A kernel filter implementing a discrete Moffat distribution in two dimensions. More...

#include <MoffatFilter.h>

Inheritance diagram for pcl::MoffatFilter:

Public Member Functions
	MoffatFilter ()=default

	MoffatFilter (const MoffatFilter &)=default

	MoffatFilter (float sigma, float beta, float epsilon, float rho, float theta=0, const String &name=String())

	MoffatFilter (float sigma, float beta=4, float epsilon=0.01, const String &name=String())

	MoffatFilter (int n, float beta, float epsilon, float rho, float theta=0, const String &name=String())

	MoffatFilter (int n, float beta=4, float epsilon=0.01, const String &name=String())

	MoffatFilter (MoffatFilter &&)=default

float	AspectRatio () const

SeparableFilter	AsSeparableFilter (float tolerance=__PCL_DEFAULT_FILTER_SEPARABILITY_TOLERANCE) const override

float	Beta () const

KernelFilter *	Clone () const override

double	FWHM () const

double	FWHMx () const

double	FWHMy () const

bool	IsSeparable () const override

MoffatFilter &	operator= (const MoffatFilter &)=default

MoffatFilter &	operator= (MoffatFilter &&)=default

void	Resize (int n) override

float	RotationAngle () const

void	Set (float sigma)

void	Set (float sigma, float beta)

void	Set (float sigma, float beta, float epsilon)

void	Set (float sigma, float beta, float epsilon, float rho)

void	Set (float sigma, float beta, float epsilon, float rho, float theta)

void	SetAspectRatio (float rho)

void	SetBeta (float beta)

void	SetRotationAngle (float theta)

void	SetSigma (float sigma)

void	SetTruncation (float epsilon)

float	Sigma () const

float	SigmaX () const

float	SigmaY () const

float	Truncation () const

Public Member Functions inherited from pcl::KernelFilter
	KernelFilter (const coefficient_matrix &F, const String &name=String())

	KernelFilter (const KernelFilter &)=default

	KernelFilter (const String &name=String())

template<typename T >
	KernelFilter (const T *k, int n, const String &name=String())

	KernelFilter (int n, const String &name=String())

template<typename T >
	KernelFilter (int n, const T &x, const String &name=String())

	KernelFilter (KernelFilter &&)=default

virtual	~KernelFilter ()

const coefficient *	Begin () const

const coefficient *	begin () const

virtual void	Clear ()

coefficient_matrix	Coefficients () const

const coefficient *	End () const

const coefficient *	end () const

void	Flip ()

KernelFilter	Flipped () const

bool	IsEmpty () const

bool	IsFlipped () const

bool	IsHighPassFilter () const

double	Modulus () const

String	Name () const

void	Normalize ()

KernelFilter	Normalized () const

int	NumberOfCoefficients () const

	operator bool () const

KernelFilter &	operator= (const coefficient &x)

KernelFilter &	operator= (const coefficient_matrix &F)

KernelFilter &	operator= (const KernelFilter &)=default

KernelFilter &	operator= (KernelFilter &&)=default

bool	operator== (const KernelFilter &f) const

const coefficient *	operator[] (int row) const

virtual void	Rename (const String &newName)

bool	SameCoefficients (const KernelFilter &f) const

int	Size () const

template<class P >
void	ToImage (GenericImage< P > &image) const

void	ToImage (ImageVariant &v) const

double	Weight () const

Additional Inherited Members
Public Types inherited from pcl::KernelFilter
using	coefficient = float

using	coefficient_matrix = GenericMatrix< coefficient >

Detailed Description

A MoffatFilter object is a specialized KernelFilter whose elements are calculated as a discrete representation of an elliptical Moffat[1] function centered at the origin:

M(x,y) = 1/(1 + x^2/sx^2 + y^2/sy^2)^beta

where sx and sy are the standard deviations of the distribution on the horizontal and vertical axes, respectively, and the beta exponent controls the shape of the function's profile. The lower the beta, the more peaked the overall shape of the function. For beta=1, the equation above corresponds to a Lorentzian function.

MoffatFilter also supports arbitrary rotation around the origin. When the filter is rotated, the coordinates x, y in the equation above are replaced by their rotated counterparts.

A MoffatFilter instance is formally defined by the following parameters:

sigma	Standard deviation of the filter distribution on the X axis (sigma > 0).
rho	The ratio sy/sx (see equation above) of the generated filter distribution (0 <= rho <= 1).
theta	Rotation angle of the horizontal axis in radians (0 <= theta < PI). This parameter only makes sense when rho < 1.
beta	Exponent controlling the overall shape of the function (beta > 0).
epsilon	Maximum truncation error of the computed filter coefficients (eps > 0).

References

[1] Moffat, A. F. J., A Theoretical Investigation of Focal Stellar Images in the Photographic Emulsion and Application to Photographic Photometry, Astronomy and Astrophysics, Vol. 3, p. 455 (1969)

See also: KernelFilter, GaussianFilter, VariableShapeFilter, LinearFilter

Definition at line 105 of file MoffatFilter.h.

Constructor & Destructor Documentation

◆ MoffatFilter() [1/7]

pcl::MoffatFilter::MoffatFilter ( )

default

Constructs an empty MoffatFilter object with default functional parameters: sigma=2, beta=4, epsilon=0.01, rho=1, theta=0.

◆ MoffatFilter() [2/7]

pcl::MoffatFilter::MoffatFilter	(	float	sigma,
		float	beta = `4`,
		float	epsilon = `0.01`,
		const String &	name = `String()`
	)

inline

Constructs a MoffatFilter object given the standard deviation sigma > 0, beta exponent > 0 and truncation error epsilon > 0. Assigns an optional name to the new filter object.

Definition at line 120 of file MoffatFilter.h.

◆ MoffatFilter() [3/7]

pcl::MoffatFilter::MoffatFilter	(	float	sigma,
		float	beta,
		float	epsilon,
		float	rho,
		float	theta = `0`,
		const String &	name = `String()`
	)

inline

Constructs a MoffatFilter object given the standard deviation sigma > 0, beta exponent > 0, truncation error epsilon > 0, aspect ratio 0 <= rho <= 1, and rotation angle 0 <= theta <= PI in radians. Assigns an optional name to the new filter object.

Definition at line 132 of file MoffatFilter.h.

◆ MoffatFilter() [4/7]

pcl::MoffatFilter::MoffatFilter	(	int	n,
		float	beta = `4`,
		float	epsilon = `0.01`,
		const String &	name = `String()`
	)

inline

Constructs a MoffatFilter object given the odd kernel size n >= 3, beta exponent > 0 and truncation error epsilon > 0. Assigns an optional name to the new filter object.

Definition at line 143 of file MoffatFilter.h.

◆ MoffatFilter() [5/7]

pcl::MoffatFilter::MoffatFilter	(	int	n,
		float	beta,
		float	epsilon,
		float	rho,
		float	theta = `0`,
		const String &	name = `String()`
	)

inline

Constructs a MoffatFilter object given the odd kernel size n >= 3, beta exponent > 0, truncation error epsilon > 0, aspect ratio 0 <= rho <= 1, and rotation angle 0 <= theta <= PI in radians. Assigns an optional name to the new filter object.

Definition at line 155 of file MoffatFilter.h.

◆ MoffatFilter() [6/7]

pcl::MoffatFilter::MoffatFilter ( const MoffatFilter & )

default

Copy constructor.

◆ MoffatFilter() [7/7]

pcl::MoffatFilter::MoffatFilter ( MoffatFilter && )

default

Move constructor.

Member Function Documentation

◆ AspectRatio()

float pcl::MoffatFilter::AspectRatio ( ) const

inline

Returns the aspect ratio of the filter distribution. This is the ratio vertical:horizontal between filter axes in the range [0,1].

Definition at line 260 of file MoffatFilter.h.

◆ AsSeparableFilter()

SeparableFilter pcl::MoffatFilter::AsSeparableFilter ( float tolerance = __PCL_DEFAULT_FILTER_SEPARABILITY_TOLERANCE ) const

inlineoverridevirtual

Returns a separable filter equivalent to this kernel filter.

MoffatFilter's reimplementation of this virtual member function returns an empty SeparableFilter object, as a Moffat filter is not separable.

Reimplemented from pcl::KernelFilter.

Definition at line 184 of file MoffatFilter.h.

◆ Beta()

float pcl::MoffatFilter::Beta ( ) const

inline

Returns the beta exponent of the Moffat filter function. The beta exponent controls the overall shape of the filter profile.

Definition at line 243 of file MoffatFilter.h.

◆ Clone()

KernelFilter* pcl::MoffatFilter::Clone ( ) const

inlineoverridevirtual

Returns a pointer to a dynamically allocated duplicate of this kernel filter.

Note: All derived classes from KernelFilter must reimplement this virtual member function.

Reimplemented from pcl::KernelFilter.

Definition at line 173 of file MoffatFilter.h.

◆ FWHM()

double pcl::MoffatFilter::FWHM ( ) const

inline

Returns the full width at half maximum, in sigma units, for the horizontal axis of the elliptical Moffat filter distribution.

This function is an alias to FWHMx().

Definition at line 301 of file MoffatFilter.h.

◆ FWHMx()

double pcl::MoffatFilter::FWHMx ( ) const

inline

Returns the full width at half maximum (FWHM), in sigma units, for the horizontal axis of the elliptical Moffat filter distribution.

Definition at line 279 of file MoffatFilter.h.

References pcl::Pow2(), and pcl::Sqrt().

◆ FWHMy()

double pcl::MoffatFilter::FWHMy ( ) const

inline

Returns the full width at half maximum (FWHM), in sigma units, for the vertical axis of the elliptical Moffat filter distribution.

Definition at line 289 of file MoffatFilter.h.

◆ IsSeparable()

bool pcl::MoffatFilter::IsSeparable ( ) const

inlineoverridevirtual

Returns true iff this filter is separable.

MoffatFilter's reimplementation of this virtual member function returns false, as a Moffat filter is not separable.

Reimplemented from pcl::KernelFilter.

Definition at line 195 of file MoffatFilter.h.

◆ operator=() [1/2]

MoffatFilter& pcl::MoffatFilter::operator= ( const MoffatFilter & )

default

Copy assignment operator. Returns a reference to this object.

◆ operator=() [2/2]

MoffatFilter& pcl::MoffatFilter::operator= ( MoffatFilter && )

default

Move assignment operator. Returns a reference to this object.

◆ Resize()

void pcl::MoffatFilter::Resize ( int n )

inlineoverridevirtual

Recalculates filter coefficients for the given odd kernel size n >= 3. This routine computes the required standard deviation to sample the Moffat function on a matrix of the specified size, preserving the current beta exponent, coefficient truncation error, aspect ratio and rotation angle.

Reimplemented from pcl::KernelFilter.

Definition at line 407 of file MoffatFilter.h.

◆ RotationAngle()

float pcl::MoffatFilter::RotationAngle ( ) const

inline

Returns the rotation angle of the filter distribution. This is the rotation angle in radians with respect to the central pixel, in the range [0,+PI].

Definition at line 270 of file MoffatFilter.h.

◆ Set() [1/5]

void pcl::MoffatFilter::Set ( float sigma )

inline

Recalculates filter coefficients for the specified sigma sigma > 0. The current beta exponent, coefficient truncation error, aspect ratio and rotation angle are not changed.

Definition at line 351 of file MoffatFilter.h.

◆ Set() [2/5]

void pcl::MoffatFilter::Set	(	float	sigma,
		float	beta
	)

inline

Recalculates filter coefficients for the specified sigma sigma > 0 and beta exponent. The current coefficient truncation error, aspect ratio and rotation angle are not changed.

Definition at line 341 of file MoffatFilter.h.

◆ Set() [3/5]

void pcl::MoffatFilter::Set	(	float	sigma,
		float	beta,
		float	epsilon
	)

inline

Recalculates filter coefficients for the specified sigma sigma > 0, beta exponent and truncation error epsilon > 0. Does not change the current aspect ratio and rotation angle.

Definition at line 331 of file MoffatFilter.h.

◆ Set() [4/5]

void pcl::MoffatFilter::Set	(	float	sigma,
		float	beta,
		float	epsilon,
		float	rho
	)

inline

Recalculates filter coefficients for the specified sigma sigma > 0, beta exponent, truncation error epsilon > 0 and aspect ratio 0 <= rho <= 1. Does not change the current rotation angle.

Definition at line 321 of file MoffatFilter.h.

◆ Set() [5/5]

void pcl::MoffatFilter::Set	(	float	sigma,
		float	beta,
		float	epsilon,
		float	rho,
		float	theta
	)

inline

Recalculates filter coefficients for the specified sigma sigma > 0, beta exponent, truncation error epsilon > 0, aspect ratio 0 <= rho <= 1 and rotation angle 0 <= theta <= PI in radians.

Definition at line 311 of file MoffatFilter.h.

◆ SetAspectRatio()

void pcl::MoffatFilter::SetAspectRatio ( float rho )

inline

This is a convenience member function, equivalent to Set( Sigma(), Beta(), Truncation(), rho ).

Definition at line 386 of file MoffatFilter.h.

◆ SetBeta()

void pcl::MoffatFilter::SetBeta ( float beta )

inline

This is a convenience member function, equivalent to Set( Sigma(), beta ).

Definition at line 368 of file MoffatFilter.h.

◆ SetRotationAngle()

void pcl::MoffatFilter::SetRotationAngle ( float theta )

inline

This is a convenience member function, equivalent to Set( Sigma(), Beta(), Truncation(), AspectRatio(), a ).

Definition at line 395 of file MoffatFilter.h.

◆ SetSigma()

void pcl::MoffatFilter::SetSigma ( float sigma )

inline

This is a convenience member function, equivalent to Set( sigma ).

Definition at line 359 of file MoffatFilter.h.

◆ SetTruncation()

void pcl::MoffatFilter::SetTruncation ( float epsilon )

inline

This is a convenience member function, equivalent to Set( Sigma(), Beta(), epsilon ).

Definition at line 377 of file MoffatFilter.h.

◆ Sigma()

float pcl::MoffatFilter::Sigma ( ) const

inline

Returns the standard deviation of the filter distribution on the X (horizontal) axis.

This function is an alias to SigmaX().

Definition at line 234 of file MoffatFilter.h.

◆ SigmaX()

float pcl::MoffatFilter::SigmaX ( ) const

inline

Returns the standard deviation of the filter distribution on the X (horizontal) axis.

Definition at line 214 of file MoffatFilter.h.

◆ SigmaY()

float pcl::MoffatFilter::SigmaY ( ) const

inline

Returns the standard deviation of the filter distribution on the Y (vertical) axis.

Definition at line 223 of file MoffatFilter.h.

◆ Truncation()

float pcl::MoffatFilter::Truncation ( ) const

inline

Returns the maximum truncation error of the filter coefficients.

Definition at line 251 of file MoffatFilter.h.

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

MoffatFilter.h

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ MoffatFilter() [1/7]

◆ MoffatFilter() [2/7]

◆ MoffatFilter() [3/7]

◆ MoffatFilter() [4/7]

◆ MoffatFilter() [5/7]

◆ MoffatFilter() [6/7]

◆ MoffatFilter() [7/7]

Member Function Documentation

◆ AspectRatio()

◆ AsSeparableFilter()

◆ Beta()

◆ Clone()

◆ FWHM()

◆ FWHMx()

◆ FWHMy()

◆ IsSeparable()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ Resize()

◆ RotationAngle()

◆ Set() [1/5]

◆ Set() [2/5]

◆ Set() [3/5]

◆ Set() [4/5]

◆ Set() [5/5]

◆ SetAspectRatio()

◆ SetBeta()

◆ SetRotationAngle()

◆ SetSigma()

◆ SetTruncation()

◆ Sigma()

◆ SigmaX()

◆ SigmaY()

◆ Truncation()