Notes on the Harris Detector

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Notes on the Harris Detector

• from Rick Szeliskis lecture notes, CSE576,
  Spring 05

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Harris corner detector

• C.Harris, M.Stephens. A Combined Corner and Edge
  Detector. 1988

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The Basic Idea

• We should easily recognize the point by looking
  through a small window
• Shifting a window in any direction should give a
  large change in intensity

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Harris Detector Basic Idea
flat regionno change in all directions
edgeno change along the edge direction
cornersignificant change in all directions
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Harris Detector Mathematics
Change of intensity for the shift u,v
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Harris Detector Mathematics
For small shifts u,v we have a bilinear
approximation
where M is a 2?2 matrix computed from image
derivatives
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Harris Detector Mathematics
Intensity change in shifting window eigenvalue
analysis
?1, ?2 eigenvalues of M
direction of the fastest change
direction of the slowest change
Ellipse E(u,v) const
(?max)-1/2
(?min)-1/2
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Harris Detector Mathematics
?2
Edge ?2 gtgt ?1
Classification of image points using eigenvalues
of M
Corner?1 and ?2 are large, ?1 ?2E
increases in all directions
?1 and ?2 are smallE is almost constant in all
directions
Edge ?1 gtgt ?2
Flat region
?1
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Harris Detector Mathematics
Measure of corner response
(k empirical constant, k 0.04-0.06)
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Harris Detector Mathematics
?2
Edge
Corner

• R depends only on eigenvalues of M
• R is large for a corner
• R is negative with large magnitude for an edge
• R is small for a flat region

R lt 0
R gt 0
Edge
Flat
R lt 0
R small
?1
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Harris Detector

• The Algorithm
• Find points with large corner response function
  R (R gt threshold)
• Take the points of local maxima of R

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Harris Detector Workflow
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Harris Detector Workflow
Compute corner response R
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Harris Detector Workflow
Find points with large corner response
Rgtthreshold
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Harris Detector Workflow
Take only the points of local maxima of R
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Harris Detector Workflow
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Harris Detector Summary

• Average intensity change in direction u,v can
  be expressed as a bilinear form
• Describe a point in terms of eigenvalues of
  Mmeasure of corner response
• A good (corner) point should have a large
  intensity change in all directions, i.e. R should
  be large positive

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Harris Detector Some Properties

• Rotation invariance

Ellipse rotates but its shape (i.e. eigenvalues)
remains the same
Corner response R is invariant to image rotation
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Harris Detector Some Properties

• Partial invariance to affine intensity change

• Only derivatives are used gt invariance to
  intensity shift I ? I b

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Harris Detector Some Properties

• But non-invariant to image scale!

All points will be classified as edges
Corner !
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Harris Detector Some Properties

• Quality of Harris detector for different scale
  changes

Repeatability rate
correspondences possible correspondences
C.Schmid et.al. Evaluation of Interest Point
Detectors. IJCV 2000
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Models of Image Change

• Geometry
• Rotation
• Similarity (rotation uniform scale)
• Affine (scale dependent on direction)valid for
  orthographic camera, locally planar object
• Photometry
• Affine intensity change (I ? a I b)

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Rotation Invariant Detection

• Harris Corner Detector

C.Schmid et.al. Evaluation of Interest Point
Detectors. IJCV 2000