Henrik Skov Midtiby [email protected]...
Transcript of Henrik Skov Midtiby [email protected]...
![Page 2: Henrik Skov Midtiby hemi@mmmi.sdu.dk 2014-11-05henrikmidtiby.github.io/downloads/2014-11-05featurespresentation.pdf · Henrik Skov Midtibyhemi@mmmi.sdu.dk Created Date: 10/31/2014](https://reader034.fdocuments.in/reader034/viewer/2022052103/603e4406a56b564b250d765c/html5/thumbnails/2.jpg)
Detection of round objects
http://www.mathworks.se/products/image/examples.html?file=/products/demos/shipping/images/ipexroundness.html
![Page 3: Henrik Skov Midtiby hemi@mmmi.sdu.dk 2014-11-05henrikmidtiby.github.io/downloads/2014-11-05featurespresentation.pdf · Henrik Skov Midtibyhemi@mmmi.sdu.dk Created Date: 10/31/2014](https://reader034.fdocuments.in/reader034/viewer/2022052103/603e4406a56b564b250d765c/html5/thumbnails/3.jpg)
Bottle recognition
![Page 4: Henrik Skov Midtiby hemi@mmmi.sdu.dk 2014-11-05henrikmidtiby.github.io/downloads/2014-11-05featurespresentation.pdf · Henrik Skov Midtibyhemi@mmmi.sdu.dk Created Date: 10/31/2014](https://reader034.fdocuments.in/reader034/viewer/2022052103/603e4406a56b564b250d765c/html5/thumbnails/4.jpg)
Optical character recognition (OCR)
http://www.identifont.com/similar?25H
![Page 5: Henrik Skov Midtiby hemi@mmmi.sdu.dk 2014-11-05henrikmidtiby.github.io/downloads/2014-11-05featurespresentation.pdf · Henrik Skov Midtibyhemi@mmmi.sdu.dk Created Date: 10/31/2014](https://reader034.fdocuments.in/reader034/viewer/2022052103/603e4406a56b564b250d765c/html5/thumbnails/5.jpg)
Plant recognition
Cornflower (BBCH12) Nightshade (BBCH12)
![Page 6: Henrik Skov Midtiby hemi@mmmi.sdu.dk 2014-11-05henrikmidtiby.github.io/downloads/2014-11-05featurespresentation.pdf · Henrik Skov Midtibyhemi@mmmi.sdu.dk Created Date: 10/31/2014](https://reader034.fdocuments.in/reader034/viewer/2022052103/603e4406a56b564b250d765c/html5/thumbnails/6.jpg)
Feature based object recognition
Input image Preprocessed image
Object descriptors
area
perimeter
Matched objects
![Page 7: Henrik Skov Midtiby hemi@mmmi.sdu.dk 2014-11-05henrikmidtiby.github.io/downloads/2014-11-05featurespresentation.pdf · Henrik Skov Midtibyhemi@mmmi.sdu.dk Created Date: 10/31/2014](https://reader034.fdocuments.in/reader034/viewer/2022052103/603e4406a56b564b250d765c/html5/thumbnails/7.jpg)
Feature based object recognition
Input image Preprocessed image
Object descriptors
area
perimeter
Matched objects
Preprocessing
Feature extraction
Classifier
![Page 8: Henrik Skov Midtiby hemi@mmmi.sdu.dk 2014-11-05henrikmidtiby.github.io/downloads/2014-11-05featurespresentation.pdf · Henrik Skov Midtibyhemi@mmmi.sdu.dk Created Date: 10/31/2014](https://reader034.fdocuments.in/reader034/viewer/2022052103/603e4406a56b564b250d765c/html5/thumbnails/8.jpg)
Example: Circle detection
Features:
I area
I perimeter
Combination
4π · area
perimeter2
Maximum value for a circle
4π · πr2
(2πr)2=
4π · πr2
4π2r2= 1
![Page 9: Henrik Skov Midtiby hemi@mmmi.sdu.dk 2014-11-05henrikmidtiby.github.io/downloads/2014-11-05featurespresentation.pdf · Henrik Skov Midtibyhemi@mmmi.sdu.dk Created Date: 10/31/2014](https://reader034.fdocuments.in/reader034/viewer/2022052103/603e4406a56b564b250d765c/html5/thumbnails/9.jpg)
Example: Circle detection
Features:
I area
I perimeter
Combination
4π · area
perimeter2
Maximum value for a circle
4π · πr2
(2πr)2=
4π · πr2
4π2r2= 1
![Page 10: Henrik Skov Midtiby hemi@mmmi.sdu.dk 2014-11-05henrikmidtiby.github.io/downloads/2014-11-05featurespresentation.pdf · Henrik Skov Midtibyhemi@mmmi.sdu.dk Created Date: 10/31/2014](https://reader034.fdocuments.in/reader034/viewer/2022052103/603e4406a56b564b250d765c/html5/thumbnails/10.jpg)
Example: Circle detection
Features:
I area
I perimeter
Combination
4π · area
perimeter2
Maximum value for a circle
4π · πr2
(2πr)2=
4π · πr2
4π2r2= 1
![Page 11: Henrik Skov Midtiby hemi@mmmi.sdu.dk 2014-11-05henrikmidtiby.github.io/downloads/2014-11-05featurespresentation.pdf · Henrik Skov Midtibyhemi@mmmi.sdu.dk Created Date: 10/31/2014](https://reader034.fdocuments.in/reader034/viewer/2022052103/603e4406a56b564b250d765c/html5/thumbnails/11.jpg)
Example: Circle detection continued
http://www.mathworks.se/products/image/examples.html?file=/products/demos/shipping/images/ipexroundness.html
![Page 12: Henrik Skov Midtiby hemi@mmmi.sdu.dk 2014-11-05henrikmidtiby.github.io/downloads/2014-11-05featurespresentation.pdf · Henrik Skov Midtibyhemi@mmmi.sdu.dk Created Date: 10/31/2014](https://reader034.fdocuments.in/reader034/viewer/2022052103/603e4406a56b564b250d765c/html5/thumbnails/12.jpg)
Parameter types
ReconstructiveDescriptive
![Page 13: Henrik Skov Midtiby hemi@mmmi.sdu.dk 2014-11-05henrikmidtiby.github.io/downloads/2014-11-05featurespresentation.pdf · Henrik Skov Midtibyhemi@mmmi.sdu.dk Created Date: 10/31/2014](https://reader034.fdocuments.in/reader034/viewer/2022052103/603e4406a56b564b250d765c/html5/thumbnails/13.jpg)
Example: Height and width of bounding box
![Page 14: Henrik Skov Midtiby hemi@mmmi.sdu.dk 2014-11-05henrikmidtiby.github.io/downloads/2014-11-05featurespresentation.pdf · Henrik Skov Midtibyhemi@mmmi.sdu.dk Created Date: 10/31/2014](https://reader034.fdocuments.in/reader034/viewer/2022052103/603e4406a56b564b250d765c/html5/thumbnails/14.jpg)
Desired properties of features
I Discriminative power (determined by the classification task)I Invariant to
I TranslationI ScaleI Rotation
![Page 15: Henrik Skov Midtiby hemi@mmmi.sdu.dk 2014-11-05henrikmidtiby.github.io/downloads/2014-11-05featurespresentation.pdf · Henrik Skov Midtibyhemi@mmmi.sdu.dk Created Date: 10/31/2014](https://reader034.fdocuments.in/reader034/viewer/2022052103/603e4406a56b564b250d765c/html5/thumbnails/15.jpg)
Case: Digit recognition
![Page 16: Henrik Skov Midtiby hemi@mmmi.sdu.dk 2014-11-05henrikmidtiby.github.io/downloads/2014-11-05featurespresentation.pdf · Henrik Skov Midtibyhemi@mmmi.sdu.dk Created Date: 10/31/2014](https://reader034.fdocuments.in/reader034/viewer/2022052103/603e4406a56b564b250d765c/html5/thumbnails/16.jpg)
Feature space
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Feature space
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Feature space
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Feature space
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Feature space
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![Page 21: Henrik Skov Midtiby hemi@mmmi.sdu.dk 2014-11-05henrikmidtiby.github.io/downloads/2014-11-05featurespresentation.pdf · Henrik Skov Midtibyhemi@mmmi.sdu.dk Created Date: 10/31/2014](https://reader034.fdocuments.in/reader034/viewer/2022052103/603e4406a56b564b250d765c/html5/thumbnails/21.jpg)
Feature example
Convex hull Max ferret, symmetry, . . .
![Page 22: Henrik Skov Midtiby hemi@mmmi.sdu.dk 2014-11-05henrikmidtiby.github.io/downloads/2014-11-05featurespresentation.pdf · Henrik Skov Midtibyhemi@mmmi.sdu.dk Created Date: 10/31/2014](https://reader034.fdocuments.in/reader034/viewer/2022052103/603e4406a56b564b250d765c/html5/thumbnails/22.jpg)
Feature example
Convex hull
Max ferret, symmetry, . . .
![Page 23: Henrik Skov Midtiby hemi@mmmi.sdu.dk 2014-11-05henrikmidtiby.github.io/downloads/2014-11-05featurespresentation.pdf · Henrik Skov Midtibyhemi@mmmi.sdu.dk Created Date: 10/31/2014](https://reader034.fdocuments.in/reader034/viewer/2022052103/603e4406a56b564b250d765c/html5/thumbnails/23.jpg)
Feature example
Convex hull
Max ferret, symmetry, . . .
![Page 24: Henrik Skov Midtiby hemi@mmmi.sdu.dk 2014-11-05henrikmidtiby.github.io/downloads/2014-11-05featurespresentation.pdf · Henrik Skov Midtibyhemi@mmmi.sdu.dk Created Date: 10/31/2014](https://reader034.fdocuments.in/reader034/viewer/2022052103/603e4406a56b564b250d765c/html5/thumbnails/24.jpg)
Feature example
Convex hull Max ferret, symmetry, . . .
![Page 25: Henrik Skov Midtiby hemi@mmmi.sdu.dk 2014-11-05henrikmidtiby.github.io/downloads/2014-11-05featurespresentation.pdf · Henrik Skov Midtibyhemi@mmmi.sdu.dk Created Date: 10/31/2014](https://reader034.fdocuments.in/reader034/viewer/2022052103/603e4406a56b564b250d765c/html5/thumbnails/25.jpg)
Raw moments
I (x , y) intensity of image at location x , y
Mij =∑x
∑y
x i · y j · I (x , y)
Centroid coordinates in terms of raw moments
x =M10
M00=
∑x
∑y x · I (x , y)∑
x
∑y I (x , y)
y =M01
M00=
∑x
∑y y · I (x , y)∑
x
∑y I (x , y)
http://en.wikipedia.org/wiki/Invariant_Moments
![Page 26: Henrik Skov Midtiby hemi@mmmi.sdu.dk 2014-11-05henrikmidtiby.github.io/downloads/2014-11-05featurespresentation.pdf · Henrik Skov Midtibyhemi@mmmi.sdu.dk Created Date: 10/31/2014](https://reader034.fdocuments.in/reader034/viewer/2022052103/603e4406a56b564b250d765c/html5/thumbnails/26.jpg)
Central moments
Place object centroid in (0, 0)This makes central moments invariant to translation.
µpq =∑x
∑y
(x − x)p · (y − y)q · I (x , y)
![Page 27: Henrik Skov Midtiby hemi@mmmi.sdu.dk 2014-11-05henrikmidtiby.github.io/downloads/2014-11-05featurespresentation.pdf · Henrik Skov Midtibyhemi@mmmi.sdu.dk Created Date: 10/31/2014](https://reader034.fdocuments.in/reader034/viewer/2022052103/603e4406a56b564b250d765c/html5/thumbnails/27.jpg)
Central moments from raw moments
µ20 =∑x
∑y
(x − x)2 · (y − y)0 · I (x , y)
=∑x
∑y
(x2 − 2x · x + x2) · I (x , y)
=∑x
∑y
x2 · I (x , y) − 2 · x ·∑x
∑y
x · I (x , y)
+ x2∑x
∑y
I (x , y)
= M20 − 2 · x ·M10 + x2 ·M00
= M20 − 2 · M10
M00·M10 +
(M10
M00
)2
·M00
= M20 −M10
M00·M10 = M20 − x ·M10
![Page 28: Henrik Skov Midtiby hemi@mmmi.sdu.dk 2014-11-05henrikmidtiby.github.io/downloads/2014-11-05featurespresentation.pdf · Henrik Skov Midtibyhemi@mmmi.sdu.dk Created Date: 10/31/2014](https://reader034.fdocuments.in/reader034/viewer/2022052103/603e4406a56b564b250d765c/html5/thumbnails/28.jpg)
Object orientation
Covariance matrix
µ′20 = µ20/µ00 = M20/M00 − x2
µ′02 = µ02/µ00 = M02/M00 − y2
µ′11 = µ11/µ00 = M11/M00 − x y
cov[I (x , y)] =
[µ′20 µ′11µ′11 µ′02
].
Orientation of largest eigenvalue (and of object)
Θ =1
2arctan
(2µ′11
µ′20 − µ′02
)
![Page 29: Henrik Skov Midtiby hemi@mmmi.sdu.dk 2014-11-05henrikmidtiby.github.io/downloads/2014-11-05featurespresentation.pdf · Henrik Skov Midtibyhemi@mmmi.sdu.dk Created Date: 10/31/2014](https://reader034.fdocuments.in/reader034/viewer/2022052103/603e4406a56b564b250d765c/html5/thumbnails/29.jpg)
Central moments from raw moments
µ00 = M00
µ01 = 0
µ10 = 0
µ11 = M11 − xM01 = M11 − yM10
µ20 = M20 − xM10
µ02 = M02 − yM01
µ21 = M21 − 2xM11 − yM20 + 2x2M01
µ12 = M12 − 2yM11 − xM02 + 2y2M10
µ30 = M30 − 3xM20 + 2x2M10
µ03 = M03 − 3yM02 + 2y2M01
![Page 32: Henrik Skov Midtiby hemi@mmmi.sdu.dk 2014-11-05henrikmidtiby.github.io/downloads/2014-11-05featurespresentation.pdf · Henrik Skov Midtibyhemi@mmmi.sdu.dk Created Date: 10/31/2014](https://reader034.fdocuments.in/reader034/viewer/2022052103/603e4406a56b564b250d765c/html5/thumbnails/32.jpg)
Scale invariant moments
ηij =µij
µ(1+ i+j
2 )00
![Page 33: Henrik Skov Midtiby hemi@mmmi.sdu.dk 2014-11-05henrikmidtiby.github.io/downloads/2014-11-05featurespresentation.pdf · Henrik Skov Midtibyhemi@mmmi.sdu.dk Created Date: 10/31/2014](https://reader034.fdocuments.in/reader034/viewer/2022052103/603e4406a56b564b250d765c/html5/thumbnails/33.jpg)
Rotation invariant moments – Hu moments
I1 = η20 + η02
I2 = (η20 − η02)2 + 4η211
I3 = (η30 − 3η12)2 + (3η21 − η03)2
I4 = (η30 + η12)2 + (η21 + η03)2
I5 = (η30 − 3η12)(η30 + η12)[(η30 + η12)2 − 3(η21 + η03)2]
+ (3η21 − η03)(η21 + η03)[3(η30 + η12)2 − (η21 + η03)2]
I6 = (η20 − η02)[(η30 + η12)2 − (η21 + η03)2]
+ 4η11(η30 + η12)(η21 + η03)
I7 = (3η21 − η03)(η30 + η12)[(η30 + η12)2 − 3(η21 + η03)2]
− (η30 − 3η12)(η21 + η03)[3(η30 + η12)2 − (η21 + η03)2]
![Page 34: Henrik Skov Midtiby hemi@mmmi.sdu.dk 2014-11-05henrikmidtiby.github.io/downloads/2014-11-05featurespresentation.pdf · Henrik Skov Midtibyhemi@mmmi.sdu.dk Created Date: 10/31/2014](https://reader034.fdocuments.in/reader034/viewer/2022052103/603e4406a56b564b250d765c/html5/thumbnails/34.jpg)
Hu moments
Learning OpenCV, Bradski & Kaehler, 2008
![Page 35: Henrik Skov Midtiby hemi@mmmi.sdu.dk 2014-11-05henrikmidtiby.github.io/downloads/2014-11-05featurespresentation.pdf · Henrik Skov Midtibyhemi@mmmi.sdu.dk Created Date: 10/31/2014](https://reader034.fdocuments.in/reader034/viewer/2022052103/603e4406a56b564b250d765c/html5/thumbnails/35.jpg)
Hu moments
Pattern Recognition, Theodoridis & Koutroumbas, 2006
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Hu moments – Interpretation
I1 Angular momentum
I7 Skew invariant, changes sign when object is mirrored
![Page 37: Henrik Skov Midtiby hemi@mmmi.sdu.dk 2014-11-05henrikmidtiby.github.io/downloads/2014-11-05featurespresentation.pdf · Henrik Skov Midtibyhemi@mmmi.sdu.dk Created Date: 10/31/2014](https://reader034.fdocuments.in/reader034/viewer/2022052103/603e4406a56b564b250d765c/html5/thumbnails/37.jpg)
Features from sudoku digits
Some example data from digit recognition.Now with better features
I area
I perimeter
I central moments
I Hu moments
![Page 38: Henrik Skov Midtiby hemi@mmmi.sdu.dk 2014-11-05henrikmidtiby.github.io/downloads/2014-11-05featurespresentation.pdf · Henrik Skov Midtibyhemi@mmmi.sdu.dk Created Date: 10/31/2014](https://reader034.fdocuments.in/reader034/viewer/2022052103/603e4406a56b564b250d765c/html5/thumbnails/38.jpg)
Sudoku digits
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Sudoku digits
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Sudoku digits
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Features from sudoku digits
Some example data from digit recognition.Now with better features
I area
I perimeter
I central moments
I Hu moments – Is not enough alone (6 vs. 9)
![Page 42: Henrik Skov Midtiby hemi@mmmi.sdu.dk 2014-11-05henrikmidtiby.github.io/downloads/2014-11-05featurespresentation.pdf · Henrik Skov Midtibyhemi@mmmi.sdu.dk Created Date: 10/31/2014](https://reader034.fdocuments.in/reader034/viewer/2022052103/603e4406a56b564b250d765c/html5/thumbnails/42.jpg)
Summary
I feature based object recognition can be used for several tasks
I features are derived from objects
I choosing good features are important