#include <vpRobust.h>

Public Types
enum	vpRobustEstimatorType { TUKEY, CAUCHY, HUBER }

Public Member Functions
	vpRobust ()

	vpRobust (const vpRobust &other)

virtual	~vpRobust ()

double	getMedianAbsoluteDeviation ()

double	getMinMedianAbsoluteDeviation ()

void	MEstimator (const vpRobustEstimatorType method, const vpColVector &residues, vpColVector &weights)

vpRobust &	operator= (const vpRobust &other)

vpRobust &	operator= (const vpRobust &&other)

void	setMinMedianAbsoluteDeviation (double mad_min)

Deprecated functions
vp_deprecated	vpRobust (unsigned int n_data)

void	MEstimator (const vpRobustEstimatorType method, const vpColVector &residues, const vpColVector &all_residues, vpColVector &weights)

vp_deprecated void	setIteration (unsigned int iter)

vp_deprecated void	setThreshold (double mad_min)

vp_deprecated vpColVector	simultMEstimator (vpColVector &residues)

Detailed Description

Contains an M-estimator and various influence function.

This class implements an M-estimator with Tukey, Cauchy or Huber influence function [8] which allow uncertain measures to be less likely considered and in some cases completely rejected, thus inferring that the data is not normally distributed.

When using a robust estimate of the mean, it is usual to normalize the distribution to center the data around zero. In the case of a median operator, the normalized residue is given by:

$\overline{r_i} = r_i - {Med}(r_i)$ where ${Med}(r_i)$ is the median value of the residue vector $r$ .

The Median Absolute Deviation (MAD) representing one standard deviation of the normal distribution is given by:

$\sigma = 1.48 \; {Med}(|\overline{r_i}|)$

This class allows to set the minimum value of $\sigma$ using setMinMedianAbsoluteDeviation().

This estimated standard deviation $\sigma$ can accordingly be used with a tuning variable for different influence functions.

Let us consider the weight function $w(r)$ with $r$ the residual vector of the parameters to estimate.

Using Huber influence function, with a constant such as $a=1.21 \; \sigma$ we have
$w(r_i) = \left\{ \begin{array}{ll} 1 & \mbox{if } |r_i| \leq a \\ \frac{a}{|r_i|} & \mbox{else} \end{array} \right.$
Using Tukey influence function, with a constant such as $b=4.68 \; \sigma$ we have
$w(r_i) = \left\{ \begin{array}{ll} {\left(1 - {\left(\frac{r_i}{b}\right)}^2 \right)}^2 & \mbox{if } |r_i| \leq b \\ 0 & \mbox{else} \end{array} \right.$
Using Cauchy influence function, with a constant such as $c=2.38 \; \sigma$ we have
$w(r_i) = \frac{1}{(1 + {(r_i/c)}^2)}$

Given the influence function and the residual vector, the weights are updated in MEstimator().

Examples:: testTukeyEstimator.cpp.

Definition at line 88 of file vpRobust.h.

Member Enumeration Documentation

enum vpRobust::vpRobustEstimatorType

Enumeration of influence functions.

Enumerator
TUKEY	Tukey influence function.
CAUCHY	Cauchy influence function.
HUBER	Huber influence function.

Definition at line 92 of file vpRobust.h.

Constructor & Destructor Documentation

vpRobust::vpRobust ( )

Default constructor.

Definition at line 59 of file vpRobust.cpp.

vpRobust::vpRobust ( const vpRobust & other )

Copy constructor.

Definition at line 71 of file vpRobust.cpp.

virtual vpRobust::~vpRobust ( )

inlinevirtual

Destructor.

Definition at line 124 of file vpRobust.h.

vpRobust::vpRobust ( unsigned int n_data )

explicit

Deprecated:: You should rather use the default constructor.

Parameters

n_data : Size of the data vector.

Definition at line 312 of file vpRobust.cpp.

References vpColVector::resize(), and vpCDEBUG.

Member Function Documentation

double vpRobust::getMedianAbsoluteDeviation ( )

inline

Return residual vector Median Absolute Deviation (MAD). This value is updated after a call to MEstimator(). It corresponds to value of $\sigma = 1.48{Med}(|r_i - {Med}(r_i)|)$ . This value cannot be lower than the min value returned by getMinMedianAbsoluteDeviation() or set with setMinMedianAbsoluteDeviation().

See also: setMinMedianAbsoluteDeviation()

Definition at line 135 of file vpRobust.h.

double vpRobust::getMinMedianAbsoluteDeviation ( )

inline

Return the min value used to threshold residual vector Median Absolute Deviation (MAD). This value corresponds to the mimimal value of $\sigma$ computed in MEstimator().

See also: setMinMedianAbsoluteDeviation()

Definition at line 143 of file vpRobust.h.

void vpRobust::MEstimator	(	const vpRobustEstimatorType	method,
		const vpColVector &	residues,
		vpColVector &	weights
	)

Calculate an M-estimate given a particular influence function using MAD (Median Absolute Deviation) as a scale estimate at each iteration.

Parameters

[in]	method	: Type of influence function.
[in]	residues	: Vector of residues of the parameters to estimate.
[out]	weights	: Vector of weights . Values are in [0, 1]. A value near zero means that the data is an outlier.

Examples:: testTukeyEstimator.cpp.

Definition at line 137 of file vpRobust.cpp.

References CAUCHY, vpArray2D< Type >::getRows(), HUBER, vpColVector::resize(), vpMath::sqr(), and TUKEY.

Referenced by vpPoseFeatures::computePose(), vpMbEdgeKltTracker::computeVVS(), vpMbEdgeTracker::computeVVSWeights(), vpMbTracker::computeVVSWeights(), vpMeLine::leastSquare(), vpMeEllipse::leastSquareRobust(), vpPose::poseVirtualVSrobust(), and vpHomography::robust().

void vpRobust::MEstimator	(	const vpRobustEstimatorType	method,
		const vpColVector &	residues,
		const vpColVector &	all_residues,
		vpColVector &	weights
	)

Compute the weights according a residue vector and a PsiFunction.

Definition at line 327 of file vpRobust.cpp.

References CAUCHY, vpArray2D< Type >::data, vpArray2D< Type >::getRows(), HUBER, vpColVector::resize(), TUKEY, and vpCDEBUG.

vpRobust & vpRobust::operator= ( const vpRobust & other )

Copy operator.

Definition at line 76 of file vpRobust.cpp.

vpRobust & vpRobust::operator= ( const vpRobust && other )

Move operator.

Definition at line 95 of file vpRobust.cpp.

References vpColVector::resize().

vp_deprecated void vpRobust::setIteration ( unsigned int iter )

inline

Deprecated:: Set iteration. This function is to call before simultMEstimator().

Parameters

iter	: The first call iter should be set to 0.

Definition at line 176 of file vpRobust.h.

void vpRobust::setMinMedianAbsoluteDeviation ( double mad_min )

inline

Set minimal median absolute deviation (MAD) value corresponding to the mimimal value of $\sigma$ computed in MEstimator() with $\sigma = 1.48{Med}(|r_i - {Med}(r_i)|)$ .

Parameters

mad_min : Minimal Median Absolute Deviation value. Default value is set to 0.0017 in the default constructor.

See also: getMinMedianAbsoluteDeviation()

Examples:: testTukeyEstimator.cpp.

Definition at line 161 of file vpRobust.h.

Referenced by vpPoseFeatures::computePose(), vpMbEdgeKltTracker::computeVVS(), vpMbDepthNormalTracker::computeVVSInit(), vpMbKltTracker::computeVVSInit(), vpMbEdgeTracker::computeVVSInit(), vpMeLine::leastSquare(), vpMeEllipse::leastSquareRobust(), and vpPose::poseVirtualVSrobust().

vp_deprecated void vpRobust::setThreshold ( double mad_min )

inline

Deprecated:: You should rather use setMinMedianAbsoluteDeviation(). Set minimal median absolute deviation (MAD) value. Given the input vector or residual, when MAD(residual) < mad_min we set MAD(residual) = mad_min.

Parameters

mad_min : Minimal Median Absolute Deviation value. Default value is set to 0.0017 in the default constructor.

Definition at line 185 of file vpRobust.h.

vpColVector vpRobust::simultMEstimator ( vpColVector & residues )

Deprecated:: This function is useless. Calculate an Mestimate with a simultaneous scale estimate using HUBER's influence function

Parameters

[in] residues : Vector of residues. The content of the vector is changed.

Returns: Returns a vector of weights associated to each residue.

Definition at line 421 of file vpRobust.cpp.

References CAUCHY, vpArray2D< Type >::getRows(), HUBER, vpMath::sqr(), and TUKEY.

Public Types

Public Member Functions

Detailed Description

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation