lecture 3: 2d edge detection and moving beyond edges
TRANSCRIPT
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Lecture 3: 2D edge detectionand moving beyond edges
Dr. Richard E. Turner ([email protected])
October 17, 2013
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Recap of last lecture
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Recap of last lecture
image
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Recap of last lecture
image Gaussianblur
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Recap of last lecture
image Gaussianblur
differentiate
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Recap of last lecture
image Gaussianblur
differentiate locateextrema
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Recap of last lecture
image Gaussianblur
differentiate locateextrema
threshold
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Recap of last lecture
image Gaussianblur
differentiate locateextrema
threshold
convolutionlowpass filter
o frequency
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Recap of last lecture
image Gaussianblur
differentiate locateextrema
threshold
convolutionlowpass filter
convolutionhighpass filter
o o frequency
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Recap of last lecture
image Gaussianblur
differentiate locateextrema
threshold
convolutionlowpass filter
convolutionhighpass filter
o o
X frequency
=
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Recap of last lecture
image Gaussianblur
differentiate locateextrema
threshold
convolutionlowpass filter
convolutionhighpass filter
bandpass filter
o o
X frequency
=
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Recap of last lecture
image Gaussianblur
differentiate locateextrema
threshold
convolutionlowpass filter
convolutionhighpass filter
bandpass filter
linear operations are commutative and associative
o o
X frequency
=
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Recap of last lecture
image Gaussianblur
differentiate locateextrema
threshold
convolutionlowpass filter
convolutionhighpass filter
bandpass filter
linear operations are commutative and associative
o o
image Gaussianblur
differentiate
X frequency
=
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Recap of last lecture
image Gaussianblur
differentiate locateextrema
threshold
convolutionlowpass filter
convolutionhighpass filter
bandpass filter
linear operations are commutative and associative
o o
image differentiate
X frequency
=
Gaussianblur
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Recap of last lecture
image Gaussianblur
differentiate locateextrema
threshold
convolutionlowpass filter
convolutionhighpass filter
bandpass filter
linear operations are commutative and associative
o o
image blur with derivative of Gaussian
X frequency
=
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Recap of last lecture
image Gaussianblur
differentiate locateextrema
threshold
convolutionlowpass filter
convolutionhighpass filter
bandpass filter
linear operations are commutative and associative
o o
image blur with derivative of Gaussian
X frequency
=
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Today
• Is there a correct level of blur for edge detection?
• Edge detection in 2D
– Canny edge detection– Marr Hildreth edge detection
• Moving beyond edges
– why edges aren’t sufficient for computer vision
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Discrete approximation of the Gaussian filter
1 2 3 4 5 6 7 8 9 ... N
N = number of pixels in 1D image
discreteapprox
continuousGaussian
=⇒ Trade-off between comp. complexity and high-frequency artifacts
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Truncation of the Gaussian filter
1 2 3 4 5 6 7 8 9... K
N = number of pixels in 1D image
discreteapprox
continuousGaussian
K = truncated approximation
peak height
peak height1000
=⇒ Trade-off between comp. complexity and high-frequency artifacts
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Truncation of the Gaussian filter
1 2 3 4 5 6 7 8 9... K
N = number of pixels in 1D image
discreteapprox
continuousGaussian
K = truncated approximation
peak height
peak height1000
=⇒ Trade-off between computational complexity and high-frequency artifacts
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Convolution
imag
efil
ter aa b c
d e fg h i
filtered image
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Convolution
imag
efil
ter aa b c
d e fg h i
filtered image
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Is this the right thing to do?
imag
efil
ter aa b c
d e fg h i a b c
d e fg h i
filtered image
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Is this the right thing to do?
imag
efil
ter aa b c
d e fg h i a b c
d e fg h i
filtered image
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Convolution
imag
efil
ter aa b c
d e fg h i i h g
f e lc b a
flip
filtered image
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Convolution
imag
efil
ter aa b c
d e fg h i i h g
f e lc b a
flip
filtered image
convolution = correlation when the filter is symmetric e.g. isotropic Gaussian
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Convolution
imag
efil
ter aa b c
d e fg h i i h g
f e lc b a
filtered image
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Convolution
imag
efil
ter aa b c
d e fg h i
i h gf e lc b a
filtered image
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Convolution
imag
efil
ter aa b c
d e fg h i
i h gf e lc b a
filtered image
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Convolution
imag
efil
ter aa b c
d e fg h i
i h gf e lc b a
filtered image
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What’s the computational cost?
imag
efil
ter aa b c
d e fg h i i h g
f e lc b a
filtered image
K by K matrix N by M pixel image
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What’s the computational cost?
imag
efil
ter aa b c
d e fg h i i h g
f e lc b a
filtered image
K by K matrix N by M pixel image
NB. K = 2n+1 in your notes
computational cost = NMK2
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Can we speed this up when the filter is separable?
image
filter aa b c
d e fg h i
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Can we speed this up when the filter is separable?
image
filter aa b c
d e fg h i
a'b'c'
a' b' c'
aa b cb d ec e f
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Can we speed this up when the filter is separable?
image
filter aa b c
d e fg h i
a'b'c'
a' b' c'
aa b cb d ec e f
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Can we speed this up when the filter is separable?
image
filter aa b c
d e fg h i
a'b'c'
a' b' c'
aa b cb d ec e f
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Can we speed this up when the filter is separable?
image
filter aa b c
d e fg h i
a'b'c'
a' b' c'
aa b cb d ec e f
![Page 38: Lecture 3: 2D edge detection and moving beyond edges](https://reader031.vdocuments.us/reader031/viewer/2022011915/61d7dd6d646c180bad228750/html5/thumbnails/38.jpg)
Can we speed this up when the filter is separable?
image
filter aa b c
d e fg h i
c'b'a'
a'b'c'
a' b' c'
aa b cb d ec e f
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Can we speed this up when the filter is separable?
image
filter aa b c
d e fg h i
c'b'a'
a'b'c'
a' b' c'
aa b cb d ec e f
![Page 40: Lecture 3: 2D edge detection and moving beyond edges](https://reader031.vdocuments.us/reader031/viewer/2022011915/61d7dd6d646c180bad228750/html5/thumbnails/40.jpg)
Can we speed this up when the filter is separable?
image
filter aa b c
d e fg h i
c'b'a'
a'b'c'
a' b' c'
aa b cb d ec e f
![Page 41: Lecture 3: 2D edge detection and moving beyond edges](https://reader031.vdocuments.us/reader031/viewer/2022011915/61d7dd6d646c180bad228750/html5/thumbnails/41.jpg)
Can we speed this up when the filter is separable?
image
filter aa b c
d e fg h i
c'b'a'
a'b'c'
a' b' c'
aa b cb d ec e f
![Page 42: Lecture 3: 2D edge detection and moving beyond edges](https://reader031.vdocuments.us/reader031/viewer/2022011915/61d7dd6d646c180bad228750/html5/thumbnails/42.jpg)
Can we speed this up when the filter is separable?
image
filter aa b c
d e fg h i
c'b'a'
a'b'c'
a' b' c'
aa b cb d ec e f
![Page 43: Lecture 3: 2D edge detection and moving beyond edges](https://reader031.vdocuments.us/reader031/viewer/2022011915/61d7dd6d646c180bad228750/html5/thumbnails/43.jpg)
Can we speed this up when the filter is separable?
image
filter aa b c
d e fg h i
c'b'a'
a'b'c'
a' b' c'
aa b cb d ec e f
![Page 44: Lecture 3: 2D edge detection and moving beyond edges](https://reader031.vdocuments.us/reader031/viewer/2022011915/61d7dd6d646c180bad228750/html5/thumbnails/44.jpg)
Can we speed this up when the filter is separable?
image
filter aa b c
d e fg h i
c'b'a'
a'b'c'
a' b' c'
aa b cb d ec e f
![Page 45: Lecture 3: 2D edge detection and moving beyond edges](https://reader031.vdocuments.us/reader031/viewer/2022011915/61d7dd6d646c180bad228750/html5/thumbnails/45.jpg)
Can we speed this up when the filter is separable?
image
filter aa b c
d e fg h i
c'b'a'
a'b'c'
a' b' c'
aa b cb d ec e f
![Page 46: Lecture 3: 2D edge detection and moving beyond edges](https://reader031.vdocuments.us/reader031/viewer/2022011915/61d7dd6d646c180bad228750/html5/thumbnails/46.jpg)
Can we speed this up when the filter is separable?
imag
efil
ter aa b c
d e fg h i
c' b' a'
a'b'c'
a' b' c'
aa b cb d ec e f filtered
image
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Can we speed this up when the filter is separable?
imag
efil
ter aa b c
d e fg h i
c' b' a'
a'b'c'
a' b' c'
aa b cb d ec e f filtered
image
![Page 48: Lecture 3: 2D edge detection and moving beyond edges](https://reader031.vdocuments.us/reader031/viewer/2022011915/61d7dd6d646c180bad228750/html5/thumbnails/48.jpg)
Can we speed this up when the filter is separable?
imag
efil
ter aa b c
d e fg h i
c' b' a'
a'b'c'
a' b' c'
aa b cb d ec e f filtered
image
![Page 49: Lecture 3: 2D edge detection and moving beyond edges](https://reader031.vdocuments.us/reader031/viewer/2022011915/61d7dd6d646c180bad228750/html5/thumbnails/49.jpg)
Can we speed this up when the filter is separable?
imag
efil
ter aa b c
d e fg h i
c' b' a'
a'b'c'
a' b' c'
aa b cb d ec e f filtered
image
![Page 50: Lecture 3: 2D edge detection and moving beyond edges](https://reader031.vdocuments.us/reader031/viewer/2022011915/61d7dd6d646c180bad228750/html5/thumbnails/50.jpg)
Can we speed this up when the filter is separable?
imag
efil
ter aa b c
d e fg h i
c' b' a'
a'b'c'
a' b' c'
aa b cb d ec e f filtered
image
![Page 51: Lecture 3: 2D edge detection and moving beyond edges](https://reader031.vdocuments.us/reader031/viewer/2022011915/61d7dd6d646c180bad228750/html5/thumbnails/51.jpg)
Can we speed this up when the filter is separable?
imag
efil
ter aa b c
d e fg h i
c' b' a'
a'b'c'
a' b' c'
aa b cb d ec e f filtered
image
![Page 52: Lecture 3: 2D edge detection and moving beyond edges](https://reader031.vdocuments.us/reader031/viewer/2022011915/61d7dd6d646c180bad228750/html5/thumbnails/52.jpg)
Can we speed this up when the filter is separable?
imag
efil
ter aa b c
d e fg h i
c' b' a'
a'b'c'
a' b' c'
aa b cb d ec e f filtered
image
![Page 53: Lecture 3: 2D edge detection and moving beyond edges](https://reader031.vdocuments.us/reader031/viewer/2022011915/61d7dd6d646c180bad228750/html5/thumbnails/53.jpg)
Can we speed this up when the filter is separable?
imag
efil
ter aa b c
d e fg h i
c' b' a'
a'b'c'
a' b' c'
aa b cb d ec e f filtered
image
![Page 54: Lecture 3: 2D edge detection and moving beyond edges](https://reader031.vdocuments.us/reader031/viewer/2022011915/61d7dd6d646c180bad228750/html5/thumbnails/54.jpg)
What is the new computational cost?
imag
efil
ter aa b c
d e fg h i
c' b' a'
a'b'c'
a' b' c'
aa b cb d ec e f filtered
image
c'b'a'
N by M pixel image
K dimensionalvectors
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What is the new computational cost?
imag
efil
ter aa b c
d e fg h i
c' b' a'
a'b'c'
a' b' c'
aa b cb d ec e f filtered
image
c'b'a'
new computational cost is = 2NMK
N by M pixel image
K dimensionalvectors
![Page 56: Lecture 3: 2D edge detection and moving beyond edges](https://reader031.vdocuments.us/reader031/viewer/2022011915/61d7dd6d646c180bad228750/html5/thumbnails/56.jpg)
What is the new computational cost?
imag
efil
ter aa b c
d e fg h i
c' b' a'
a'b'c'
a' b' c'
aa b cb d ec e f filtered
image
c'b'a'
old computational cost was = NMK
new computational cost is = 2NMK2
N by M pixel image
K dimensionalvectors
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Aperture problem
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Aperture problem
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Aperture problem
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Aperture problem
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Aperture problem
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Aperture problem
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Aperture problem
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Aperture problem
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Aperture problem
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Aperture problem
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Aperture problem
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Aperture problem
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Aperture problem
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Aperture problem
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Which way do you think the edge is moving?
a
b
c
de
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Aperture problem
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Aperture problem
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Aperture problem
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Aperture problem
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Aperture problem
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Aperture problem
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Aperture problem
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Aperture problem
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Aperture problem
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Aperture problem
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Aperture problem
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Aperture problem
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Aperture problem
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Aperture problem
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Problem with edge-features
=⇒ Edges can only tell us about the component of motionperpedicular to the edge
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What about corners?
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What about corners?
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What about corners?
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What about corners?
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What about corners?
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What about corners?
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What about corners?
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What about corners?
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What about corners?
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What about corners?
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What about corners?
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What about corners?
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What about corners?
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What about corners?
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What about corners?
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What about corners?
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What about corners?
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What about corners?
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What about corners?
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What about corners?
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What about corners?
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What about corners?
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What about corners?
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What about corners?