Motion Analysis

Question 1

Image as functions

Answer 1

Each image is a snapshot of intensity values over spatial domain (x,y)
Sequence of images can be stacked in the temporal domain to analyze motion over time

Question 2

Optical flow

Answer 2

Represents apparent motion of brightness patterns in an image sequence
Optical flow != motion field

Question 3

Motion field

Answer 3

Actual 3D motion projected into the image plane
Challenges to optical flow:
Object moves but image intensity does not change
Illumination changes create apparent motion

Question 4

Brightness constancy assumption

Answer 4

Assumes brightness of pixel remains constant over time
Ix, Iy = spatial intensity gradients
It = Temporal intensity gradients
u, v = horizontal and vertical components of pixel velocity

Question 5

Aperture problem

Answer 5

Motion along edges is ambiguous because the flow is only measurable perpendicular to the edge

Question 6

Lucas-Kanade method

Answer 6

Assumes constant velocity in local neighborhood
Uses least-squares to solve for motion
A: gradient matrix, spatial and temporal derivatives,
b: brightness difference

Question 7

Optical flow fails in

Answer 7

in non-constant brightness eg. changing illumination
complex motion eg. water waves, snow, fire

Question 8

Temporal derivative

Answer 8

Rate of change of intensity I(x,y,t) with respect to time t
partial I / partial t
Relates to brightness constancy eqn

Question 9

Spatial derivative

Answer 9

Measures how the intensity of an image changes over space in the x or y direction.

Rate of change of pixel intensity with respect to spatial coords, partial I / partial x or y

Sharp changes