1. Optical Flow

2. Problem Problems in motion estimation Approaches: Applications Noise,
color (intensity) smoothness,
lighting (shadowing effects),
occlusion,
abrupt movements, etc
Approaches:
Block matching,
Generalized block matching,
Optical flow (block-based, Horn-Schunck etc)
Bayesian, etc.
Applications
Video coding and compression,
Segmentation
Object reconstruction (structure-from-motion)
Detection and tracking, etc.

3. Motion description î í ì = Y y X x 2D motion:
p = [x(t),y(t)]  p’= [x(t+ t0), y(t+t0)] 
d(t) = [x(t+ t0)-x(t),y(t+t0)-y(t)] 
3D motion:
Α = [ Χ1, Υ1, Ζ1 ]Τ  Β = [ Χ2, Υ2, Ζ2 ]Τ 
= R T
Basic projection models:
Orthographic
Perspective î í ì = Y y X x

4. Optical Flow Basic assumptions: Normal flow:
Image is smooth locally
Pixel intensity does not change over time (no lighting changes)
Normal flow:
Second order differential equation:

5. Block-based Optical Flow Estimation
Optical flow estimation within a block (smoothness assumption): all pixels of the block have the same motion
Error:
Motion equation:
and

6. Horn-Schunck
We want an optical flow field that satisfies the Optical Flow Equation with the minimum variance between the vectors (smoothness)
Gauss-Seidel

7. Derivative Estimation with Finite differences

8. Example 1

9. Example 2

10. Example 3: frame reconstruction

11. Application Examples