22. October 2011

A Connection between Motion Blur and the Fourier Transform

Motion blur usually occurs in an image, when the camera was moved with respect to the subject. Motion blur has an interesting effect on the Fourier-transformed image, as pointed out by D. Burschka at University of Technology, Munich. Here is an example how the Fourier-transformed images of toy images look like that have been subject to motion blur.

Consider two images; one showing only horizontal motion blur, the other showing only vertical motion blur (left side of figure). Rendering the (logarithmic) magnitude of the Fourier transforms (right side of figure), one can observe a relation between the direction of the motion and the shape of the Fourier transform.