1 robust estimation techniques in real-time robot vision ezio malis, eric marchand inria sophia,...

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Robust estimation techniques in real-time robot vision

Ezio Malis, Eric Marchand

INRIA Sophia, projet ICARE

INRIA Rennes, projet Lagadic

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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

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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 case20% 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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Weights in IRLS

Threshold c is given by:

with the scale computed using the MAD

This cost function is not differentiable

Tukey M-estimators

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


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 outliers: m=5 samples, p = 95%

• 40% of outliers: m=13 samples, p = 95%

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Robust tracking

Homography estimation

Robust version of the ESM

algorithm [Benhimane-Malis 04]

Uses M-estimators

QuickTime™ et undécompresseur codec YUV420

sont requis pour visionner cette image.



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 tracking algorithms

Classical 2 1/2 D control law

Contour-based tracking[Comport IROS’04]

Hybrid Contour/texture tracking[Pressigout ICRA’06]





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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

QuickTime™ et undécompresseur


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Classical tracking algorithms

Robust control laws [Comport, ITRO’06] 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

1 robust estimation techniques in real-time robot vision ezio malis, eric marchand inria sophia,...

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