Independent Motion Estimation

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Independent Motion Estimation

• Luv Kohli
• COMP290-089
• Multiple View Geometry
• May 7, 2003

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Outline

• The motion segmentation problem
• Motivation
• Background
• Recursive RANSAC
• More sophisticated algorithms
• Results

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Motion segmentation

• The problem according to Phil Torr how to detect
  a set of independently moving objects in the 2D
  projection of an otherwise rigid scene, given
  that the camera is moving in an arbitrary and
  unpredetermined manner

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Motivation

• Many practical applications for motion
  segmentation
• Navigation
• Image compression and representation
• Video indexing
• Recovery of 3D structure
• Difficult to generalize for all types of scenes

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Background

• The methods thus far proposed for motion
  segmentation can be split into several categories
• Methods for a stationary camera do not
  distinguish several independently moving objects
  in the scene can determine that there is motion
  but now how many objects

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Background (2)

• Methods based on image motion constraints
• For example, compute velocities in the image
  using a local correspondence scheme and group
  similar velocities

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Background (3)

• Methods that require knowledge of the camera
  motion
• Methods based on world constraints and epipolar
  geometry
• An object undergoing a rigid transformation is
  equivalent to a camera moving in the opposite
  direction effective motion can be described by
  epipolar geometry

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Recursive RANSAC

• RANSAC can be used to robustly estimate the
  fundamental matrix
• Determines a highly probable solution to the
  problem and separates matches into a set of
  inliers and a set of outliers
• Outliers may correspond to a second rigid motion
  in the scene

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Recursive RANSAC (2)

• Run RANSAC on set of putative matches to get
  inliers and outliers
• Remove inliers from putative match set, and run
  RANSAC on outliers
• This can be repeated multiple times, but
  generally it is difficult to fit data for more
  than 2 or 3 objects
• Each matrix can then be improved through
  nonlinear minimization

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Degeneracy

• Data is degenerate if insufficient to determine a
  unique solution
• This can cause many problems especially when
  there is a significant level of noise in the data
• Phil Torr created the PLUNDER (Pick Least
  UNDEgenerate Randomly) algorithm for detecting
  degeneracy

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Degeneracy (2)

• The PLUNDER algorithm essentially determines
  which model (affinity, projectivity, etc.) a data
  set is consistent with
• Fundamental matrices for different subsets of
  data can be estimated using different models
• Phil Torrs thesis goes into much more detail

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Results (Rec. RANSAC)
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Results (putative)
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Results (segmentation)
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Results (segmentation)
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Results (outliers)
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Results (epipolar)
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Results (epipolar)
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Results
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Results (putative)
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Results (segmentation)
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Results (segmentation)
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Results (outliers)
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Results (epipolar)
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Results (epipolar)
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Results
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Results (putative)
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Results (segmentation)
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Results (segmentation)
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Results (outliers)
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Results (epipolar)
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Results (epipolar)
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Results
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Results (putative)
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Results (segmentation)
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Results (segmentation)
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Results (outliers)
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Results (epipolar)
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Results (epipolar)
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References

• P.H.S. Torr and D.W. Murray. Outlier detection
  and motion segmentation. In P.S. Schenker,
  editor, Sensor Fusion VI, pages 432-443. SPIE
  volume 2059, 1993. Boston.
• P.H.S. Torr. Motion Segmentation and Outlier
  Detection. Ph.D Thesis, Department of Engineering
  Science, University of Oxford, 1995.