Magnitude and Phase of Images

# Magnitude and Phase of Images

In the audio part of the course, we saw how important the magnitude of the frequency components of an audio signal was to the perception of the sound, and we also saw how unimportant the phase was. We will try to see the same here for images. Our strategy is to take the images of Phyllis another former denizen of the robotics laboratory in Figure 5. We then take the Fourier transform of the images in Figure 2 and Figure 5. Then, we take the magnitude of Aaron's image and combine it with the phase of Phyllis' image and inverse Fourier transform it to give the image in Figure 6. We will also combine the phase of Aaron's image with the magnitude of Phyllis' image in Figure 7.

Figure 5: Image of Phyllis

Figure 6: Image composed of Aaron's magnitude and Phyllis' phase

Figure 7: Image composed of Aaron's phase and Phyllis' magnitude

The matlab code for this is available from
http://robotics.eecs.berkeley.edu/ mcenk/Page1.html

The apparent conclusion is that the phase is far more important than the magnitude for images. This seems peculiar, since as we shrink our field of view into a progressively smaller and smaller region the size of a pixel, the phase ought to mean less and less. In fact, if we break up the images of Aaron and Phyllis into four quadrants and repeat our experiment for each of the four quadrants, we get the poorer quality morphs of Figure 8 and 9.

Figure 8: Image composed of four quadrants, each with Aaron's magnitude and Phyllis' phase

Figure 9: Image composed of four quadrants, each with Aaron's phase and Phyllis' magnitude

It can actually be verified that when the quadrants become somewhat smaller than the size of the face in the images, that magnitude actually becomes as important as phase in images.