#include <ImFusion/GL/HessianAlgorithm.h>

Numerically compute the Hessian (and optionally the gradient) of a single-channel image. More...

Inheritance diagram for ImFusion::HessianAlgorithm:

Detailed Description

Numerically compute the Hessian (and optionally the gradient) of a single-channel image.

The output always contains at least one SharedImageSet for the Hessian. For 3D images, the Hessian SharedImageSet contains two SharedImages:

get(0): diagonal entries (Hxx, Hyy, Hzz) as 3-channel image
get(1): upper off-diagonal entries (Hxy, Hxz, Hyz) as 3-channel image For 2D images:
get(0): diagonal entries (Hxx, Hyy) as 2-channel image
get(1): off-diagonal entry (Hxy) as 1-channel image

If p_computeGradient is enabled, an additional SharedImageSet is appended to the output containing the gradient as a single SharedImage with dim channels (dx, dy[, dz]).

If p_computeEigenvalues is enabled, an additional SharedImageSet is appended containing the eigenvalues of the Hessian sorted in ascending order (lambda0 <= lambda1 [<= lambda2]) as a single SharedImage with dim channels.

Derivatives can be computed in pixel, image (mm), or world coordinates (see p_coordinates). For small p_sigmaSmooth (sigmaSmooth/spacing <= 1), central finite differences are used directly. For larger p_sigmaSmooth, properly normalized Gaussian derivative kernels are used.

Public Types
enum class	Coordinates { Pixel = 0 , Image , World }
	Coordinate system in which derivatives are computed. More...
Public Types inherited from ImFusion::Algorithm
enum	Status { Unknown = -1 , Success = 0 , Error = 1 , InvalidInput , IncompleteInput , OutOfMemoryHost , OutOfMemoryGPU , UnsupportedGPU , UnknownAction , AbortedByUser , User = 1000 }
	Status codes. More...

Public Member Functions
	HessianAlgorithm (SharedImageSet &input)
	Constructor. Input must contain exactly one single-channel image.
void	compute () override
	Execute the algorithm.
OwningDataList	takeOutput () override
	Return any new Data that was created by the Algorithm during the last call to compute().
std::unique_ptr< SharedImageSet >	takeHessian ()
	Take individual output components (available after compute()).
std::unique_ptr< SharedImageSet >	takeGradient ()
std::unique_ptr< SharedImageSet >	takeEigenvalues ()
std::unique_ptr< SharedImageSet >	computeEigenvalues (SharedImageSet &hessianSis)
	Compute eigenvalues of a symmetric matrix stored as a two-frame SharedImageSet (first frame: diagonal entries, second: upper off-diagonal entries).
std::unique_ptr< SharedImageSet >	computeShapeOperator (SharedImageSet &hessianSis, SharedImageSet &gradientSis)
	Compute the shape operator S = -(1/\|\|g\|\|) * P * H * P of the level sets of f, where g = grad(f), H = D^2(f), n = g/\|\|g\|\|, and P = I - n*n^T.
Public Member Functions inherited from ImFusion::Algorithm
	Algorithm ()
	Default constructor will registers a single "compute" action that calls compute() and returns status().
virtual void	setProgress (Progress *progress)
	Sets a Progress interface the algorithm can use to notify observers about its computing progress.
Progress *	progress () const
	Returns the progress interface if set.
virtual int	status () const
	Indicates the status of the last call to compute().
virtual bool	survivesDataDeletion (const Data *) const
	Indicates whether the algorithm can handle (partial) deletion of the specified data, by default this checks whether the data is in the input list.
const FactoryInfo &	factoryInfo () const
	Returns the record describing how this Algorithm was instantiated by the AlgorithmFactory.
void	setFactoryInfo (const FactoryInfo &value)
	Sets the record describing how this Algorithm was instantiated by the AlgorithmFactory.
Status	runAction (const std::string &id)
	Run the action with name id if it exists.
const std::vector< Action > &	actions ()
	Get a mapping from Action id to Action as registered in this algorithm.
Public Member Functions inherited from ImFusion::Configurable
virtual void	configure (const Properties *p)
	Configure this object instance by de-serializing the given Properties.
virtual void	configuration (Properties *p) const
	Serialize the current object configuration into the given Properties object.
virtual void	configureDefaults ()
	Retrieve the properties of this object, replaces values with their defaults and sets it again.
void	registerParameter (ParameterBase *param)
	Register the given Parameter or SubProperty, so that it will be configured during configure()/configuration().
void	unregisterParameter (const ParameterBase *param)
	Remove the given Parameter or SubProperty from the list of registered parameters.
	Configurable (const Configurable &rhs)
	Configurable (Configurable &&rhs) noexcept
Configurable &	operator= (const Configurable &)
Configurable &	operator= (Configurable &&) noexcept

Static Public Member Functions
static bool	createCompatible (const DataList &dl, Algorithm **alg)
static std::unique_ptr< TypedImage< float > >	createGaussdFilter (double sigma, double spacing, int order, bool physicalDerivativeScale=true, double finiteDiffThreshold=1.0, bool correctKernelSum=true)
	Create a 1D Gaussian derivative kernel.
Static Public Member Functions inherited from ImFusion::Algorithm
static bool	createCompatible (const DataList &data, Algorithm **a=nullptr)
	Factory function to check algorithm compatibility with input data and optionally instantiate it.

Public Attributes
Parameter< Coordinates >	p_coordinates = {"coordinates", Coordinates::Pixel, this}
	Coordinate system for the computed derivatives.
Parameter< double >	p_sigmaSmooth = {"sigmaSmooth", 0.0, this}
	Standard deviation for Gaussian pre-smoothing to stabilize derivatives.
Parameter< bool >	p_computeGradient = {"computeGradient", false, this}
	If true, compute and output the gradient in addition to the Hessian.
Parameter< bool >	p_computeEigenvalues = {"computeEigenvalues", false, this}
	If true, compute and output the eigenvalues of the Hessian (sorted ascending).
Parameter< bool >	p_splitChannels = {"splitChannels", false, this}
	If true, split all multi-channel output images into separate single-channel images.
Public Attributes inherited from ImFusion::Algorithm
Signal	signalOutputChanged
	Signal should be emitted by Algorithms when their output/result has changed.
Signal	signalParametersChanged
	Signal should be emitted by Algorithms when their parameter configuration has changed.
Public Attributes inherited from ImFusion::Configurable
Signal	signalParametersChanged
	Emitted whenever one of the registered Parameters' or SubPropertys' signalValueChanged signal was emitted.

Additional Inherited Members
Protected Member Functions inherited from ImFusion::Algorithm
void	loadDefaults ()
void	registerAction (const std::string &id, const std::string &guiName, const std::function< Algorithm::Status(void)> &action)
	Register an action to be run via runAction.
template<typename D>
void	registerAction (const std::string &id, const std::string &guiName, Algorithm::Status(D::*action)(void))
	Template version of runAction that can be used with a pointer to a member function.
void	registerAction (const Action &action)
	Register an action.
Protected Attributes inherited from ImFusion::Algorithm
std::string	m_name
	Algorithm name.
Progress *	m_progress = nullptr
	Non-owing pointer to a progress interface. May be a nullptr.
FactoryInfo	m_factoryInfo = {}
	Record describing how this algorithm was instantiated by the AlgorithmFactory.
int	m_status = Status::Unknown
	Algorithm status after last call to compute().
std::vector< Action >	m_actions
	Map of key given by the id of the action, of the available actions of this algorithm.
Protected Attributes inherited from ImFusion::Configurable
std::vector< Param >	m_params
	List of all registered Parameter and SubProperty instances.

Member Enumeration Documentation

◆ Coordinates

enum class ImFusion::HessianAlgorithm::Coordinates

strong

Coordinate system in which derivatives are computed.

Enumerator
Pixel	Derivatives w.r.t. pixel/voxel indices (spacing = 1).
Image	Derivatives w.r.t. image coordinates (using descriptor spacing, in mm).
World	Derivatives w.r.t. world coordinates (accounting for image pose).

Member Function Documentation

◆ createGaussdFilter()

std::unique_ptr< TypedImage< float > > ImFusion::HessianAlgorithm::createGaussdFilter	(	double	sigma,
		double	spacing,
		int	order,
		bool	physicalDerivativeScale = true,
		double	finiteDiffThreshold = 1.0,
		bool	correctKernelSum = true )

static

Create a 1D Gaussian derivative kernel.

Parameters

sigma	Standard deviation of the Gaussian in physical units (same units as spacing). Must be non-negative; zero or small values (sigma/spacing <= finiteDiffThreshold) fall back to central finite differences directly.
spacing	Pixel spacing along this axis.
order	Derivative order (0 = smoothing, 1 = first derivative, 2 = second derivative).
physicalDerivativeScale	If true (default), the kernel is scaled to produce derivatives in physical units. If false, the kernel operates in pixel units (used by legacy callers).
finiteDiffThreshold	Pixel-space sigma below which a central finite difference stencil is used instead of a Gaussian kernel. Pass 0.0 to always use the Gaussian kernel.
correctKernelSum	If true (default), derivative kernels are corrected so they sum to exactly zero, compensating for Gaussian tail truncation.

◆ compute()

void ImFusion::HessianAlgorithm::compute ( )

overridevirtual

Execute the algorithm.

Implements ImFusion::Algorithm.

◆ takeOutput()

OwningDataList ImFusion::HessianAlgorithm::takeOutput ( )

overridevirtual

Return any new Data that was created by the Algorithm during the last call to compute().

The default implementation will return an empty list.

Note: Since ownership of the data is transferred, you can call this method only once between calls to compute().

Reimplemented from ImFusion::Algorithm.

◆ takeHessian()

std::unique_ptr< SharedImageSet > ImFusion::HessianAlgorithm::takeHessian ( )

inline

Take individual output components (available after compute()).

These move ownership — each can only be called once.

◆ computeEigenvalues()

std::unique_ptr< SharedImageSet > ImFusion::HessianAlgorithm::computeEigenvalues ( SharedImageSet & hessianSis )

Compute eigenvalues of a symmetric matrix stored as a two-frame SharedImageSet (first frame: diagonal entries, second: upper off-diagonal entries).

Returns a SharedImageSet with a single image containing sorted eigenvalues (ascending) as channels.

◆ computeShapeOperator()

std::unique_ptr< SharedImageSet > ImFusion::HessianAlgorithm::computeShapeOperator	(	SharedImageSet &	hessianSis,
		SharedImageSet &	gradientSis )

Compute the shape operator S = -(1/||g||) * P * H * P of the level sets of f, where g = grad(f), H = D^2(f), n = g/||g||, and P = I - n*n^T.

Both inputs must be in split-channel format (p_splitChannels = true): hessianSis: [Hxx, Hyy, Hzz, Hxy, Hxz, Hyz] (3D) or [Hxx, Hyy, Hxy] (2D) gradientSis: [gx, gy, gz] (3D) or [gx, gy] (2D)

Returns a SharedImageSet in multi-channel format compatible with computeEigenvalues(): get(0): diagonal entries (Sxx, Syy[, Szz]) as multi-channel image get(1): off-diagonal entries (Sxy[, Sxz, Syz]) as multi-channel image

Member Data Documentation

◆ p_sigmaSmooth

Parameter<double> ImFusion::HessianAlgorithm::p_sigmaSmooth = {"sigmaSmooth", 0.0, this}

Standard deviation for Gaussian pre-smoothing to stabilize derivatives.

Units depend on p_coordinates: pixels for Pixel mode, mm for Image/World mode. A value of 0 disables smoothing (pure central differences). Must not be negative.

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

ImFusion/GL/HessianAlgorithm.h