How Well can Wavelet Denoising Improve the Accuracy of Computing Fundamental Matrices

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How Well can Wavelet Denoising Improve the
Accuracy of Computing Fundamental Matrices?
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Outline

• Motivation
• Fundamental matrix
• Wavelet denoising
• Experiments
• Conclusions and future work

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Motivation

• Fundamental matrix computation
• Importance
• Obtain motion parameters if the intrinsic camera
  parameters are known
• Reduce search space from 2D to 1D in image-based
  3D reconstruction
• Sensitivity It is sensitive to image noise
• Different applications of denoising
• Image processing To get visually good appearance
• Computer vision To improve the performance of
  algorithms
• Gaussian smoothing vs. Wavelet denoising
• Gaussian Difficult decision in the length of
  Gaussian filter
• Wavelet Much easier

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Questions

• What wavelet is good in computing of fundamental
  matrices?
• What kind of images could wavelets be applied to
  improve accuracy of their fundamental matrices?

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Fundamental Matrix

• A basic property

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Fundamental Matrix

• Residue

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Wavelet Denoising waveShrink

• Shrinkage function on wavelet coefficients
• Minimax threshold

Threshold
Mean
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High Frequency vs. Low Frequency
Row 20th
High-frequency region
Low-frequency region
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Denoising High-Frequency Data
The structure of data is changed after denoising
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Denoising Low-Frequency Data
The structure of data is preserved after denoising
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Experiments

• Different supports of wavelets
• Different stereo images
• Santa images
• CMU stereo images

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Santa Images
View 1
View 2
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Residues via different supports
The trend of residues goes down when the support
increases
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More Santa Images
Non-capped Santa View 1-3
Capped Santa View 1-3
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Residues on Santa Images
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CMU Stereo Images- Part 1
arch
book
books
cart
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CMU Stereo Images Part 1 (cont.)
mars
lab
pepsi
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Residues on CMU Stereo Images Part 1
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CMU Stereo Images Part 2
apple
pentagon
fruit
sandwich
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Residues on CMU Stereo Images Part 2
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Conclusions and Future Work

• Conclusions
• Wavelet of long support is preferred
• If a pair of stereo images contain no region of
  extremely high frequency, wavelet denoising tends
  to improve the accuracy of their fundamental
  matrix
• Future work
• Measure via reprojection error