Cauchy robust loss function. More...

#include <rrel_cauchy_obj.h>

Inheritance diagram for rrel_cauchy_obj:

Public Types
typedef vcl_vector< double > ::const_iterator	vect_const_iter
	The iterators used to pass in values.
typedef vcl_vector< double > ::iterator	vect_iter
	The iterators used to pass out values.
Public Member Functions
	rrel_cauchy_obj (double C)
	Constructor.
virtual	~rrel_cauchy_obj ()
	Destructor.
virtual double	rho (double u) const
	The robust loss function for the M-estimator.
virtual double	rho (double r, double s) const
	The robust loss function for the M-estimator.
virtual double	wgt (double u) const
	The weight of the residual.
virtual void	wgt (vect_const_iter res_begin, vect_const_iter res_end, vect_const_iter scale_begin, vect_iter wgt_begin) const
	Evaluate the objective function on heteroscedastic residuals.
virtual void	wgt (vect_const_iter begin, vect_const_iter end, double scale, vect_iter wgt_begin) const
	Computes the weights for homoscedastic residuals.
virtual double	wgt (double r, double s) const
	The weight of the residual.
double	wgt_fast (double u) const
	Fast version of the wgt(u) computation.
double	rho_fast (double u) const
	Fast version of the rho(u) computation.
virtual double	fcn (vect_const_iter res_begin, vect_const_iter res_end, vect_const_iter scale_begin, vnl_vector< double > *=0) const
	Evaluate the objective function on heteroscedastic residuals.
virtual double	fcn (vect_const_iter begin, vect_const_iter end, double scale, vnl_vector< double > *=0) const
	Evaluate the objective function on homoscedastic residuals.
virtual bool	requires_prior_scale () const
	False.
virtual bool	can_estimate_scale () const
	True if the objective function can estimate scale.
virtual double	scale (vect_const_iter, vect_const_iter) const
	Scale estimate.
Private Attributes
double	C_

Detailed Description

Cauchy robust loss function.

The objective function for the Cauchy M-estimator is

$\rho(u) = 0.5 \log\bigl( 1 + \frac{u^2}{c^2} \bigr),$

The associated weight function is

$w(u) = \frac{1}{1 + \frac{u^2}{c^2} },$

where u is a scale-normalized residual ( $r/\sigma$ ) and $c$ is a tuning constant. This should be used when a more gradual rejection of outliers is desired than something like the Beaton-Tukey biweight.

Definition at line 26 of file rrel_cauchy_obj.h.

Member Typedef Documentation

typedef vcl_vector<double>::const_iterator rrel_objective::vect_const_iter [inherited]

The iterators used to pass in values.

Since we don't allow member templates, we have to fix on a particular type of container for residuals. Using this typedef will allow things to easily change when member templates are allowed.

Definition at line 27 of file rrel_objective.h.

typedef vcl_vector<double>::iterator rrel_objective::vect_iter [inherited]

The iterators used to pass out values.

Definition at line 30 of file rrel_objective.h.

Constructor & Destructor Documentation

rrel_cauchy_obj::rrel_cauchy_obj ( double C )

Constructor.

Definition at line 9 of file rrel_cauchy_obj.cxx.

rrel_cauchy_obj::~rrel_cauchy_obj ( ) [virtual]

Destructor.

Definition at line 15 of file rrel_cauchy_obj.cxx.

Member Function Documentation

virtual bool rrel_objective::can_estimate_scale ( ) const [inline, virtual, inherited]

True if the objective function can estimate scale.

Some objective functions, such as MUSE, can provide an accurate inlier scale estimate.

Reimplemented in rrel_muset_obj, and rrel_lms_obj.

Definition at line 72 of file rrel_objective.h.

double rrel_m_est_obj::fcn	(	vect_const_iter	res_begin,
		vect_const_iter	res_end,
		vect_const_iter	scale_begin,
		vnl_vector< double > *	= `0`
	)		const `[virtual, inherited]`

Evaluate the objective function on heteroscedastic residuals.

See also:: rrel_objective::fcn.

Implements rrel_objective.

Definition at line 5 of file rrel_m_est_obj.cxx.

double rrel_m_est_obj::fcn	(	vect_const_iter	begin,
		vect_const_iter	end,
		double	scale,
		vnl_vector< double > *	= `0`
	)		const `[virtual, inherited]`

Evaluate the objective function on homoscedastic residuals.

See also:: rrel_objective::fcn.

Implements rrel_objective.

Definition at line 19 of file rrel_m_est_obj.cxx.

virtual bool rrel_m_est_obj::requires_prior_scale ( ) const [inline, virtual, inherited]

False.

In general, most M-estimators work quite well with an estimated scale. The scale estimate should be robust, but not necessarily efficient (e.g. MAD scale estimate.)

Implements rrel_objective.

Definition at line 73 of file rrel_m_est_obj.h.

double rrel_cauchy_obj::rho ( double u ) const [virtual]

The robust loss function for the M-estimator.

Implements rrel_m_est_obj.

Definition at line 21 of file rrel_cauchy_obj.cxx.

virtual double rrel_cauchy_obj::rho	(	double	r,
		double	s
	)		const `[inline, virtual]`

The robust loss function for the M-estimator.

Overriding the overloaded version rho(u) hides the superclass' implementation of this version of rho(). This implementation simply calls the superclass' version of the same routine. r is the residual and s is the scale for that residual.

Reimplemented from rrel_m_est_obj.

Definition at line 44 of file rrel_cauchy_obj.h.

double rrel_cauchy_obj::rho_fast ( double u ) const [inline]

Fast version of the rho(u) computation.

Definition at line 91 of file rrel_cauchy_obj.h.

virtual double rrel_objective::scale	(	vect_const_iter	,
		vect_const_iter
	)		const `[inline, virtual, inherited]`

Scale estimate.

The result is undefined if can_estimate_scale() is false.

Reimplemented in rrel_muset_obj, and rrel_lms_obj.

Definition at line 76 of file rrel_objective.h.

double rrel_cauchy_obj::wgt ( double u ) const [virtual]

The weight of the residual.

Implements rrel_m_est_obj.

Definition at line 27 of file rrel_cauchy_obj.cxx.

virtual void rrel_cauchy_obj::wgt	(	vect_const_iter	res_begin,
		vect_const_iter	res_end,
		vect_const_iter	scale_begin,
		vect_iter	wgt_begin
	)		const `[inline, virtual]`

Evaluate the objective function on heteroscedastic residuals.

Overriding the overloaded version wgt(u) hides the superclass' implementation of this version of wgt(). This implementation simply calls the superclass' version of the same routine.

See also:: rrel_wls_obj::wgt()

Reimplemented from rrel_m_est_obj.

Definition at line 55 of file rrel_cauchy_obj.h.

virtual void rrel_cauchy_obj::wgt	(	vect_const_iter	begin,
		vect_const_iter	end,
		double	scale,
		vect_iter	wgt_begin
	)		const `[inline, virtual]`

Computes the weights for homoscedastic residuals.

Overriding the overloaded version wgt(u) hides the superclass' implementation of this version of wgt(). This implementation simply calls the superclass' version of the same routine.

See also:: rrel_wls_obj::wgt()

Reimplemented from rrel_m_est_obj.

Definition at line 65 of file rrel_cauchy_obj.h.

virtual double rrel_cauchy_obj::wgt	(	double	r,
		double	s
	)		const `[inline, virtual]`

The weight of the residual.

Overriding the overloaded version wgt(u) hides the superclass' implementation of this version of wgt(). This implementation simply calls the superclass' version of the same routine. r is the residual and s is the scale for that residual.

Reimplemented from rrel_m_est_obj.

Definition at line 76 of file rrel_cauchy_obj.h.

double rrel_cauchy_obj::wgt_fast ( double u ) const [inline]

Fast version of the wgt(u) computation.

Definition at line 97 of file rrel_cauchy_obj.h.

Member Data Documentation

double rrel_cauchy_obj::C_ [private]

Definition at line 87 of file rrel_cauchy_obj.h.

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

contrib/rpl/rrel/rrel_cauchy_obj.h
contrib/rpl/rrel/rrel_cauchy_obj.cxx

Public Types

Public Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation