F03181

1
Object Tracking Using the Gabor Wavelet Transform
and the Golden Section Algorithm
Chao He, Jianyu Dong, Yuan F. Zheng, and Stanley
C. Ahalt

• Department of Electrical Engineering
• The Ohio State University
• Columbus OH 43210 USA
• hec,zheng_at_ee.eng.ohio-state.edu
• Corresponding Author

2
Outlines

• Related work
• Object tracking using local intensity and mesh
• Object recognition using Gabor wavelets and grid
• Our approach
• Combine Gabor wavelets and mesh
• Stochastic feature point selection
• Affine-invariant mesh representation
• 2-D golden section searching algorithm
• Experiment result
• Summary

3
Object tracking purpose

• Track the visual objects in computer vision or
  consecutive video frames

4
Object tracking applications

• Object tracking is very important in many
  applications
• Assembly automation
• Mobile robot navigation
• Automatic target recognition and tracking
• Content-based video compression and editing

5
Related work (1) mesh tracking

• Object is represented by a triangular mesh
• Mesh node is the local maximum of intensity
  gradient
• Each node of the mesh is tracked by traditional
  motion estimation methods
• Mesh can be used to keep the object structure

6
Related work (2) object recognition

• Gabor wavelet coefficient represents the local
  feature of each grid node
• Elastic grid represents the structural
  information
• Simulated annealing algorithm is used to
  recognize the object by maximizing the local
  feature similarity and minimizing the grid
  deformation simultaneously

7
Our approach

• Combine the mesh and the Gabor wavelet
• Gabor wavelet represents the local feature
• Mesh represents the global (structure) feature
• An innovative stochastic feature point selection
  scheme
• An affine-invariant mesh representation method
• A fast 2-D golden section searching algorithm

8
System structure
Object
Gabor wavelet transform
Feature points selection
Local feature
Global feature
Golden section searching
next frame
Refinement
9
Gabor wavelets as local features

• Gabor function
• Gabor wavelet
• Scaling and rotating
• Local feature

u2
u1
10
Feature points selection (1)

• Feature point is stochastically selected based on
  Gabor energy. Points with higher energy are more
  likely to be selected. As a result, significant
  region has more feature points.
• Gabor energy computation

11
Feature points selection (2)

• E(x,y) - Gabor energy
• R(x,y) - Gaussian random variable
• Er(x,y) E(x,y) R(x,y)
• Er(x,y) gt T as feature points

40
35
30
25
20
15
10
5
0
0
20
40
60
80
100
120
140
12
Mesh representation as global feature

• Use a vector of the areas of the triangles to
  represent the global feature.

a0
a1
a2
Global feature G a0 a1 a2 a3 a4 a5 a6 a7
a4
a3
a5
a0
a7
a6

• The global feature vectors direction is
  invariant to affine transform.

13
Similarity measure

• Local feature similarity
• Global feature similarity
• Overall similarity

14
1-D Golden section algorithm

• Fibonacci numbers
• F0 F1 1, F2 F1 F0,, Fk Fk-1 Fk-2
• Golden section algorithm is the fastest algorithm
  to find the maximum of a unimodal function.

f(x)
Golden section point
Largest golden section point
Old searching region
New searching region
x
Fk-2/ Fk
1
Fk-1/ Fk
0
15
2-D golden section algorithm
Golden section point
Largest golden section point
Old searching region
New searching region
y
x
16
Similarity function

• Put the mesh to the next frame and move around.
  The similarity function is unimodal. Therefore,
  the golden-section algorithm can be applied to
  track the position of the object.

17
Refinement

• Golden-section tracks the position of the object.
• Object deformation is tracked by moving each mesh
  node in a local region to find its best matching
  position.

18
Tracking result (1)
0th frame
100th frame
19
Tracking result (2)
0th frame
100th frame
20
Summary
The new tracking algorithm has the following
features

• Combination of the mesh and the Gabor wavelet to
  represent an object
• Efficient feature point selection
• Affine-invariant mesh representation
• Fast golden section searching

Experimental results prove that the new algorithm
is effective