What is the importance of Phase in case of Multidimensional signals?

[ramdas]

I am beginner in image processing and want to do filtering in Frequency domain.

I can understand that the frequency spectrum in case of 1D waves. It denotes what frequencies are present in a wave. If we draw the phase spectrum of cos(2πft) , we get an impulse signal at −f and +f, and it is an odd function of time.

But what does Phase spectrum means in case of images or multidimensional signals? When we take the FFT of an image in MATLAB, we get a weird picture. What does this image denote?

In the books, they give a lot of mathematical equations rather than the physical implication. So can anyone provide a simple explanation about importance of Phase Spectrum in case of Multidimensional signals with a simple application of it in image processing?

 

[UltrafastPED]

If the image is a regular array of points - then there is a spatial frequency, which may vary by direction. For example, the spatial Fourier transform of a regular screen looks like a cross made of dots, with more dots fading away from the main lines.

Look up images from Fourier optics ... lenses can (and do) perform spatial Fourier transforms. The diffraction patterns shown on a transmission electron microscope ar spatial Fourier transforms of the crystal structure.