Transcript Smoothness-Based Method for Detection

Anti-Faces for Detection *
Daniel Keren
Rita Osadchy
Haifa University
Craig Gotsman
Technion
* Journal Version:
http://www.cs.technion.ac.il/~gotsman/AmendedPubl/Anti-Faces/anti-faces-pami.pdf
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
Our Contribution
• Simple detection process (inner product).
Can be implemented by convolution.
• Very fast: For an image of N pixels, usually
requires (1   ) N operations, where   0.25.
• Implicit representation.
• Uses natural image statistics.
• Simple independent detectors.
Previous Work
• Eigenfaces and Eigenface Based
Approaches.
• Neural Networks.
• Support Vector Machines.
• Fisher Linear Discriminant.
Eigenfaces for Recognition
M. Turk and A. Pentland
W
B
d  I ,W   I
2
2
 Proj ( I ,W )
2
Eigenface Based Approaches
• Probabilistic Visual Learning for Object
Representation. B. Moghaddam and A. Pentland
F
x
DFFS

DIFS
F
• Visual Learning Recognition of 3-D from
Appearance. H. Murase and S. Nayar
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
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
Training Support Vector Machines
Support Vectors
 l

f ( x )  sgn   i yi K ( x , xi )  b 
 i 1

2
K ( x , x )  exp(  || x  x || )
i
i
“Separating
functioal”
Fisher Linear Discriminant
• Eigenfaces vs. Fisherfaces: Recognition Using
Class Specific Linear Projection.
P. N. Belhumeur, P. Hespanha, and D. J. Kriegman
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.
Implicit Set Representation
• Implicit set representation is more appropriate
than an explicit one, for determining whether
an element belongs to a set.
x2  y2  1
 x 0 , y0 
The value of | x0  y0  1 | is a
very simple indicator as to
whether ( x0 , y0 ) is close to the
circle or not.
2
2
In general: characterize a set P by
P  {x / | f1 ( x ) |  1 ,... | f n ( x ) |  n }
If

is the class to be detected, the following should hold:
 P.
fi
n
should be simple to compute.
should be small.
If y   , there should be a low probability that,
for every i ,
| f i ( y ) |  i
.
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, I   iff | ( I , d ) |  ,… | ( I , d ) |  .
1
1
However… this fails miserably:
n
n
Orthogonal detectors
for pocket calculator
Many false alarms
(and failure to detect
true instance) when
using these detectors
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.
Implicit Approach for Detection
To Summarize:
• The functionals used for detection are linear:
F I   I , d 
I,d  R
n
where d is a detector for a class  , I an input
image, and n the image size.
• The functional F(I) must be large for random natural
(smooth) images, and small for the images of  .
Otherwise, there are many false alarms.
Class Detection Using Smooth
Detectors
• Boltzman distribution for smooth images:
(
I

I
)
dxdy

y
P( I )  e

2
x
It follows that E[( d , I ) 2 ] 
2

~2
d (i , j )
3
2
(i 2  j 2 )
~
where d (i , j ) are the DCT coefficients of d.
~2
2
since  d (i, j )  1, for E [( d , I ) ] to be large,
( i , j ) ( 0 , 0 )
~
d (i , j ) should be concentrated in small i, j  d is smooth.
Class Detection Using Smooth
Detectors
• 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.
Relationship between theoretical and empirical expectation
of squared inner product with detector d
E [( d , I ) 2 ]
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08

( i , j ) ( 0 , 0 )
~2
d (i , j )
(i  j )
2
2
3
2
Class Detection Using Smooth
Detectors
• Trade-off between
– Smoothness of the detector.
– Orthogonality to the training set.
• Detection:
I 
if d , I   
I 
otherwize
Schematic
Description
of
the
Detection
Schematic Description of the Detection
“Direction of smoothness”
Templates
Natural images
Eigenface method positive set
Anti-face method positive set
False Alarms in Detection
• P - f.a. probability. P << 1.
m independent detectors give P1 P2 ... Pm
• The detectors d1 , d 2 are independent if
I  I , d1  , I  I , d 2 
are independent random variables. This holds iff

~
~
d 1 (i , j ) d 2 (i , j )
( i , j ) ( 0, 0 )
(i 2  j 2 )
3
2
0
Finding the Detectors

d1 , t 
1 Choose an appropriate value M for max
tT
It should be substantially smaller than the absolute
value of the inner product of two “random images”.
2 Minimize
max d1 , t   S d1 
tT
~2
where S ( d1 )   (i  j )d1 (i, j )
2
2
( i , j ) ( 0, 0 )
The optimization is performed in DCT domain, and
the inverse DCT transform of the optimum is the
desired detector.
Finding the Detectors
3 Using a binary search on , set it so that


max
d
,
t

M
1
tT
4 Incorporate the condition for independent
detectors into the optimization scheme to find
the other detectors.
Three of the
“Esti” images
The first four
“anti-Esti”
detectors
Detection
result: all ten
“Esti” instances
were located,
without false
alarms
Eigenface method with the subspace of dimension 100
Detection Results
linear
rotation rotation
+ scale
Anti-faces
(number of
detectors)
3
4
4
12
74
145
Eigenfaces
(face-space
dimension)
Number of Eigenvalues for 90% Energy
rotation
13
rotation+scale
38
linear
68
Detection Results
Number of Number Probability
detectors of F. A. of 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.
Fisher Linear Discriminant Results:
Three random image sets
“Esti” class
(B)
(A)
(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.
Detection of 3D objects from the COIL database
Detection of COIL objects on arbitrary background
Detection Under Varying Illumination:
Model object and shadows.
Detect objects and shadows in the logarithm of the image.
Remove “shadow only” instances, using “shadow only”
detectors.
Osadchy, Keren: “Detection Under Varying
Illumination and Pose”, ICCV 2001.
Event Detection
psychology
anthology
psychological
crocodile
“Anti-psychology”
Future Research
• Develop a general face detector.
• Develop a detector with non-convex
positive set.
• Speech recognition.