Robust estimation techniques in realtime robot vision

1
Robust estimation techniques in real-time robot
vision

• Ezio Malis, Eric Marchand
• INRIA Sophia, projet ICARE
• INRIA Rennes, projet Lagadic

2
Overview

• Introduction
• Robust estimation methods
• M-estimators
• LMS and LTS
• Robust voting methods
• Hough transform
• RANSAC (Random Sample Consensus)
• Application to robotic vision
• Object tracking
• Visual servoing

3
Introduction

• Goal estimation of a set x of parameters from
• n signals measurements
• A model of these signals
• Let us define the residual
• In the ideal case we have to solve
• Unfortunately, in the general case
• Measurements are not exact
• Models do not correspond to reality

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Definitions

• Outlier
• An outlier is an aberrant measure
• Robustness of the estimation
• An estimation algorithm is said to be robust if
  its properties are maintained despite the
  presence of outliers
• Breakdown point
• This the minimum percentage of outliers which
  make the algorithm diverge

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Case study

• Estimation of the displacement between two views
• Knowing

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Least of squares

• We look for the solution of
• Where the cost function is defined by
• The optimization is performed iteratively from x0
• The solution is optimal if measurement noise is
  Gaussian

Ideal case 20 of outliers
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M-estimators
Huber81

• The cost function is modified such that
• Various choice for ?
• Large errors are penalized
• Usually require the computation of a threshold
• Efficient implementation using IRLS (Iteratively
  Reweighted Least Squares)
• Correct minimum is usually found,
• Theoretical breakdown point is still 0

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Tukey M-estimators

• Weights in IRLS
• Threshold c is given by
• with the scale computed using the MAD
• This cost function is not differentiable

with
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Tukey M-estimator Case study

• 20 of outlier 40 of outliers
• The minimum is correctly locate but
• New local minima appears
• The cost function is not differentiable

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Least Median of Squares Rousseeuw87

• Minimize the following cost function
• Cost function usually not differentiable
• High theoretical breakdown point 50
• Highly expensive minimization

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Least Median of Squares Case study

• 20 of outlier 40 of outliers
• New local minima appears
• Outliers are suppressed, along with inliers

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Hough transform

• Several alternative have been proposed
• General overview
• Discretization of the parameters space
  (hypercubes in the space state)
• Accumulators are associated with these hypercubes
• Estimate x from a minimal set of measures
• Each estimation is a vote
• Accumulator with the most significant value
• gives the best estimate
• Main issues
• How to discretize ?
• Search space increases exponentially with
• the number of parameters
• Very robust

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RANSAC (Random Sample Consensus) Fischler 81

• Minimize the following cost function
• with the threshold c computed using the MAD
• This is a non exhaustive voting method (only m
  random samples)
• For each sample
• Estimate using a minimal sample set
• Compute

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RANSAC Case study

• 20 of outlier 40 of outliers
• 20 of outliers m5 samples, p 95
• 40 of outliers m13 samples, p 95

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Robust tracking

• Homography estimation
• Robust version of the ESM
• algorithm Benhimane-Malis 04
• Uses M-estimators

Image EAVR - LSIIT - ULP Strasbourg
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Robust visual servoing

• Visual servoing
• Control a dynamic system degrees of freedom in
  order to reach a desired position specified in an
  image
• Robust visual servoing
• Ensure the task despite the presence of aberrant
  data (outliers)
• Various approaches
• Robust image processing algorithms
• Robust control laws

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Robust visual servoing

• Robust tracking algorithms
• Classical 2 1/2 D control law
• Contour-based tracking
• Comport IROS04
• Hybrid Contour/texture tracking
• Pressigout ICRA06

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Robust visual servoing

• Robust tracking algorithms
• Classical 2 1/2 D control law
• Tracking by matching
• Keypoint recognition using randomized tree
• Homography estimation
• RANSAC outlier rejection
• Tran 06
• Handle large (complete) occlusions

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Robust visual servoing

• Classical tracking algorithms
• Robust control laws Comport, ITRO06 based on
  M-Estimators
• No robust
  Robust

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Conclusions

• Short review of robust estimation methods
• Robustness is necessary to handle robotic task in
  real environment
• A trade-off has to be find between
• Efficiency
• Robustness
• Voting techniques (Hough, RANSAC) along with LMS,
  LTS are
• very robust although very expensive
• M-estimation is a very good trade-off