Computer Vision Foundations · free preview

Motion in the Fourier Domain

The shift theorem puts all of a moving pattern's spectrum on a delta wall tilted by its velocity.

1. A moving pattern shears its spectrum

A moving pattern shears its spectrum

2. The wall's tilt is the velocity read backwards

The wall's tilt is the velocity read backwards

3. The moving pulse

The moving pulse

4. Occlusion widens the wall

Occlusion widens the wall

5. Where the energy sits

A 1D pattern moves at velocity v=2v = 2 pixels per frame, so its spectrum lies on the line wt=−v wxw_t = -v\,w_x. Which frequency pair can appear in its Fourier transform?

6. Faster versus slower

Two identical textures translate at 1 and 4 pixels per frame respectively. How do their delta walls compare in the (wx,wt)(w_x, w_t) plane?

7. Placing energy on the wall

A pattern moves at vx=2v_x = 2 pixels per frame. Its spectrum contains spatial frequency wx=3w_x = 3. Compute the temporal frequency wtw_t that the delta wall forces, using wt=−vxwxw_t = -v_x w_x.

Practice this interactively

Free account · instant grading · spaced review that schedules itself.

Start this course for free