Cao Mengfei

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Cluster Spectrum
Correspondence

• Cao Mengfei
• 2009.7

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?.Warm-ups
?. abstract
?. a special example and its counterpart
?. extension
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Warm-ups

• Recognition based on feature
• but what if what you get
  is not what you really want?
• Semantic Analysis various methods however it
  will be great when something happens like this

• Hierarchical Semantics of Objects
• ----ICCV2005

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About Correspondence Matching(1)

• Related saying
• "????????????????????????,?????????????????????,?
  Sanjay Ranade????????Shih-hsu Chang???????????????
  Zsolt Miklós???????????Xudong Jiang??9??????????
  ?????." ???------???????????????????
• My feeling
• search for the pairwise through similarities of
  objective-data

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About Correspondence Matching(2)

• according to the ways of making use of the
  similarites

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i
i
?
?.
j
j
calculation

Compare the Similarity (i-i),(i-j),(j-i),(j-j
)
i
i
?.
accuracy
j
j
Compare Consistency (i-j) v.s. (i-j)
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issues to be taken into accounts

• (1) to find out the outliers in the first set
• (2) to find out the outliers in the second set
• robust to the outliers
• (3)to find out all the correct correspondent
  pairwises.
• robust to the noise
• Affine transformation, translation,
  scalar transformation
• illumination, rotation, diversity

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About spectral method

• Spectrum of Matrix Magical Mathematical
  Object-properties, instead of pure Consciousness.
  
• objective, descriptive, essential
• Based on eigen values eigen vectors.
• Related saying
• music is dynamic, while score is static
• movement is dynamic, while law is static

Model the reality
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Advantages
Based on math and reality
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About clustering

• Basic problem in the field of pattern recognition
• Various methods used in various situations
• after all, to cluster is to aggregate the
  objects with similar properties
• how to combine it to the former issues?

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A Spectral Technique for Correspondence Problems
Using Pairwise Constraints

• Marius Leordeanu and Martial Hebert
  International Conference of Computer Vision
  (ICCV), October, 2005

Professor
Efficient techniques for object/category
recognition
PhD Student, RI
Use of contextual information, in particular 3-D
geometry from images, for scene analysis
Vision and Autonomous Systems Center (VASC)
The Robotics Institute
Detection, tracking, and prediction in dynamic
environments
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A Spectral Technique for Correspondence
Problems Using Pairwise Constraints
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i
i
?
?.
j
j
calculation

Compare the Similarity (i-i),(i-j),(j-i),(j-j
)
i
i
?.
accuracy
j
j
Compare Consistency (i-j) v.s. (i-j)
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A Spectral Technique for Correspondence
Problems Using Pairwise Constraints
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Fundamental thoughts
main clusters
the graph associated with matrix M
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linprog-based method
CVPR  
Matrix H represents the cost matrix of the
individual correspondence (the factor ), vector x
represent the corresponding indicatory
correspondence. Anyway, xHx stands for the
correspondence-cost thus the thing is that , as
for the value, the smaller, the better, which
comes to the problem of Integer Quadratic
Programming--NP-complete thus
linear I.P.
University of California, Berkeley  
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Comparison (1)
?. Whats special? Compared to the former
occlusion and clutter
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Comparison (2)

• ?. Emulation
• 1. deformations using white noise

Ratio of time 4 1
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Comparison (3)

• 2. considering the scalar and translation
• theoretically,translation invariant is necessary
• As for the scalar transformation
• Spectral

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Comparison (4) translation
Left spectral right linprog
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Comparison (5) scale
Upper spectral down linprog
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Comparison (6)

• 3. robust to the outliers

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More experiments
our method is orders of magnitude faster then
linprog over 400 times faster on 20 points
problem sets (average time of 0.03 sec. vs 13
sec) and over 650 faster on 30 points problem
sets (0.25 sec. vs 165 sec.), on a 2.4 GHz
Pentium computer
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Comparison (7)

• ?. Practice

Spectral Clustering Based
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Comparison (8)
Linprog-based recognition
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Extension
?.
Providing the semantic layout of the scene,
learnt hSOs can have several useful applications
such as compact scene representation for scene
category classification and providing context
for enhanced object detection
?.
Recognizing objects from low resolution images
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Extension(2)
Combined with direction Affine transform
?.
?.
What tools to use, how to use(spectral clustering)
i
k
i
k
j
j
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Thanks a lot ...