lucas kanade

Question 1

What is optical flow?

Answer 1

The apparent motion of image brightness patterns between consecutive frames, represented as a vector field.

Question 3

What is the motion field?

Answer 3

The true motion of points in 3D space as projected onto the 2D image plane.

Question 5

When does optical flow differ from the motion field?

Answer 5

When brightness changes are due to lighting, reflections, or motion illusions.

Question 7

What assumption underlies optical flow estimation?

Answer 7

Brightness constancy — that a point retains the same intensity over time.

Question 9

What is the brightness constancy equation?

Answer 9

I(x, y, t) = I(x + δx, y + δy, t + δt)

Question 11

What is the optical flow constraint equation?

Answer 11

Iₓu + Iᵧv + Iₜ = 0

Question 13

What does each variable in the optical flow constraint represent?

Answer 13

Iₓ, Iᵧ are spatial gradients; Iₜ is temporal gradient; u, v are flow components.

Question 15

Why is optical flow under-constrained?

Answer 15

Because the constraint equation provides one equation for two unknowns (u and v).

Question 17

What is the aperture problem?

Answer 17

The inability to determine full motion from a small image region due to missing directional information.

Question 19

In which region is flow best estimated?

Answer 19

Corners or textured regions, where gradients exist in multiple directions.

Question 21

What is the Lucas–Kanade method?

Answer 21

A technique to estimate constant optical flow over a small window using least squares.

Question 23

What type of region does Lucas–Kanade assume?

Answer 23

A small window where motion is constant across all pixels.

Question 25

What system does Lucas–Kanade solve?

Answer 25

An overdetermined system of optical flow constraints using least squares.

Question 27

What is the matrix form of the Lucas–Kanade solution?

Answer 27

AᵀA · [u v]ᵀ = -Aᵀb

Question 29

What happens if you try to compute flow in a flat region?

Answer 29

You can't — the gradients are too small to provide useful information.

Question 31

Why does motion on an edge cause flow ambiguity?

Answer 31

Because gradient information exists in only one direction — you can't resolve full flow.

Question 33

What is used to compute image gradients Iₓ and Iᵧ in practice?

Answer 33

Finite difference approximations or convolution filters like Sobel.

Question 35

What is coarse-to-fine estimation in optical flow?

Answer 35

A multiscale method that starts at low resolution and refines flow estimates at higher resolutions.

Question 37

Why is coarse-to-fine estimation used?

Answer 37

To handle large motions that exceed one pixel, which basic methods can't resolve.

Question 39

What is the main limitation of standard Lucas–Kanade?

Answer 39

It assumes small motion — fails when motion between frames is large.

Question 41

What does the vector [u, v] represent in optical flow?

Answer 41

The displacement (in x and y) of a pixel over time, in pixels per frame.

Question 43

What is the unit of optical flow?

Answer 43

Pixels per frame.

Question 45

How is the temporal gradient Iₜ estimated?

Answer 45

By taking the difference in intensity between corresponding pixels in two frames.

Question 47

What is the main challenge in optical flow computation?

Answer 47

Recovering accurate motion from limited local gradient information, especially in noisy or textureless regions.

Question 49

What is the goal of the optical flow algorithm?

Answer 49

To estimate how each pixel in an image moves from one frame to the next.

Question 51

What is the best type of image region for optical flow estimation?

Answer 51

Corner or textured regions with non-zero gradients in multiple directions.