Contour Matching Using Epipolar Geometry (PAMI, April 2000)

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Contour Matching UsingEpipolar Geometry(PAMI,
April 2000)

• 2004. 6. 4
• Young Ki Baik

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Contour matching

• Key idea
• Initial matching refinement from the matched sets
  of contours.

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Contour matching

• Several primitives to match
• Points / Straight lines
• Both points and straight lines
• Line segments
• Contour
• A set of chained image points.

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Contour matching

• Previous contour matching methods
• Smoothness constraints of the contour
• Smoothness constraints on the second derivative
  of velocity
• Or minimization of curvature variations
• Contour matching methods
• Contour matching using Epipolar geometry

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Contour matching

• Assumption
• The images are taken with a moving camera and the
  scene is static.
• The intensity value of a region does not change
  much as the camera moves.
• If a space contour is observed by two cameras,
  there can be matching between images of the
  contour in image space with the same parametric
  value.

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Epipolar geometry

• Fundamental matrix F

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Contour parameterization

• Let C(S) be a space curve parameterized by
• arc length S.
• are projected contours of C(S).

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Epipolar geometry for Contour
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Contour matching algorithm

• Algorithm (Initial matching)
• Step1Find contours in each image
• Using a zero-crossing edge detector and an edge
  linker.
• Step2Find a set of seed matches
• Using classical correlation-based matching
  technique.
• Step3Compute the epipolar geometry
• Using 8-point algorithm (Hartley)

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Contour matching algorithm

• Algorithm (Contour matching)
• Step4For each contour point, do steps 5-7
• Step5Find the initial estimation
• Step6Match points
• Using the epipolar constraint and correlation.
• Step7Choose the major corresponding contour.
• Discard contours which match to minor
  corresponding contours.

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Contour matching algorithm

• Step5 Find the initial estimation ( 1)
• Finding contour point correspondence.
• Using epipolar line

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Contour matching algorithm

• Step5 Find the initial estimation ( 2 )
• Finding contour point correspondence.

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Contour matching algorithm

• Step5 Find the initial estimation ( 3 )
• Fast Finding contour point correspondence.
• q nearest neighbors ( ) of
  .
• Let match points be .
• Let is .
• is initial estimate location.

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Contour matching algorithm

• Step6 Match point
• Finding contour point correspondence.
• Using the epipolar constraint and correlation.

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Contour matching algorithm

• Step7Choose the major corresponding contour
• Major corresponding contour
• All matches not on the major corresponding
  contour are removed.

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Contour matching algorithm

• Algorithm (Re-computing)
• Step8Re-compute the epipolar geometry
• Using points in matched contours.
• Step9For each contour point, rematch along the
  contour
• Using epipolar constraint

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Extension to contour matching in three views
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Contour matching result

• Mosaic box image set

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Contour matching result

• Etc. image set

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Conclusion

• Contour matching algorithm uses Geometric
  constraints has been presented.
• Fail case
• Bad initial match
• Lack of corner features
• Simple repetition of a pattern
• Highly blurred patterns
• Computing time 17sec
• Number of contours 1084
• Number of points 18831
• SGI O2 workstation with an R10000 2.6 processor