Optical Flow and Motion
The optical flow constraint equation, the aperture problem, and Lucas-Kanade, Horn-Schunck, and pyramids.
Key Terms
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Textbook Reference
Topics Covered
- 1Brightness constancy and the optical flow constraint equation
- 2The aperture problem and why flow is underdetermined locally
- 3Lucas-Kanade: local constancy, the normal equations, and reliability from M
- 4Horn-Schunck: global smoothness and the variational solution
- 5Coarse-to-fine pyramids and iterative warping for large motion
Learning Outcomes
- Derive the optical flow constraint from brightness constancy
- Contrast the Lucas-Kanade and Horn-Schunck assumptions and solutions
- Explain how pyramids extend flow estimation to large displacements
Derivation walkthrough
From two video frames to a motion field
Seven stages, 22 steps: brightness constancy, the linearised flow constraint, the aperture problem, Lucas–Kanade least squares, dense regularisation, and the motion field it produces. Switch to step mode to advance the picture and the algebra one line at a time.
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Stage 1 · Step 1 of 3
Frame tSample two frames Δt apart
Take the reference frame. Each pixel stores one brightness value at image position (x, y) and time t.
Key idea
u and v are velocities in pixels per unit time. With Δt = 1 frame they read directly as a pixel displacement.
Playing. Selecting any stage or step pauses playback so you can inspect it.
Lecture PDFs
Optical Flow and Motion
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