Arak::ArakPosteriorGaussianObs Class Reference

#include <point_obs.hpp>

Inheritance diagram for Arak::ArakPosteriorGaussianObs:

[legend]Collaboration diagram for Arak::ArakPosteriorGaussianObs:

[legend]List of all members.

Detailed Description

An posterior Arak process conditioned on color measurements with Gaussian noise.

The posterior potential is given by

$F(\chi) = F_{\textit{prior}}(\chi) + \sum_{i = 1}^n (\mu_{\chi(t_i)} - y_i)^2 / 2\sigma_{\chi(t_i)}^2$

where $t_i$ is the location of a test point, $\chi(t_i)$ is its true color, $y_i$ is the observed value, and $\mu_c$ and $\sigma_c^2$ are the conditional mean and variance of the observation given the true color is $c$ .

This potential is additively decomposable so the posterior Arak process has the spatial Markov property.

Definition at line 110 of file point_obs.hpp.

Public Member Functions

ArakPosteriorGaussianObs (const ArakProcess &prior, const Arak::Util::PropertyMap &props)

Stream constructor.

virtual ~ArakPosteriorGaussianObs ()

Destructor.

virtual double scale () const

Returns the scale of this Arak process.

virtual double logMeasure () const

Computes the (log) measure associated with the Arak process for the coloring.

virtual double potential () const

Computes the potential associated with this posterior Arak process.

virtual void visualize (CGAL::Qt_widget &widget) const

Renders a graphical representation of this Arak posterior using the supplied widget.

Protected Attributes

const ArakProcess & prior

The prior process.

std::vector< Geometry::Point > points

A vector of points for which observations are available.

std::vector< double > obs

A vector of the observations for each point.

std::vector< QueryPointPotential * > potentials

A vector of potentials, one per observation.

double whiteMean

The mean color observation for a white point.

double blackMean

The mean color observation for a black point.

double whiteVar

The variance of observations of white points.

double blackVar

The variance of observations of black points.

double lp

The current potential arising from observations.

Constructor & Destructor Documentation

ArakPosteriorGaussianObs::ArakPosteriorGaussianObs ( const ArakProcess & prior,

const Arak::Util::PropertyMap & props

)

Stream constructor.
The parameters of the posterior are read from a file with the following format:

* n * point-1-x point-1-y point-1-obs * point-2-x point-2-y point-2-obs * ... * point-n-x point-n-y point-n-obs *

Parameters:

c The coloring whose probability is evaluated. This is fixed for each process object so that likelihood changes due to coloring updates can be processed efficiently.

props the properties that define the posterior

Definition at line 9 of file point_obs.cpp.
References Arak::Coloring::addQueryPoints(), blackMean, blackVar, lp, obs, Arak::Geometry::Point, points, potentials, prior, Arak::Util::PropertyMap, whiteMean, and whiteVar.

ArakPosteriorGaussianObs::~ArakPosteriorGaussianObs ( ) [virtual]

Destructor.

Definition at line 56 of file point_obs.cpp.
References potentials.

Member Function Documentation

double ArakPosteriorGaussianObs::logMeasure ( ) const [virtual]

Computes the (log) measure associated with the Arak process for the coloring.
(This is actually multiplied by an elementary Poisson measure over the vertex locations to yield the coloring measure.)

Returns:
the measure of the coloring

Implements Arak::ArakProcess.
Definition at line 48 of file point_obs.cpp.
References Arak::ArakProcess::logMeasure(), and prior.

double ArakPosteriorGaussianObs::potential ( ) const [virtual]

Computes the potential associated with this posterior Arak process.

Returns:
the current potential

See also:
ArakProcess

Implements Arak::ArakProcess.
Definition at line 52 of file point_obs.cpp.
References lp, Arak::ArakProcess::potential(), and prior.

virtual double Arak::ArakPosteriorGaussianObs::scale ( ) const [inline, virtual]

Returns the scale of this Arak process.

Implements Arak::ArakProcess.
Definition at line 191 of file point_obs.hpp.
References prior, and Arak::ArakProcess::scale().

void ArakPosteriorGaussianObs::visualize ( CGAL::Qt_widget & widget ) const [virtual]

Renders a graphical representation of this Arak posterior using the supplied widget.
The Gaussian observations are rendered as disks of varying gray level.

Parameters:

widget the widget on which to visualize the process

Reimplemented from Arak::ArakProcess.
Definition at line 61 of file point_obs.cpp.
References blackMean, blackVar, obs, points, whiteMean, and whiteVar.

Member Data Documentation

double Arak::ArakPosteriorGaussianObs::blackMean [protected]

The mean color observation for a black point.

Definition at line 143 of file point_obs.hpp.
Referenced by ArakPosteriorGaussianObs(), and visualize().

double Arak::ArakPosteriorGaussianObs::blackVar [protected]

The variance of observations of black points.

Definition at line 153 of file point_obs.hpp.
Referenced by ArakPosteriorGaussianObs(), and visualize().

double Arak::ArakPosteriorGaussianObs::lp [protected]

The current potential arising from observations.

Definition at line 158 of file point_obs.hpp.
Referenced by ArakPosteriorGaussianObs(), and potential().

std::vector<double> Arak::ArakPosteriorGaussianObs::obs [protected]

A vector of the observations for each point.
The indices used in points index into this vector.
Definition at line 128 of file point_obs.hpp.
Referenced by ArakPosteriorGaussianObs(), and visualize().

std::vector<Geometry::Point> Arak::ArakPosteriorGaussianObs::points [protected]

A vector of points for which observations are available.

Definition at line 122 of file point_obs.hpp.
Referenced by ArakPosteriorGaussianObs(), and visualize().

std::vector<QueryPointPotential*> Arak::ArakPosteriorGaussianObs::potentials [protected]

A vector of potentials, one per observation.

Definition at line 133 of file point_obs.hpp.
Referenced by ArakPosteriorGaussianObs(), and ~ArakPosteriorGaussianObs().

const ArakProcess& Arak::ArakPosteriorGaussianObs::prior [protected]

The prior process.

Definition at line 117 of file point_obs.hpp.
Referenced by logMeasure(), potential(), and scale().

double Arak::ArakPosteriorGaussianObs::whiteMean [protected]

The mean color observation for a white point.

Definition at line 138 of file point_obs.hpp.
Referenced by ArakPosteriorGaussianObs(), and visualize().

double Arak::ArakPosteriorGaussianObs::whiteVar [protected]

The variance of observations of white points.

Definition at line 148 of file point_obs.hpp.
Referenced by ArakPosteriorGaussianObs(), and visualize().

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

Generated on Wed May 25 14:41:26 2005 for Arak by

1.3.6


Public Member Functions
	ArakPosteriorGaussianObs (const ArakProcess &prior, const Arak::Util::PropertyMap &props)
	Stream constructor.
virtual	~ArakPosteriorGaussianObs ()
	Destructor.
virtual double	scale () const
	Returns the scale of this Arak process.
virtual double	logMeasure () const
	Computes the (log) measure associated with the Arak process for the coloring.
virtual double	potential () const
	Computes the potential associated with this posterior Arak process.
virtual void	visualize (CGAL::Qt_widget &widget) const
	Renders a graphical representation of this Arak posterior using the supplied widget.
Protected Attributes
const ArakProcess &	prior
	The prior process.
std::vector< Geometry::Point >	points
	A vector of points for which observations are available.
std::vector< double >	obs
	A vector of the observations for each point.
std::vector< QueryPointPotential * >	potentials
	A vector of potentials, one per observation.
double	whiteMean
	The mean color observation for a white point.
double	blackMean
	The mean color observation for a black point.
double	whiteVar
	The variance of observations of white points.
double	blackVar
	The variance of observations of black points.
double	lp
	The current potential arising from observations.