Kernel Density objective function. More...

#include <rrel_kernel_density_obj.h>

Inheritance diagram for rrel_kernel_density_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_kernel_density_obj (rrel_kernel_scale_type scale_type=RREL_KERNEL_MAD)
	Constructor.
virtual	~rrel_kernel_density_obj ()
	Destructor.
virtual double	fcn (vect_const_iter res_begin, vect_const_iter res_end, vect_const_iter scale_begin, vnl_vector< double > *param_vector=0) const
	Evaluate the objective function on heteroscedastic residuals.
virtual double	fcn (vect_const_iter res_begin, vect_const_iter res_end, double prior_scale=0, vnl_vector< double > *=0) const
	Evaluate the objective function on homoscedastic residuals.
virtual void	set_scale_type (rrel_kernel_scale_type t=RREL_KERNEL_MAD)
	Set the type of the scale.
virtual bool	requires_prior_scale () const
	Depends on the scale type used.
void	fix_x ()
	x is set to 0;.
double	best_x (vect_const_iter res_begin, vect_const_iter res_end, double scale=0) const
	The mode of the density estimate which maximizes the estimated kernel density.
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 Member Functions
double	bandwidth (vect_const_iter res_begin, vect_const_iter res_end, double prior_scale) const
	Calculate the bandwidth.
double	kernel_density (vect_const_iter res_begin, vect_const_iter res_end, double x, double h) const
	Given a kernel and the bandwidth, the estimated density of residuals.
double	kernel_function (double u) const
	Kernel function K(u).
Private Attributes
rrel_kernel_scale_type	scale_type_
bool	fix_x_

Detailed Description

Kernel Density objective function.

Implements the Kernel Density Estimation as presented in the paper "Robust Computer Vision through Kernel Density" by Chen and Meer, 2002. Given residuals ri, i = 1,...,n, the cost function is the estimated density f(x) based on a kernel function K(u) and a bandwidth h as f(x) = -1 / (nh) * sum( K(u) ) where u = (ri-x)/h K(u) = 1.09375 * (1 - u^2)^3 h = [243 * R(K) / 35 / Mu(K)^2 / n]^0.2 * scale The scale can be provided as a prior scale, or computed by MAD or MUSE.

Definition at line 27 of file rrel_kernel_density_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_kernel_density_obj::rrel_kernel_density_obj ( rrel_kernel_scale_type scale_type = RREL_KERNEL_MAD )

Constructor.

Definition at line 25 of file rrel_kernel_density_obj.cxx.

virtual rrel_kernel_density_obj::~rrel_kernel_density_obj ( ) [inline, virtual]

Destructor.

Definition at line 34 of file rrel_kernel_density_obj.h.

Member Function Documentation

double rrel_kernel_density_obj::bandwidth	(	vect_const_iter	res_begin,
		vect_const_iter	res_end,
		double	prior_scale
	)		const `[private]`

Calculate the bandwidth.

Definition at line 117 of file rrel_kernel_density_obj.cxx.

double rrel_kernel_density_obj::best_x	(	vect_const_iter	res_begin,
		vect_const_iter	res_end,
		double	scale = `0`
	)		const

The mode of the density estimate which maximizes the estimated kernel density.

The value can be used to shift the estimated parameters.

Definition at line 54 of file rrel_kernel_density_obj.cxx.

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

Evaluate the objective function on heteroscedastic residuals.

Not implemented.

See also:: rrel_objective::fcn.

Implements rrel_objective.

Definition at line 32 of file rrel_kernel_density_obj.cxx.

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

Evaluate the objective function on homoscedastic residuals.

prior_scale is needed if the type RREL_KERNEL_PRIOR is used.

See also:: rrel_objective::fcn.

Implements rrel_objective.

Definition at line 41 of file rrel_kernel_density_obj.cxx.

void rrel_kernel_density_obj::fix_x ( ) [inline]

x is set to 0;.

Definition at line 63 of file rrel_kernel_density_obj.h.

double rrel_kernel_density_obj::kernel_density	(	vect_const_iter	res_begin,
		vect_const_iter	res_end,
		double	x,
		double	h
	)		const `[private]`

Given a kernel and the bandwidth, the estimated density of residuals.

Definition at line 169 of file rrel_kernel_density_obj.cxx.

double rrel_kernel_density_obj::kernel_function ( double u ) const [private]

Kernel function K(u).

Definition at line 184 of file rrel_kernel_density_obj.cxx.

virtual bool rrel_kernel_density_obj::requires_prior_scale ( ) const [inline, virtual]

Depends on the scale type used.

See also:: rrel_objective::requires_prior_scale.

Implements rrel_objective.

Definition at line 59 of file rrel_kernel_density_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.

virtual void rrel_kernel_density_obj::set_scale_type ( rrel_kernel_scale_type t = RREL_KERNEL_MAD ) [inline, virtual]

Set the type of the scale.

RREL_KERNEL_MAD uses median absolute deviations to estimate the scale. RREL_KERNEL_PRIOR uses the prior scale provided. RREL_KERNEL_MUSE uses MUSE to estimate the scale.

Definition at line 54 of file rrel_kernel_density_obj.h.

Member Data Documentation

bool rrel_kernel_density_obj::fix_x_ [private]

Definition at line 84 of file rrel_kernel_density_obj.h.

rrel_kernel_scale_type rrel_kernel_density_obj::scale_type_ [private]

Definition at line 82 of file rrel_kernel_density_obj.h.

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

contrib/rpl/rrel/rrel_kernel_density_obj.h
contrib/rpl/rrel/rrel_kernel_density_obj.cxx

Public Types

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation