1. Motion Estimation I What affects the induced image motion? Camera motion Object motion Scene structure This lesson – unconstrained flow-fields Next lesson – constrained by global parametric transformations

2. Example Flow Fields Separate hardcopy transparency…

3. The Aperture Problem

4. Copyright, 1996 © Dale Carnegie & Associates, Inc. Not enough info in local regions

5. The Aperture Problem Copyright, 1996 © Dale Carnegie & Associates, Inc. Not enough info in local regions

6. The Aperture Problem Copyright, 1996 © Dale Carnegie & Associates, Inc.

7. The Aperture Problem Copyright, 1996 © Dale Carnegie & Associates, Inc. Information is propagated from regions with high certainty (e.g., corners) to regions with low certainty.

8. Such info propagation can cause optical illusions…

9. B.C. Equation + Gradient based methods (Horn &Schunk, Lucase & Kanade) + Region based methods (Correlation, SSD, Normalized correlation)  on the blackboard… Copyright, 1996 © Dale Carnegie & Associates, Inc.

10. Additional constraints Copyright, 1996 © Dale Carnegie & Associates, Inc. Increase aperture: [e.g., Lucas & Kanade] Local singularities at degenerate image regions. Increase analysis window to large image regions => Global model constraints: Numerically stable, but requires prior model selection: Planar (2D) world model [e.g., Bergen-et-al:92, Irani-et-al:92+94, Black-et-al] 3D world model [e.g., Hanna-et-al:91+93, Stein & Shashua:97, Irani-et-al:1999] Spatial smoothness: [e.g., Horn & Schunk:81, Anandan:89] A heuristic -- violated at depth discontinuities

11. ==> small u and v... u=10 pixels u=5 pixels u=2.5 pixels u=1.25 pixels image I image J iterate refine + Pyramid of image JPyramid of image I image I image J Coarse-to-Fine Estimation

12. Two-Frame Flow Estimation NASA sequence2-frame flow-field