to understand the transformation of the space domain of an image into its frequency domain with 2D Fourier Transform. As far as I understand it one basically gets a set of 2D waves that when combined together form the height map of the individual pixels intensity of lets say a gray sacale image.
What I did not understand is how a sharp edge of an image can be represented in the frequency domain without loss of information (e.g. a black and white chess board)? As far as I am concerned it would take an infinite amount of 2D waves but the number of frequencies in the domain is limited to the number of pixels in the space domain.
Another way to think about a 2D photograph is to consider it in frequency domain ... I created a software project which parses a 2D image to visit each pixel using a hilbert curve mapping to define the pixel visit sequence to create a 1D array of light intensity values which gets sent into an inverse Fourier Transform process to output audio ... each pixel in 1D array gets its own sin curve frequency ... spread out one octave across entire length of pixels ... magnitude of each frequency oscillator determined by light intensity of given pixel ... of course audio is in time domain ... it then does a normal Discrete Fourier Transform on this audio to output same data in its frequency domain representation ... it then applies in reverse the same hilbert curve mapping to output a 2D image ... as you may expect the output image matches the input image even though in the middle it transitioned through being audio