lecture 06: harris corner detector - penn state
TRANSCRIPT
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CSE486, Penn StateRobert Collins
Lecture 06:Harris Corner Detector
Reading: T&V Section 4.3
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CSE486, Penn StateRobert Collins
Motivation: Matchng ProblemVision tasks such as stereo and motion estimation requirefinding corresponding features across two or more views.
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CSE486, Penn StateRobert Collins
Motivation: Patch Matching
Camps, PSU
==??
Task: find the best (most similar) patch in a second image
Elements to be matched are image patches of fixed size
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CSE486, Penn StateRobert Collins
Not all Patches are Created Equal!
Camps, PSU
==??
Inituition: this would be a good patch for matching, sinceit is very distinctive (there is only one patch in the secondframe that looks similar).
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CSE486, Penn StateRobert Collins
==??
Not all Patches are Created Equal!
Camps, PSU
Inituition: this would be a BAD patch for matching, sinceit is not very distinctive (there are many similar patchesin the second frame)
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CSE486, Penn StateRobert Collins
What are Corners?
M.Hebert, CMU• They are good features to match!
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CSE486, Penn StateRobert Collins
Corner Points: Basic Idea
C.Dyer, UWisc
• We should easily recognize the point by looking at intensity values within a small window
• Shifting the window in any direction should yield a large change in appearance.
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CSE486, Penn StateRobert Collins Appearance Change in
Neighborhood of a PatchInteractive“demo”
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CSE486, Penn StateRobert Collins
Harris Corner Detector: Basic Idea
C.Dyer, UWisc
Harris corner detector gives a mathematicalapproach for determining which case holds.
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CSE486, Penn StateRobert Collins
Harris Detector: Mathematics
C.Dyer, UWisc
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CSE486, Penn StateRobert Collins
Harris Detector: Intuition
C.Dyer, UWisc
For nearly constant patches, this will be near 0.For very distinctive patches, this will be larger.Hence... we want patches where E(u,v) is LARGE.
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CSE486, Penn StateRobert Collins
Taylor Series for 2D Functions
(Higher order terms)
First partial derivatives
Second partial derivatives
Third partial derivatives
First order approx
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CSE486, Penn StateRobert Collins
Harris Corner Derivation
First order approx
Rewrite as matrix equation
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CSE486, Penn StateRobert Collins
Harris Detector: Mathematics
C.Dyer, UWisc
Note: these are just products ofcomponents of the gradient, Ix, Iy
Windowing function - computing aweighted sum (simplest case, w=1)
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CSE486, Penn StateRobert Collins
Intuitive Way to Understand Harris
Treat gradient vectors as a set of (dx,dy) pointswith a center of mass defined as being at (0,0).
Fit an ellipse to that set of points via scatter matrix
Analyze ellipse parameters for varying cases…
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CSE486, Penn StateRobert Collins
Example: Cases and 2D DerivativesM
.Heb
ert,
CM
U
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CSE486, Penn StateRobert Collins
Plotting Derivatives as 2D PointsM
.Heb
ert,
CM
U
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CSE486, Penn StateRobert Collins
Fitting Ellipse to each Set of PointsM
.Heb
ert,
CM
U
λ1~λ2 = small
λ1 large; λ2 = smallλ1~λ2 = large
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CSE486, Penn StateRobert Collins
Classification via Eigenvalues
C.Dyer, UWisc
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CSE486, Penn StateRobert Collins
Corner Response Measure
C.Dyer, UWisc
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CSE486, Penn StateRobert Collins
Corner Response Map
R=0
R=28
R=65
R=104
R=142
lambda1
lambda2
(0,0)
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CSE486, Penn StateRobert Collins
Corner Response Map
R=0
R=28
R=65
R=104
R=142
lambda1
lambda2
|R| small“Flat”
R < 0 “Edge”
R < 0 “E
dge”
R large“Corner”
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CSE486, Penn StateRobert Collins
Corner Response Example
Harris R score. Ix, Iy computed using Sobel operator Windowing function w = Gaussian, sigma=1
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CSE486, Penn StateRobert Collins
Corner Response Example
Threshold: R < -10000(edges)
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CSE486, Penn StateRobert Collins
Corner Response Example
Threshold: > 10000(corners)
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CSE486, Penn StateRobert Collins
Corner Response Example
Threshold: -10000 < R < 10000(neither edges nor corners)
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CSE486, Penn StateRobert Collins
Harris Corner Detection Algorithm
M.Hebert, CMU
6. Threshold on value of R. Compute nonmax suppression.