Analysis of Contour Motions

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Analysis of Contour Motions Ce Liu William T.
Freeman Edward H. Adelson
Neural Information Processing Systems Conference
2006
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1. Introduction
3. Forming edgelets boundary fragments

• Conditioned on the grouping, the graphical model
  for motion is a Gaussian MRF

• Spatial boundary fragment extraction
• Steerable filters to obtain edge energy for each
  orientation band
• Track boundary fragments in frame 1 (using
  Canny-like threshold)
• Boundary fragments lines or curves with small
  curvature
• Edgelet temporal tracking with uncertainties
• Frame 1 edgelet (x, y, q)
• Frame 2 orientation energy of q
• A Gaussian pdf is fit with the weight of
  orientation energy
• 1D uncertainty of motion (even for T-junctions)

Existing algorithms cannot correctly analyze the
motion of textureless objects under occlusion
5. Inference
One frame of motion sequence
Output of our contour motion algorithm
Output of the state-of-the-art optical flow
algorithm 1
6. Results
All results generated using the same parameter
settings. The running time varies from ten
seconds to a few minutes in MATLAB, as a function
of the number of boundary fragments.
4. Forming contours
graphical model for grouping motion

• Problem regions caused by the occlusions of
  textureless objects
• Corners spurious T- or L-junctions
• Lines boundary ownership
• Flat regions illusory boundaries

• Grouping machinery switch variables (attached to
  every end of the fragments)
• Exclusive one end connects to at most one other
  end
• Reversible if end (i,ti) connects to (j,tj),
  then (j,tj) connects to (i,ti), i.e. S(i,ti)
  (j,tj), S(j,tj)(i,ti), or S(S(i,ti))(i,ti)

• Our approach simultaneous grouping and motion
  analysis
• Multi-level contour representation
• Formulate graphical model that favors good
  contour and motion criteria
• Inference using importance sampling

Reciprocity constraint
Legal contours
More legal contours
Grouping ambiguity
Example fragments

• Affinity metric terms
• Motion similarity
• Curve smoothness
• Contrast consistency
• The graphical model for grouping

2.Three levels of contour representation
Edgelet
Boundary fragment
Contour
1 T. Brox et al. High accuracy optical flow
estimation based on a theory for warping. ECCV
2004