Robust%20Moving%20Least-squares%20Fitting%20with%20Sharp%20Features

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Robust Moving Least-squares Fitting with Sharp
Features

• Shachar Fleishman
• Daniel Cohen-Or
• Claudio T. Silva

University of Utah Tel-Aviv
university
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Surface reconstruction

• Noise
• Smooth surface
• Smooth sharp features
• Method for identifying and reconstructing sharp
  features

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Point set surfaces (Levin 98)

• Defines a smooth surface using a projection
  operator

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Point set surfaces

• Defines a smooth surface using a projection
  operator
• Noisy point set
• The surface S is defined

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The MLS projection overview

• Find a point q on the surfaces whose normal goes
  through the projected point x
• q is the projection of x

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The MLS projection overview

• Find a point q on the surfaces whose normal goes
  through the projected point x
• q is the projection of x
• Improve approximation order using polynomial fit

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Sharp features

• Smoothed out
• Ambiguous

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Sharp features

• Smoothed out
• Ambiguous
• Classify

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Projection near sharp feature
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Projection near sharp feature
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Projection near sharp feature
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Classification

• Using outlier identification algorithm
• That fits a polynomial patch to a neighborhood

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Classification

• Using outlier identification algorithm
• That fits a polynomial patch to a neighborhood

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Statistics 101

• Find the center of a set of points

mean
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Statistics 101

• Find the center of a set of points
• Robustly using median

median
mean
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Regression with backward search

• Loop
• Fit a model
• Remove point withmaximal residual
• Until no more outliers

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Regression with backward search

• Outliers can have a significant influence of the
  fitted model

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Regression with forward search (Atkinson and
Riani)

• Start with an initial good but crude surface
• LMS (least median of squares)
• Incrementally improve the fit
• Monitor the search

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Monitoring the forward search
Residual plot
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Monitoring the forward search
Residual plot
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Results
Polynomial fit allows reconstruction of curved
edges
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Results
Noisy input
Reconstructed
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Results
Outliers are ignored
Misaligned regions are determined to be two
regions
Local decision may cause inconsistencies
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Summary

• Classification of noisy point sets to smooth
  regions
• Application to PSS
• Reconstruct surfaces with sharp features from
  noisy data
• Improve the stability of the projection
• Local decisions may result different
  neighborhoods for adjacent points
• Can be applied to other surface reconstruction
  methods such as the MPU

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Acknowledgements

• Department of Energy under the VIEWS program and
  the MICS office
• The National Science Foundation under grants
  CCF-0401498, EIA-0323604, and OISE-0405402
• A University of Utah Seed Grant
• The Israel Science Foundation (founded by the
  Israel Academy of Sciences and Humanities), and
  the Israeli Ministry of Science