This class implements robust estimator functions. More...

#include <Estimator.h>

Public Types
enum	EstimatorType : uint32_t { ET_INVALID = 0u , ET_SQUARE , ET_LINEAR , ET_HUBER , ET_TUKEY , ET_CAUCHY }
	Definition of individual robust estimator types. More...

using	EstimatorTypes = std::vector< EstimatorType >
	Definition of a vector holding estimator types.

Static Public Member Functions
template<EstimatorType tEstimator>
static constexpr bool	needSigma ()
	Returns whether an estimator needs a standard deviation for computation.

template<EstimatorType tEstimator>
static constexpr bool	isStandardEstimator ()
	Returns whether an estimator is the standard square error estimator.

static bool	isStandardEstimator (const EstimatorType estimator)
	Returns whether an estimator is the standard square error estimator.

static bool	needSigma (const EstimatorType estimator)
	Returns whether a given estimator needs a standard deviation for computation.

template<EstimatorType tEstimator>
static Scalar	robustError (const Scalar value, const Scalar sigma=0)
	Returns the robust error of a residual error for a specified estimator.

static Scalar	robustError (const Scalar value, const Scalar sigma, const EstimatorType estimator)
	Returns the robust error of a given residual error for a specified estimator.

template<EstimatorType tEstimator>
static Scalar	robustErrorSquare (const Scalar sqrValue, const Scalar sqrSigma=0)
	Returns the robust error of a squared residual error for a specified estimator.

static Scalar	robustErrorSquare (const Scalar sqrValue, const Scalar sqrSigma, const EstimatorType estimator)
	Returns the robust error of a given squared residual error for a specified estimator.

template<EstimatorType tEstimator>
static Scalar	robustWeight (const Scalar value, const Scalar sigma=0)
	Returns the weight in relation to a error for a given residual error and a specified estimator.

static Scalar	robustWeight (const Scalar value, const Scalar sigma, const EstimatorType estimator)
	Returns the weight in relation to a error for a given residual error and a specified estimator.

template<EstimatorType tEstimator>
static Scalar	robustWeightSquare (const Scalar sqrValue, const Scalar sqrSigma=0)
	Returns the weight in relation to a squared error for a given residual error and a specified estimator.

static Scalar	robustWeightSquare (const Scalar sqrValue, const Scalar sqrSigma, const EstimatorType estimator)
	Returns the weight in relation to a squared error for a given residual error and a specified estimator.

template<EstimatorType tEstimator>
static Scalar	determineSigma (const Scalar *errors, const size_t number, const size_t modelParameters)
	Determines the sigma for a specific set of residual errors and a specified estimator.

static Scalar	determineSigma (const Scalar *errors, const size_t number, const size_t modelParameters, const EstimatorType estimator)
	Determines the sigma for a specific set of residual errors and a specified estimator.

template<EstimatorType tEstimator>
static Scalar	determineSigma (const Scalar errors, const unsigned int indices, const size_t numberIndices, const size_t modelParameters)
	Determines the sigma for a specific subset of residual errors and a specified estimator.

static Scalar	determineSigma (const Scalar errors, const unsigned int indices, const size_t numberIndices, const size_t modelParameters, const EstimatorType estimator)
	Determines the sigma for a specific subset of residual errors and a specified estimator.

template<EstimatorType tEstimator>
static Scalar	determineSigmaSquare (const Scalar *sqrErrors, const size_t number, const size_t modelParameters)
	Determines the squared sigma for a specific set of squared residual errors and a specified estimator.

static Scalar	determineSigmaSquare (const Scalar *sqrErrors, const size_t number, const size_t modelParameters, const EstimatorType estimator)
	Determines the squared sigma for a specific set of squared residual errors and a specified estimator.

template<EstimatorType tEstimator>
static Scalar	determineSigmaSquare (const Scalar sqrErrors, const unsigned int indices, const size_t numberIndices, const size_t modelParameters)
	Determines the squared sigma for a specific set of squared residual errors and a specified estimator.

static Scalar	determineSigmaSquare (const Scalar sqrErrors, const unsigned int indices, const size_t numberIndices, const size_t modelParameters, const EstimatorType estimator)
	Determines the squared sigma for a specific set of squared residual errors and a specified estimator.

template<Estimator::EstimatorType tEstimator>
static Scalar	determineRobustError (const Scalar *sqrErrors, const size_t number, const size_t modelParameters)
	Determines the overall robust error for set of given squared errors, a specified estimator and the dimension of the model.

static constexpr Scalar	maximalWeight ()
	Returns the maximal weight for any estimator which is used to clamp extremely high weights (for tiny errors).

static constexpr Scalar	invMaximalWeight ()
	Returns the inverse maximal weight for any estimator which is used to clamp extremely high weights (for tiny errors).

static std::string	translateEstimatorType (const EstimatorType estimatorType)
	Translates a given estimator type into a readable string.

static EstimatorType	translateEstimatorType (const std::string &estimatorType)
	Translates a readable name of an estimator type to it's value.

static const EstimatorTypes &	estimatorTypes ()
	Returns all existing valid estimator types.

Static Protected Member Functions
template<EstimatorType tEstimator>
static Scalar	sigmaTuningConstant ()
	Returns the tuning constant allowing to determine a 95 percent efficiency on the standard normal distribution for individual estimators.

Detailed Description

This class implements robust estimator functions.

See 'Parameter Estimation Techniques: A Tutorial with Application to Conic Fitting', Zhengyou Zhang, 1997 for detailed information.

Member Typedef Documentation

◆ EstimatorTypes

using Ocean::Geometry::Estimator::EstimatorTypes = std::vector<EstimatorType>

Definition of a vector holding estimator types.

Member Enumeration Documentation

◆ EstimatorType

enum Ocean::Geometry::Estimator::EstimatorType : uint32_t

Definition of individual robust estimator types.

Enumerator
ET_INVALID	An invalid estimator type.
ET_SQUARE	The standard square error estimator (L2). The estimation function is defined by: p(x) = x^2 / 2 The weighting function is given by: w(x) = 1
ET_LINEAR	The linear estimator (L1). The estimation function is defined by: p(x) = \|x\| The weighting function is given by: w(x) = 1 / \|x\|
ET_HUBER	The Huber estimator type. The estimation function is defined by: p(x, s) = x^2 / 2, if \|x\| <= s = s * (\|x\| - s / 2), else The weighting function is given by: w(x, s) = 1, if \|x\| <= s = s / \|x\|, else The sigma tuning constant is given as: 1.345
ET_TUKEY	The Tukey estimator. The estimation function is defined by: p(x, s) = s^2 / 6 * (1 - (1 - (x / s)^2)^3), if \|x\| <= s = s^2 / 6, else The weighting function is given by: w(x, s) = (1 - (x / s)^2)^2, if \|x\| <= s = 0, else The sigma tuning constant is given as: 4.6851
ET_CAUCHY	The Cauchy estimator. The estimation function is defined by: p(x, s) = s^2 / 2 * log(1 + (x / s)^2) The weighting function is defined by: w(x, s) = 1 / (1 + (x / s)^2) The sigma tuning constant is given as: 2.3849

Member Function Documentation

◆ determineRobustError()

template<Estimator::EstimatorType tEstimator>

Scalar Ocean::Geometry::Estimator::determineRobustError	(	const Scalar *	sqrErrors,
		const size_t	number,
		const size_t	modelParameters
	)

inlinestatic

Determines the overall robust error for set of given squared errors, a specified estimator and the dimension of the model.

Parameters

sqrErrors	The squared error values for which the overall robust error will be determined
number	The number of provided squared error values, with range [1, infinity)
modelParameters	Number of parameters that define the model that has to be optimized (the dimension of the model), with range [1, infinity)

Returns: Resulting overall robust error for the given set of squared errors

Template Parameters

tEstimator Robust error estimator to be used

◆ determineSigma() [1/4]

template<Estimator::EstimatorType tEstimator>

Scalar Ocean::Geometry::Estimator::determineSigma	(	const Scalar *	errors,
		const size_t	number,
		const size_t	modelParameters
	)

inlinestatic

Determines the sigma for a specific set of residual errors and a specified estimator.

Parameters

errors	Residual errors for that the corresponding sigma has to be determined
number	The number of provided residual errors, with range [1, infinity)
modelParameters	Number of the parameter that define the model

Returns: Resulting sigma

Template Parameters

tEstimator Type of the estimator to use

◆ determineSigma() [2/4]

Scalar Ocean::Geometry::Estimator::determineSigma	(	const Scalar *	errors,
		const size_t	number,
		const size_t	modelParameters,
		const EstimatorType	estimator
	)

inlinestatic

Determines the sigma for a specific set of residual errors and a specified estimator.

Parameters

errors	Residual errors for that the corresponding sigma has to be determined
number	The number of provided residual errors, with range [1, infinity)
modelParameters	Number of the parameter that define the model
estimator	Type of the estimator to use

Returns: Resulting sigma

◆ determineSigma() [3/4]

template<Estimator::EstimatorType tEstimator>

Scalar Ocean::Geometry::Estimator::determineSigma	(	const Scalar *	errors,
		const unsigned int *	indices,
		const size_t	numberIndices,
		const size_t	modelParameters
	)

inlinestatic

Determines the sigma for a specific subset of residual errors and a specified estimator.

Parameters

errors	Residual errors for that the corresponding sigma has to be determined
indices	Indices of the subset of the residual errors, beware: no range check is applied
numberIndices	Number of provided indices, with range [1, infinity)
modelParameters	Number of the parameter that define the model, with range [1, infinity)

Returns: Resulting sigma

Template Parameters

tEstimator Type of the estimator to use

◆ determineSigma() [4/4]

Scalar Ocean::Geometry::Estimator::determineSigma	(	const Scalar *	errors,
		const unsigned int *	indices,
		const size_t	numberIndices,
		const size_t	modelParameters,
		const EstimatorType	estimator
	)

inlinestatic

Determines the sigma for a specific subset of residual errors and a specified estimator.

Parameters

errors	Residual errors for that the corresponding sigma has to be determined
indices	Indices of the subset of the residual errors, beware: no range check is applied
numberIndices	Number of provided indices, with range [1, infinity)
modelParameters	Number of the parameter that define the model
estimator	Type of the estimator to use

Returns: Resulting sigma

◆ determineSigmaSquare() [1/4]

template<Estimator::EstimatorType tEstimator>

Scalar Ocean::Geometry::Estimator::determineSigmaSquare	(	const Scalar *	sqrErrors,
		const size_t	number,
		const size_t	modelParameters
	)

inlinestatic

Determines the squared sigma for a specific set of squared residual errors and a specified estimator.

Parameters

sqrErrors	Squared residual errors for that the corresponding sigma has to be determined
number	The number of provided residual errors, with range [1, infinity)
modelParameters	Number of the parameter that define the model

Returns: Resulting sigma (not the squared sigma)

Template Parameters

tEstimator Type of the estimator to use

◆ determineSigmaSquare() [2/4]

Scalar Ocean::Geometry::Estimator::determineSigmaSquare	(	const Scalar *	sqrErrors,
		const size_t	number,
		const size_t	modelParameters,
		const EstimatorType	estimator
	)

inlinestatic

Determines the squared sigma for a specific set of squared residual errors and a specified estimator.

Parameters

sqrErrors	Squared residual errors for that the corresponding sigma has to be determined
number	The number of provided residual errors, with range [1, infinity)
modelParameters	Number of the parameter that define the model
estimator	Type of the estimator to use

Returns: Resulting sigma (not the squared sigma)

◆ determineSigmaSquare() [3/4]

template<Estimator::EstimatorType tEstimator>

Scalar Ocean::Geometry::Estimator::determineSigmaSquare	(	const Scalar *	sqrErrors,
		const unsigned int *	indices,
		const size_t	numberIndices,
		const size_t	modelParameters
	)

inlinestatic

Determines the squared sigma for a specific set of squared residual errors and a specified estimator.

Parameters

sqrErrors	Squared residual errors for that the corresponding sigma has to be determined
indices	Indices of the subset of the residual errors, beware: no range check is applied
numberIndices	Number of provided indices, with range [1, infinity)
modelParameters	Number of the parameter that define the model

Returns: Resulting sigma (not the squared sigma)

Template Parameters

tEstimator Type of the estimator to use

◆ determineSigmaSquare() [4/4]

Scalar Ocean::Geometry::Estimator::determineSigmaSquare	(	const Scalar *	sqrErrors,
		const unsigned int *	indices,
		const size_t	numberIndices,
		const size_t	modelParameters,
		const EstimatorType	estimator
	)

inlinestatic

Determines the squared sigma for a specific set of squared residual errors and a specified estimator.

Parameters

sqrErrors	Squared residual errors for that the corresponding sigma has to be determined
indices	Indices of the subset of the residual errors, beware: no range check is applied
numberIndices	Number of provided indices, with range [1, infinity)
modelParameters	Number of the parameter that define the model
estimator	Type of the estimator to use

Returns: Resulting sigma (not the squared sigma)

◆ estimatorTypes()

static const EstimatorTypes & Ocean::Geometry::Estimator::estimatorTypes ( )

static

Returns all existing valid estimator types.

Returns: The valid estimator types

◆ invMaximalWeight()

constexpr Scalar Ocean::Geometry::Estimator::invMaximalWeight ( )

staticconstexpr

Returns the inverse maximal weight for any estimator which is used to clamp extremely high weights (for tiny errors).

Returns: Returns 1 / maximalWeight()

◆ isStandardEstimator() [1/2]

template<Estimator::EstimatorType tEstimator>

constexpr bool Ocean::Geometry::Estimator::isStandardEstimator ( )

staticconstexpr

Returns whether an estimator is the standard square error estimator.

Returns: True, if so

Template Parameters

tEstimator Estimator to check

◆ isStandardEstimator() [2/2]

bool Ocean::Geometry::Estimator::isStandardEstimator ( const EstimatorType estimator )

inlinestatic

Returns whether an estimator is the standard square error estimator.

Parameters

estimator The estimator to check

Returns: True, if so

◆ maximalWeight()

constexpr Scalar Ocean::Geometry::Estimator::maximalWeight ( )

staticconstexpr

Returns the maximal weight for any estimator which is used to clamp extremely high weights (for tiny errors).

Returns: The maximal weight to be applied

◆ needSigma() [1/2]

template<Estimator::EstimatorType tEstimator>

constexpr bool Ocean::Geometry::Estimator::needSigma ( )

staticconstexpr

Returns whether an estimator needs a standard deviation for computation.

Template Parameters

tEstimator Estimator for that the dependency is requested

Returns: True, if so

◆ needSigma() [2/2]

bool Ocean::Geometry::Estimator::needSigma ( const EstimatorType estimator )

inlinestatic

Returns whether a given estimator needs a standard deviation for computation.

Parameters

estimator The estimator for that the dependency is requested

Returns: True, if so

◆ robustError() [1/2]

Scalar Ocean::Geometry::Estimator::robustError	(	const Scalar	value,
		const Scalar	sigma,
		const EstimatorType	estimator
	)

inlinestatic

Returns the robust error of a given residual error for a specified estimator.

Parameters

value	The residual error to return the robust error for, with range (-infinity, infinity)
sigma	The standard deviation of the expected residual error, with range (0, infinity) if 'needSigma(estimator) == true', otherwise 0
estimator	The type of the estimator to use

Returns: The resulting robust error, with range [0, infinity)

See also: needSigma().

◆ robustError() [2/2]

template<Estimator::EstimatorType tEstimator>

Scalar Ocean::Geometry::Estimator::robustError	(	const Scalar	value,
		const Scalar	sigma = `0`
	)

inlinestatic

Returns the robust error of a residual error for a specified estimator.

Parameters

value	The residual error to return the robust error for, with range (-infinity, infinity)
sigma	The standard deviation of the expected residual error, with range (0, infinity) if 'needSigma<tEstimator>() == true', otherwise 0

Returns: The resulting robust error, with range [0, infinity)

Template Parameters

tEstimator Type of the estimator to use

See also: needSigma().

◆ robustErrorSquare() [1/2]

Scalar Ocean::Geometry::Estimator::robustErrorSquare	(	const Scalar	sqrValue,
		const Scalar	sqrSigma,
		const EstimatorType	estimator
	)

inlinestatic

Returns the robust error of a given squared residual error for a specified estimator.

Parameters

sqrValue	The squared residual error to return the robust error for, with range [0, infinity)
sqrSigma	The squared standard deviation (the variance) of the expected residual error, with range (0, infinity) if 'needSigma(estimator) == true', otherwise 0
estimator	Type of the estimator to use

Returns: The resulting robust error, with range [0, infinity)

See also: needSigma().

◆ robustErrorSquare() [2/2]

template<Estimator::EstimatorType tEstimator>

Scalar Ocean::Geometry::Estimator::robustErrorSquare	(	const Scalar	sqrValue,
		const Scalar	sqrSigma = `0`
	)

inlinestatic

Returns the robust error of a squared residual error for a specified estimator.

Parameters

sqrValue	The squared residual error to return the robust error for, with range [0, infinity)
sqrSigma	The squared standard deviation (the variance) of the expected residual error, with range (0, infinity) if 'needSigma<tEstimator>() == true', otherwise 0

Returns: The resulting robust error, with range [0, infinity)

Template Parameters

tEstimator Type of the estimator to use

See also: needSigma().

◆ robustWeight() [1/2]

Scalar Ocean::Geometry::Estimator::robustWeight	(	const Scalar	value,
		const Scalar	sigma,
		const EstimatorType	estimator
	)

inlinestatic

Returns the weight in relation to a error for a given residual error and a specified estimator.

Parameters

value	The residual error to return the weight for
sigma	The standard deviation of the expected residual error
estimator	Type of the estimator to use

Returns: Resulting weight

◆ robustWeight() [2/2]

template<Estimator::EstimatorType tEstimator>

Scalar Ocean::Geometry::Estimator::robustWeight	(	const Scalar	value,
		const Scalar	sigma = `0`
	)

inlinestatic

Returns the weight in relation to a error for a given residual error and a specified estimator.

Parameters

value	The residual error to return the weight for
sigma	The standard deviation of the expected residual error, beware: provide a valid standard deviation if necessary with range (0, infinity)

Returns: Resulting weight

Template Parameters

tEstimator Type of the estimator to use

◆ robustWeightSquare() [1/2]

Scalar Ocean::Geometry::Estimator::robustWeightSquare	(	const Scalar	sqrValue,
		const Scalar	sqrSigma,
		const EstimatorType	estimator
	)

inlinestatic

Returns the weight in relation to a squared error for a given residual error and a specified estimator.

Parameters

sqrValue	The squared residual error to return the weight for
sqrSigma	The squared standard deviation (the variance) of the expected residual error
estimator	Type of the estimator to use

Returns: Resulting weight (not the squared result), with range [0, infinity)

◆ robustWeightSquare() [2/2]

template<Estimator::EstimatorType tEstimator>

Scalar Ocean::Geometry::Estimator::robustWeightSquare	(	const Scalar	sqrValue,
		const Scalar	sqrSigma = `0`
	)

inlinestatic

Returns the weight in relation to a squared error for a given residual error and a specified estimator.

Parameters

sqrValue	The squared residual error to return the weight for
sqrSigma	The squared standard deviation (the variance) of the expected residual error, beware: provide a valid standard deviation if necessary with range (0, infinity)

Returns: Resulting weight (not the squared result), with range [0, infinity)

Template Parameters

tEstimator Type of the estimator to use

◆ sigmaTuningConstant()

template<Estimator::EstimatorType tEstimator>

Scalar Ocean::Geometry::Estimator::sigmaTuningConstant ( )

inlinestaticprotected

Returns the tuning constant allowing to determine a 95 percent efficiency on the standard normal distribution for individual estimators.

Returns: Tuning constant

◆ translateEstimatorType() [1/2]

static std::string Ocean::Geometry::Estimator::translateEstimatorType ( const EstimatorType estimatorType )

static

Translates a given estimator type into a readable string.

Parameters

estimatorType The type of the estimator to translate

Returns: The readable string, 'Invalid' if unknown

◆ translateEstimatorType() [2/2]

static EstimatorType Ocean::Geometry::Estimator::translateEstimatorType ( const std::string & estimatorType )

static

Translates a readable name of an estimator type to it's value.

Parameters

estimatorType The name of the estimator type for which the value will be returned

Returns: The estimator type, ET_INVALID if invalid

The documentation for this class was generated from the following file:

Estimator.h

Public Types

Static Public Member Functions

Static Protected Member Functions

Detailed Description

Member Typedef Documentation

◆ EstimatorTypes

Member Enumeration Documentation

◆ EstimatorType

Member Function Documentation

◆ determineRobustError()

◆ determineSigma() [1/4]

◆ determineSigma() [2/4]

◆ determineSigma() [3/4]

◆ determineSigma() [4/4]

◆ determineSigmaSquare() [1/4]

◆ determineSigmaSquare() [2/4]

◆ determineSigmaSquare() [3/4]

◆ determineSigmaSquare() [4/4]

◆ estimatorTypes()

◆ invMaximalWeight()

◆ isStandardEstimator() [1/2]

◆ isStandardEstimator() [2/2]

◆ maximalWeight()

◆ needSigma() [1/2]

◆ needSigma() [2/2]

◆ robustError() [1/2]

◆ robustError() [2/2]

◆ robustErrorSquare() [1/2]

◆ robustErrorSquare() [2/2]

◆ robustWeight() [1/2]

◆ robustWeight() [2/2]

◆ robustWeightSquare() [1/2]

◆ robustWeightSquare() [2/2]

◆ sigmaTuningConstant()

◆ translateEstimatorType() [1/2]

◆ translateEstimatorType() [2/2]