i3d::PDESolver< VOXELIN, VOXELOUT > Class Template Reference

This class is together with class PDESolverFunction the root abstract class for wide family of classes which implements segmentation methods and image preprocessing filters. All these offsprings of this base class have one common feature. The key idea of those methods or filters is described by partial differential equation. The execution of the methods or application of the filters has in the background the solution of the underlying PDE. More...

#include <LevelSet.h>

Inheritance diagram for i3d::PDESolver< VOXELIN, VOXELOUT >:

List of all members.


Public Member Functions
void	InitializeOutput ()
	Initialize the output image (Memory allocation, Resolution settings, etc.).
virtual bool	Convergence ()
	If returns true the iteration proccess stops.
virtual void	Initialize ()
	Initialize the computation.
virtual void	InitializeIteration ()
	Initialize computation for one iteration step.
virtual void	ComputeChange ()
	Compute the $\tau$ part of the equation.
virtual void	ApplyChange ()
	Add the $\tau$ part of the equation to the solution.
virtual void	Execute ()
	This method implements the main iterative proccess of solution finding.
bool	EstimateDistanceInOnePoint (size_t index, size_t neighbors, VOXELOUT offset)
void	SetMaximumNumberOfIterations (size_t max)
	Set the maximum number of iterations.
size_t	GetMaximumNumberOfIterations ()
	Get the maximum number of iterations.
void	SetSpacing (float x, float y, float z)
	Set the spacing between voxels.
void	SetSpacing (Vector3d< float > vec)
	Set the spacing between voxels.
void	GetSpacing (float x, float y, float *z)
	Get the spacing between voxels.
virtual void	SetGlobalTimeStep (VOXELOUT t)
	Set the fixed global time step ( $\tau$ ).
VOXELOUT	GetGlobalTimeStep ()
	Get the fixed global time step ( $\tau$ ).
Protected Attributes
Image3d< VOXELIN > &	Input
	Input image.
Image3d< VOXELOUT > &	Output
	Output Image.
size_t	ElapsedIteration
	Number of Elapsed Iteration during computations.
size_t	MaximumIteration
	Maximum number of iterations.
VOXELOUT	InputIsoValue
Vector3d< float >	Spacing
	Spacing of the LevelSet lattice.
size_t	Dimensions
	Number of dimensions (2 or 3).

Detailed Description

template<class VOXELIN, class VOXELOUT>
class i3d::PDESolver< VOXELIN, VOXELOUT >

The partial differential equation, which is the core off all offsprings of this class, has following "general form":

$u_t = F(u_x,u_y,u_z,u_{xx},u_{yy},u_{zz},u_{xxx},...),$

where F is some function of spatial derivatives. The temporal derivation can be for example discretised by the forward Euler operator in following way.

$\frac{u^{n+1}- u^{n}}{\tau} = F(u_x,u_y,u_z,u_{xx},u_{yy},u_{zz},u_{xxx},...),$

This leads to following explicit scheme:

$u^{n+1} = u^{n} + \tau F(u_x,u_y,u_z,u_{xx},u_{yy},u_{zz},u_{xxx},...),$

From this follows, that we have some initial state (input image, initial state of the segmentation, etc. ) we iteratively modify this state (we compute the filter on the image, we try to find correct segmentation) and after some time we find the solution of the equation.

This class together with class PDESolverFunction implements above suggested functionality. The PDESolver class (and their offsprings) take control of the iteration proccess, it handles the input and the output (memory allocation, etc.) and it implements the iterative solver of PDE equation. It has also an pointer to the "Function" object (PDESolverFunction and offsprings), which is responsible for computation of the $\tau F(...)$ part of the equation. There is no need to instantiate a "Function" object (i. e. PDESolverFunction class) from the user point of view. The user should only instantiate some offspring of PDESolver class. The "Function" object is instantiated automatically by the "Solver" object.

More detailed description
The constructor of every offspring of this class has two parameters -- references to Input and Output image (Image3d objects). The user should only supply correctly initialised (allocated and loaded) Input image. The output image is automatically initialised to the correct state. There are some methods which should the user use to adjust the default settings (Spacing between voxels, maximum number of the iterations, the time step $\tau$ and so on). The core functionality (iterative proccess of solution finding) is implemented in the method PDESolver::Execute(). The code listing of this method is shown bellow. In first the Input is copied to Output by the InitializeOutput() method. Second the virtual method Initialize() is called to allow some necessary initialization steps, which are not common for all inherited classes. The iterative process starts after that. The method ComputeChange() calls method PDESolverFunction::ComputeUpdateData(), which computes the $F(u_x,u_y,u_z,u_{xx},u_{yy},u_{zz},u_{xxx},...)$ part of the equation. This method also computes the posible maximum time step $\tau$ which can be used to add the $F(u_x,u_y,u_z,u_{xx},u_{yy},u_{zz},u_{xxx},...)$ part to $u^n $ . The addition of $\tau F(u_x,u_y,u_z,u_{xx},u_{yy},u_{zz},u_{xxx},...)$ to $ u^n $ provides the ApplyChange() method. The loop ends if the Convergence() method returns true.

  template <class VOXELIN, class VOXELOUT> void PDESolver<VOXELIN, VOXELOUT>::Execute()
  {
    InitializeOutput();
    Initialize();
    while (! Convergence())
    {
	InitializeIteration();
	ComputeChange();
	ApplyChange();
	++ElapsedIteration;
    }
  }

Diagram of Data and Control flow between Solver object (PDESolver offspring) and Function Object (PDESolverFunction offsprint)

Simple example of usage
In the code sequence bellow is shown the simple example how should be used the offsprings of the PDESolver class. After instantiation with two parameters, where the input parameter is correctly allocated and the ouput is only declared, some adjustment is done (setting the spacing and timestep). After that the main Execute() method is called. The last two lines are used only for converting the float output to gray leveels image.

  #include <LevelSet.h>
  #include <image3d.h>
  .....
   
   Image3d<GRAY8> i;
   Image3d<float> fimg;
   i.ReadImage('input.tif'); // read input image
   AOSTVFilter<GRAY8,float> TV(i,fimg); // instantiate  the filter  
   TV.SetMaximumNumberOfIterations(3); // Set the number of iterations to 2
   TV.SetSpacing(1.0,1.0,2.0); // Set the spacing of spatial discretisation to 1,1,2
   TV.SetGlobalTimeStep(5.0); // Set the global time step
   TV.Execute(); // Perform the work of the filter
   FloatToGray8NoWeight(fimg,i); //Convert the output float image to gray8 image
   i.SaveImage('output.tif'); // save the output of the filter

   ......

Author:: Jan Hubený xhubeny@fi.muni.cz

Date:: 2005

Member Function Documentation

template<class VOXELIN, class VOXELOUT>

bool i3d::PDESolver< VOXELIN, VOXELOUT >::EstimateDistanceInOnePoint	(	size_t	index,
		size_t *	neighbors,
		VOXELOUT *	offset
	)

Input: index - index into image array, neighbors - array with indices of the central point neighborhood output offset - distance of the nearest point on the interface to the point of index return value true - is near the interface false - is not near the interface

Member Data Documentation

template<class VOXELIN, class VOXELOUT>

VOXELOUT i3d::PDESolver< VOXELIN, VOXELOUT >::InputIsoValue [protected]

Value of the isoline(surface), which will be taken as the zero level set, from the input image

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

LevelSet.h
LevelSet.cc

i3dlib

Documentation

i3d::PDESolver< VOXELIN, VOXELOUT > Class Template Reference

Public Member Functions

Protected Attributes

Detailed Description

template<class VOXELIN, class VOXELOUT> class i3d::PDESolver< VOXELIN, VOXELOUT >

Member Function Documentation

Member Data Documentation

template<class VOXELIN, class VOXELOUT>
class i3d::PDESolver< VOXELIN, VOXELOUT >