F03181 - PowerPoint PPT Presentation

Title: F03181


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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

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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

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Object tracking purpose

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

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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

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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

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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

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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

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

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

u2
u1
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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

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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
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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.

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Similarity measure

• Local feature similarity
• Global feature similarity
• Overall similarity

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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
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2-D golden section algorithm
Golden section point
Largest golden section point
Old searching region
New searching region
y
x
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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.

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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.

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Tracking result (1)
0th frame
100th frame
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Tracking result (2)
0th frame
100th frame
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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