Motion and Motion Boundary Estimation by Probabilistic Inference on a Hierarchical Graph

1
Motion and Motion Boundary Estimation by
Probabilistic Inference on a Hierarchical
Graph Xuming He, Shuang Wu, Alan Yuille Dept. of
Statistics, UCLA
Experiments
Key Ideas

• Data energy for velocity u
• Robust to motion boundaries -- adaptive windows
  M

• Overall performance comparable to
  state-of-the-art (standard) computer vision
  methods.

• Model velocity smoothness and motion boundaries
  at many scales simultaneously.
• Motivation hierarchical theories of the visual
  cortex (e.g., Lee and Mumford JOSA 2003).
• Capture complexities of natural images and
  motions.
• Representation motion segmentation templates. at
  multiple scales.

• Data energy for motion boundaries s
• Cues (i) motion discontinuities vd, (ii)
  partial occlusion mo, (iii) static edges sb,

• Performance around boundary is improved compared
  to standard computer vision methods.
• We make more small errors elsewhere due to
  quantization in our current implementation.

• Motion and motion-boundary interaction
• Boundary smoothness prior imposed by
  consistency of s between neighboring levels.
• Velocity smoothness prior imposed by
  consistency of u between different levels.

• Hierarchical Motion Model
• Graph hierarchy of layers (lattice based).
• Motion-segmentation templates (u,s) defined at
  graph nodes u velocity, s segmentation.
• Graph edges between neighboring layers.

• Results better on tougher images (far right)?

Motion our method Black .
TV-L1 ground boundary
Anandan truth
Inference

• Bottom-up and top-down.
• Bottom-up propagates proposals for node states
  using approximate (relaxed) models
• (constraint satisfaction pruned DP).
• Top-down validates, modifies, the bottom-up
  proposals to estimate optimal (MAP) solution.

Conclusions

• We proposed a hierarchical model of motion
  estimation (cf. visual cortex hierarchy).
• Competitive to state-of-the-art computer vision.
• Extensions (i) couple additional cues, (ii)
  psychophysics, (iii) neuroscience.