anti-faces for detection daniel keren rita osadchy haifa university craig gotsman technion journal...
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Anti-Faces for Detection
Daniel Keren Rita OsadchyHaifa University
Craig Gotsman Technion
*
* Journal Version:
http://www.cs.technion.ac.il/~gotsman/AmendedPubl/Anti-Faces/anti-faces-pami.pdf
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Problem Definition
Given a set T of training images from an object class , locate all instances of any member of in test image P.
Images from training set Test image
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• Simple detection process (inner product). Can be implemented by convolution.
• Very fast: For an image of N pixels, usually requires operations, where
• Implicit representation.
• Uses natural image statistics.
• Simple independent detectors.
Our Contribution
N)1( .25.0
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Previous Work
• Eigenfaces and Eigenface Based Approaches.
• Neural Networks.
• Support Vector Machines.
• Fisher Linear Discriminant.
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Eigenfaces for RecognitionM. Turk and A. Pentland
),(Proj, 222 WIIWId
B
W
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• Probabilistic Visual Learning for Object Representation. B. Moghaddam and A. Pentland
Eigenface Based Approaches
DIFS
DFFS
F
F x
• Visual Learning Recognition of 3-D from Appearance. H. Murase and S. Nayar
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Neural Networks for Face Detection
• Neural Network Based Face Detection.
H. Rowly, S. Baluja, and T. Kanade
• Rotation Invariant Neural Network Based Face Detection.
H. Rowly, S. Baluja, and T. Kanade
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Training Support Vector Machines
• Training Support Vector Machines: an Application to Face Detection. E. Osuna, R. Freund, and F. Girosi
• Training Support Vector Machines for 3-D Object Recognition.
M. Pontil and A. Verri
• A General Framework for Object Detection.C.P. Papageorgiou, M. Oren, and T. Poggio
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Training Support Vector Machines
margin
Support Vectors
bxxKyxf ii
l
ii ),(sgn)(
1
)||||exp(),(2
ixx
ixxK
“Separating functioal”
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Fisher Linear Discriminant
• Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection. P. N.
Belhumeur, P. Hespanha, and D. J. Kriegman
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Drawbacks of the Described Methods• Eigenface based methods:
– Very high dimension of face-space is needed.– Distance to face-space is a weak discriminator
between class images and non-class natural images.
• Neural networks, SVM:– Long learning time. – Strong training data dependency.– Many operations on input image are required.
• Fisher Linear Discriminant :– Too simple.
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• Implicit set representation is more appropriate than an explicit one, for determining whether an element belongs to a set.
Implicit Set Representation
122 yx
00 , yx
The value of is a very simple indicator as to
whether is close to the circle or not.
|1| 2200 yx
),(00
yx
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In general: characterize a set P by
}|)(|,...|)(|/{11 nn
xfxfxP
if should be simple to compute.
n should be small.
If , there should be a low probability that,
iii
yf |)(|for every ,
.
If is the class to be detected, the following should hold:
.
P
y
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Implicit Set Representation
The natural extension of this idea to detection is:
Find functionals which attain a small value on the object class , and use them for detection. The first guess: inner product with vectors orthogonal to ‘s elements. So, iff ,… .
However… this fails miserably:
I11
|),(| dInn
dI |),(|
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Orthogonal detectors for pocket calculator
Many false alarms (and failure to detect true instance) when using these detectors
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Implicit Set Representation
Conclusion: It’s not enough for the detectors to attain small values on the object class, they also have to attain larger values on “random” images.
Our model for random smooth.
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Implicit Approach for Detection
where d is a detector for a class , I an input image, and n the image size.
nRdIdIIF , ,
• The functionals used for detection are linear:
• The functional F(I) must be large for random natural (smooth) images, and small for the images of . Otherwise, there are many false alarms.
To Summarize:
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Class Detection Using Smooth Detectors
• Boltzman distribution for smooth images:
eIP )( dxdyx y
II )( 22
)0,0(),( 22
22
2
3
)(
),(~]),[(
ji ji
jidIdE
where ),(~ jid are the DCT coefficients of d.
It follows that
,1),(~2 jidsince ]),[( 2IdEfor to be large,
),(~ jid should be concentrated in small ji, d is smooth.
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• The average response of a smooth detector on a smooth image is large.
• This relation was checked on 6,500 different detectors, each one on 14,440 natural images.
Class Detection Using Smooth Detectors
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0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.080
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Relationship between theoretical and empirical expectation of squared inner product with detector d
]2),[( IdE
)0,0(),( 2
3
)(
),(~
22
2
ji ji
jid
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Class Detection Using Smooth Detectors
• Trade-off between – Smoothness of the detector.– Orthogonality to the training set.
• Detection:
otherwize
, if
I
IdI
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Schematic Description of the Detection
Templates
Natural images
Eigenface method positive set
Anti-face method positive set
“Direction of smoothness”
Schematic Description of the Detection
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False Alarms in Detection
• P - f.a. probability. P << 1.
m independent detectors give m
PPP ...21
• The detectors are independent if
02
3
)(
),(~),(~
22
21 ji
jidjid
)0,0(),( ji
21
, , , dIIdII 2
,1
dd
are independent random variables. This holds iff
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Finding the Detectors
1 Choose an appropriate value M for It should be substantially smaller than the absolute
value of the inner product of two “random images”.
2 Minimize
The optimization is performed in DCT domain, and the inverse DCT transform of the optimum is the desired detector.
tdTt
,max 1
11
,max dStdTt
),(~)()( where2
1
22
1 jidjidS)0,0(),( ji
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Finding the Detectors
3 Using a binary search on , set it so that
4 Incorporate the condition for independent detectors into the optimization scheme to find the other detectors.
MtdTt
,max1
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Three of the “Esti” images
The first four “anti-Esti” detectors
Detection result: all ten
“Esti” instances were located, without false
alarms
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Eigenface method with the subspace of dimension 100
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Detection Results
Number of Eigenvalues for 90% Energy
rotation rotation+ scale
linear
Anti-faces(number ofdetectors)
3 4 4
Eigenfaces(face-spacedimension)
12 74 145
rotation rotation+scale linear
13 38 68
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Detection ResultsNumber ofdetectors
Numberof F. A.
Probabilityof F.A.
1 4892 0.034
2 211 0.0015
3 3 0.00002
4 0 0.0
The results refer to “rotate + scale” case.
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Fisher Linear Discriminant Results:
“Esti” classThree random image sets
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(A) (B)
(C)
(A) and (B) Anti-Faces with 8 detectors.
(C) Eigenface method with the subspace of dimension 8. Eigenface method requires the subspace of dimension 30 for correct detection.
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Detection of 3D objects from the COIL database
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Detection of COIL objects on arbitrary background
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Detection Under Varying Illumination:
Detect objects and shadows in the logarithm of the image.
Model object and shadows.
Remove “shadow only” instances, using “shadow only” detectors.
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Osadchy, Keren: “Detection Under Varying Illumination and Pose”, ICCV 2001.
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psychology psychological crocodile
anthology “Anti-psychology”
Event Detection
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Future Research
• Develop a general face detector.
• Develop a detector with non-convex positive set.
• Speech recognition.