LPP

HOG: A New Local Image Descriptor for Fast
Human Detection
Andy {andy@ulsan.islab.ac.kr}
Qing Jun Wang and Ru Bo Zhang
IEEE International Symposium on Knowledge Acquisition and Modeling Workshop, 2008.
pp.640

643 21

22 Dec. 2008, Wuhan
2
Intelligent Systems Lab.
Problem setting
Goal: design algorithm for human detection able to perform in real

time
Proposed solution:

Use a combination of Histogram of Oriented Gradients (HOG) as a feature
vector.

Decrease feature

space dimensionality using Locality Preserving Projection
(LPP)

Use Support Vector Machine (SVM) algorithm in reduced feature space to
train the classifier
3
Intelligent Systems Lab.
HOG
general scheme
4
Intelligent Systems Lab.
Typical person detection scheme using SVM
In practice, effect is very
small (about 1%) while
some computational
time is required*
*
Navneet Dalal and Bill Triggs. Histograms of Oriented Gradients for Human Detection.
In Proceedings of the IEEE Conference on Computer Vision and
Pattern Recognition, SanDiego, USA, June 2005. Vol. II, pp. 886

893.
5
Intelligent Systems Lab.
Computing gradients
Mask
Type
1D
centered
1D
uncentered
1D
cubic

corrected
2x2 diagonal
3x3 Sobel
Operator
[

1, 0, 1]
[

1, 1]
[1,

8, 0, 8,

1]
Miss rate
at 10
−4
FPPW
11%
12.5%
12%
12.5%
14%
6
Intelligent Systems Lab.
Accumulate weight votes over spatial cells
•
How many bins should be in histogram?
•
Should we use oriented or non

oriented gradients?
•
How to select weights?
•
Should we use overlapped blocks or not? If yes, then how
big should be the overlap?
•
What block size should we use?
z
7
Intelligent Systems Lab.
Accumulate weight votes over spatial cells
•
How many bins should be in histogram?
•
Should we use oriented or non

oriented gradients?
•
How to select weights?
•
Should we use overlapped blocks or not? If yes, then how
big should be the overlap?
•
What block size should we use?
8
Intelligent Systems Lab.
Accumulate weight votes over spatial cells
•
How many bins should be in histogram?
•
Should we use oriented or non

oriented gradients?
•
How to select weights?
•
Should we use overlapped blocks or not? If yes, then how
big should be the overlap?
•
What block size should we use?
9
Intelligent Systems Lab.
Contrast normalization

L2

norm followed by clipping (limiting the maximum values of v to 0.2) and renormalising
10
Intelligent Systems Lab.
Making feature vector
Variants of HOG descriptors. (a) A rectangular HOG (R

HOG) descriptor with 3
×
3 blocks of cells.
(b) Circular HOG (C

HOG) descriptor with the central cell divided into angular sectors as in shape
contexts. (c) A C

HOG descriptor with a single central cell.
11
Intelligent Systems Lab.
HOG feature vector for one block
120
101
97
47
110
101
95
45
30
25
15
10
25
25
15
0
80
70
70
50
40
30
30
20
5
10
10
5
10
20
20
5
Angle
Magnitude
Binary voting
Magnitude voting
Feature vector extends while window moves
12
Intelligent Systems Lab.
HOG example
In each triplet: (1) the input image, (2) the corresponding R

HOG feature vector (only the dominant
orientation of each cell is shown),
(3)
the dominant orientations selected by the SVM (obtained
by multiplying the feature vector by the corresponding weights from the linear SVM).
13
Intelligent Systems Lab.
Support Vector Machine (SVM)
14
Intelligent Systems Lab.
Problem setting for SVM
x
1
x
2
w
T
x + b < 0
w
T
x + b > 0
A hyper

plane in the feature space
(Unit

length) normal vector of the
hyper

plane:
n
denotes +1
denotes

1
15
Intelligent Systems Lab.
x
1
x
2
How would you classify these points
using a linear discriminant function in
order to minimize the error rate?
denotes +1
denotes

1
Infinite number of answers!
Which one is the best?
Problem setting for SVM
16
Intelligent Systems Lab.
Large Margin Linear Classifier
We know that
The margin width is:
x
1
x
2
denotes +1
denotes

1
Margin
x
+
x
+
x

n
Support Vectors
17
Intelligent Systems Lab.
Large Margin Linear Classifier
Formulation:
x
1
x
2
denotes +1
denotes

1
Margin
x
+
x
+
x

n
such that
18
Intelligent Systems Lab.
Large Margin Linear Classifier
Formulation:
x
1
x
2
denotes +1
denotes

1
Margin
x
+
x
+
x

n
such that
19
Intelligent Systems Lab.
Large Margin Linear Classifier
Formulation:
x
1
x
2
denotes +1
denotes

1
Margin
x
+
x
+
x

n
such that
20
Intelligent Systems Lab.
Solving the Optimization Problem
s.t.
Quadratic
programming
with linear
constraints
s.t.
Lagrangian
Function
21
Intelligent Systems Lab.
Solving the Optimization Problem
s.t.
22
Intelligent Systems Lab.
Solving the Optimization Problem
s.t.
s.t.
, and
Lagrangian Dual
Problem
23
Intelligent Systems Lab.
Solving the Optimization Problem
The solution has the form:
From KKT condition, we know:
Thus, only support vectors have
x
1
x
2
x
+
x
+
x

Support Vectors
24
Intelligent Systems Lab.
Solving the Optimization Problem
The linear discriminant function is:
Notice it relies on a
dot product
between the test point
x
and the support v
ectors
x
i
Also keep in mind that solving the optimization problem involved computing
the
dot products
x
i
T
x
j
between all pairs of training points
25
Intelligent Systems Lab.
Large Margin Linear Classifier
What if data is not linear separable?
(noisy data, outliers, etc.)
Slack variables
ξ
i
can be added
to allow miss

classification of dif
ficult or noisy data points
x
1
x
2
denotes +1
denotes

1
26
Intelligent Systems Lab.
Large Margin Linear Classifier
Formulation:
such that
Parameter
C
can be viewed as a way to control over

fitting.
27
Intelligent Systems Lab.
Large Margin Linear Classifier
Formulation: (Lagrangian Dual Problem)
such that
28
Intelligent Systems Lab.
Datasets that are linearly separable with noise work out great:
0
x
0
x
x
2
0
x
But what are we going to do if the dataset is just too hard?
How about
…
mapping data to a higher

dimensional space:
Non

linear SVMs
29
Intelligent Systems Lab.
General idea: the original input space can be mapped to some higher

dime
nsional feature space where the training set is separable:
Φ
:
x
→
φ
(
x
)
Non

linear SVMs: Feature Space
30
Intelligent Systems Lab.
With this mapping, our discriminant function is now:
No need to know this mapping explicitly, because we only use the
dot product
o
f feature vectors in both the training and test.
A
kernel function
is defined as a function that corresponds to a dot product of
two feature vectors in some expanded feature space:
Non

linear SVMs: The Kernel Trick
31
Intelligent Systems Lab.
Linear kernel:
Examples of commonly

used kernel functions:
Polynomial kernel:
Gaussian (Radial

Basis Function (RBF) ) kernel:
Non

linear SVMs: The Kernel Trick
32
Intelligent Systems Lab.
Nonlinear SVM: Optimization
Formulation: (Lagrangian Dual Problem)
such that
The solution of the discriminant function is
The optimization technique is the same.
33
Intelligent Systems Lab.
Support Vector Machine: Algorithm
1. Choose a kernel function
2. Choose a value for
C
3. Solve the quadratic programming problem (many algorithms and software
packages available)
4. Construct the discriminant function from the support vectors
34
Intelligent Systems Lab.
Summary: Support Vector Machine
1. Large Margin Classifier
Better generalization ability & less over

fitting
2. The Kernel Trick
Map data points to higher dimensional space in order to make them
linearly separable.
Since only dot product is used, we do not need to represent the
mapping explicitly.
35
Intelligent Systems Lab.
Back to the proposed paper
36
Intelligent Systems Lab.
Proposed algorithm parameters

Bins in histogram:
8

Cell size: 4x4 pixels

Block size:
2x2
cells (8x8 pixels)

Image size: 64x128 pixels (
8x16
blocks)

Feature vector size:
2x2
x
8
x
8x16
=4096
37
Intelligent Systems Lab.
LPP Algorithm
Main idea: find matrix which will project original data into a space with lower
dimensionality while preserving similarity between data (data which are close to
each other in original space should be close after projection)
38
Intelligent Systems Lab.
LPP Algorithm
Is it correct?
Add constraints
Can be represented as a generalized eigenvalue problem
Is it correct?
By selecting
d
smallest eigenvalues and corresponding eigenvectors dimensionality reduction is achieved
39
Intelligent Systems Lab.
Solving different scale problem
40
Intelligent Systems Lab.
Some results
Dimension
d
Detection rate
PCA

HOG
features (labeled’ *’)
vs
LPP

HOG features
(labeled
˅
’)
Detection example
41
Intelligent Systems Lab.
Conclusions

Fast human detection algorithm based on HOG features is presented

no information about computational speed is given

Proposed method is similar to PCA

HOG

feature space dimensionality decreased using LPP

why do we need to make LPP instead of finding eigenvectors from
original feature space?

some equations seems to be wrong

Reference papers are very few
Navneet Dalal
“
Finding People in Images and Videos
”
PhD Thesis. Institut National Polytechnique de Grenoble / INRIA Grenoble ,
Grenoble, July 2006.
Navneet Dalal and Bill Triggs, “Histograms of Oriented Gradients for Human Detection”
. In Proceedings of the IEEE Conference
on Computer Vision and Pattern Recognition, SanDiego, USA, June 2005. Vol. II, pp. 886

893.
Paisitkriangkrai, S.
,
Shen, C.
and
Zhang, J.
“Performance evaluation of local features in human classification and detection”, IET
Computer Vision, vol.2, issue 4, pp.236

246,December 2008
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