gtsam::noiseModel::mEstimator::L2WithDeadZone Class Reference

Detailed Description

L2WithDeadZone implements a standard L2 penalty, but with a dead zone of width 2*k, centered at the origin.

The resulting penalty within the dead zone is always zero, and grows quadratically outside the dead zone. In this sense, the L2WithDeadZone penalty is "robust to inliers", rather than being robust to outliers. This penalty can be used to create barrier functions in a general way.

This model has a scalar parameter "k".

• Loss \rho(x) = 0 if |x|<k, 0.5(k-|x|)² otherwise
• Derivative \phi(x) = 0 if |x|<k, (-k+x) if x>k, (k+x) if x<-k
• Weight w(x) = \phi(x)/x = 0 if |x|<k, (-k+x)/x if x>k, (k+x)/x if x<-k

Inheritance diagram for gtsam::noiseModel::mEstimator::L2WithDeadZone:

Public Member Functions
	L2WithDeadZone (double k=1.0, const ReweightScheme reweight=Block)
double	weight (double distance) const override
	This method is responsible for returning the weight function for a given amount of error.
double	loss (double distance) const override
	This method is responsible for returning the total penalty for a given amount of error.
void	print (const std::string &s) const override
bool	equals (const Base &expected, double tol=1e-8) const override
double	modelParameter () const
Public Member Functions inherited from gtsam::noiseModel::mEstimator::Base
	Base (const ReweightScheme reweight=Block)
ReweightScheme	reweightScheme () const
	Returns the reweight scheme, as explained in ReweightScheme.
double	sqrtWeight (double distance) const
Vector	weight (const Vector &error) const
	produce a weight vector according to an error vector and the implemented robust function
Vector	sqrtWeight (const Vector &error) const
	square root version of the weight function
void	reweight (Vector &error) const
	reweight block matrices and a vector according to their weight implementation
void	reweight (std::vector< Matrix > &A, Vector &error) const
void	reweight (Matrix &A, Vector &error) const
void	reweight (Matrix &A1, Matrix &A2, Vector &error) const
void	reweight (Matrix &A1, Matrix &A2, Matrix &A3, Vector &error) const

Static Public Member Functions
static shared_ptr	Create (double k, const ReweightScheme reweight=Block)

Public Types
typedef boost::shared_ptr< L2WithDeadZone >	shared_ptr
Public Types inherited from gtsam::noiseModel::mEstimator::Base
enum	ReweightScheme { Scalar , Block }
	the rows can be weighted independently according to the error or uniformly with the norm of the right hand side
typedef boost::shared_ptr< Base >	shared_ptr

Protected Attributes
double	k_
Protected Attributes inherited from gtsam::noiseModel::mEstimator::Base
ReweightScheme	reweight_
	Strategy for reweighting.

Friends
class	boost::serialization::access
	Serialization function.

Member Function Documentation

equals()

bool gtsam::noiseModel::mEstimator::L2WithDeadZone::equals ( const Base & expected, double tol = 1e-8 ) const

overridevirtual

Implements gtsam::noiseModel::mEstimator::Base.

loss()

double gtsam::noiseModel::mEstimator::L2WithDeadZone::loss ( double distance ) const

overridevirtual

This method is responsible for returning the total penalty for a given amount of error.

For example, this method is responsible for implementing the quadratic function for an L2 penalty, the absolute value function for an L1 penalty, etc.

TODO(mikebosse): When the loss function has as input the norm of the error vector, then it prevents implementations of asymmeric loss functions. It would be better for this function to accept the vector and internally call the norm if necessary.

This returns \rho(x) in mEstimator

Reimplemented from gtsam::noiseModel::mEstimator::Base.

print()

void gtsam::noiseModel::mEstimator::L2WithDeadZone::print ( const std::string & s = "" ) const

overridevirtual

Implements gtsam::noiseModel::mEstimator::Base.

weight()

double gtsam::noiseModel::mEstimator::L2WithDeadZone::weight ( double distance ) const

overridevirtual

This method is responsible for returning the weight function for a given amount of error.

The weight function is related to the analytic derivative of the loss function. See https://members.loria.fr/MOBerger/Enseignement/Master2/Documents/ZhangIVC-97-01.pdf for details. This method is required when optimizing cost functions with robust penalties using iteratively re-weighted least squares.

This returns w(x) in mEstimator

Implements gtsam::noiseModel::mEstimator::Base.

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

• /tmp/gtsam-4.2-docs.H5EUbA/src/gtsam/linear/LossFunctions.h
• /tmp/gtsam-4.2-docs.H5EUbA/src/gtsam/linear/LossFunctions.cpp