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/*=========================================================================
*
* Copyright Insight Software Consortium
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0.txt
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
*=========================================================================*/
#ifndef itkBSplineScatteredDataPointSetToImageFilter_h
#define itkBSplineScatteredDataPointSetToImageFilter_h
#include "itkPointSetToImageFilter.h"
#include "itkBSplineKernelFunction.h"
#include "itkCoxDeBoorBSplineKernelFunction.h"
#include "itkVectorContainer.h"
#include "vnl/vnl_matrix.h"
namespace itk
{
/** \class BSplineScatteredDataPointSetToImageFilter
* \brief Image filter which provides a B-spline output approximation.
*
* Given an n-D image with scattered data, this filter finds
* a fast approximation to that irregularly spaced data using uniform
* B-splines. The traditional method of inverting the observation
* matrix to find a least-squares fit is made obsolete. Therefore,
* memory issues are not a concern and inverting large matrices is
* not applicable. In addition, this allows fitting to be multi-threaded.
* This class generalizes from Lee's original paper to encompass
* n-D data in m-D parametric space and any *feasible* B-spline order as well
* as the option of specifying a confidence value for each point.
*
* In addition to specifying the input point set, one must specify the number
* of control points. The specified number of control points must be
* greater than m_SplineOrder. If one wishes to use the multilevel component of
* this algorithm, one must also specify the number of levels in the
* hierarchy. If this is desired, the number of control points becomes
* the number of control points for the coarsest level. The algorithm
* then increases the number of control points at each level so that
* the B-spline n-D grid is refined to twice the previous level.
*
* There are two parts to fitting scattered data: the parameterization
* assignment problem and the fitting problem given a parameterization.
* This filter only addresses the second problem in that the user must
* provide a parametric value for each scattered datum. Different parametric
* assignment schemes result in different B-spline object outputs.
*
* This filter is general in that it accepts n-D scattered data in m-D parametric
* dimensions. Input to this filter is an m-D point set with a Vector data type
* of n dimensions. This means that the parametric values are stored in the
* points container of the point set whereas the scattered data are stored in
* the points data container of the point set.
*
* Typical B-spline objects include curves, which have a parametric dimension of
* 1 and a data dimension of 2 or 3 (depending on the space in which the curve
* resides) and deformation fields which commonly have parametric and data
* dimensions of 2 or 3 (again depending on the space of the field).
* As an example, a curve through a set of 2D points has data dimension 2 and
* parametric dimension 1. The univariate curve could be represented as: <x(u),y(u)>
* Another example is a 3D deformation of 3D points, which has parametric
* dimension 3 and data dimension 3 and can be represented as:
* <dx(u,v,w), dy(u,v,w), dz(u,v,w)>. However, as mentioned before, the code is
* general such that, if the user wanted, she could model a time varying 3-D
* displacement field which resides in 4-D space as
* <dx(u, v, w, t), dy(u, v, w, t), dz(u, v, w, t)>.
*
* The output is an image defining the sampled B-spline parametric domain where
* each pixel houses the sampled B-spline object value. For a curve fit to 3-D
* points, the output is a 1-D image where each voxel contains a vector with
* the approximated (x,y,z) location. The continuous, finite, rectilinear domain
* (as well as the sampling rate) is specified via the combination of the SetSpacing()
* and SetSize() functions. For a 2-D deformation on 2-D points, the output is a 2-D image
* where each voxel contains the approximated (dx, dy) vector.
*
* The parameterization must be specified using SetPoint, where the actual
* coordinates of the point are set via SetPointData. For example, to compute a
* spline through the (ordered) 2D points (5,6) and (7,8), you should use:
*
* \code
* typedef itk::Vector< float, 2 > DataType;
* PointSetType::PointType param0;
* param0[0] = 0.0;
* DataType p0;
* p0[0] = 10.0; p0[1]= 10.0;
* pointSet->SetPoint(0, param0);
* pointSet->SetPointData( 0, p0 );
*
* PointSetType::PointType param1;
* param1[0] = 1.0;
* DataType p1;
* p1[0] = 80.0; p1[1]= 50.0;
* pointSet->SetPoint(1, param1);
* pointSet->SetPointData( 1, p1 );
* \endcode
*
* \author Nicholas J. Tustison
*
* This code was contributed in the Insight Journal paper:
* "N-D C^k B-Spline Scattered Data Approximation"
* by Nicholas J. Tustison, James C. Gee
* https://hdl.handle.net/1926/140
* http://www.insight-journal.org/browse/publication/57
*
*
* \par REFERENCE
* S. Lee, G. Wolberg, and S. Y. Shin, "Scattered Data Interpolation
* with Multilevel B-Splines", IEEE Transactions on Visualization and
* Computer Graphics, 3(3):228-244, 1997.
*
* \par REFERENCE
* N.J. Tustison and J.C. Gee, "Generalized n-D C^k Scattered Data Approximation
* with Confidence Values", Proceedings of the MIAR conference, August 2006.
*
* \ingroup ITKImageGrid
*/
template< typename TInputPointSet, typename TOutputImage >
class ITK_TEMPLATE_EXPORT BSplineScatteredDataPointSetToImageFilter:
public PointSetToImageFilter< TInputPointSet, TOutputImage >
{
public:
/** Standard class typedefs. */
typedef BSplineScatteredDataPointSetToImageFilter Self;
typedef PointSetToImageFilter<TInputPointSet, TOutputImage> Superclass;
typedef SmartPointer<Self> Pointer;
typedef SmartPointer<const Self> ConstPointer;
/** Method for creation through the object factory. */
itkNewMacro( Self );
/** Run-time type information (and related methods). */
itkTypeMacro( BSplineScatteredDataPointSetToImageFilter,
PointSetToImageFilter );
/** Extract dimension from the output image. */
itkStaticConstMacro( ImageDimension, unsigned int,
TOutputImage::ImageDimension );
typedef TOutputImage ImageType;
typedef TInputPointSet PointSetType;
/** Image typedef support. */
typedef typename ImageType::PixelType PixelType;
typedef typename ImageType::RegionType RegionType;
typedef typename ImageType::SizeType SizeType;
typedef typename ImageType::IndexType IndexType;
/** PointSet typedef support. */
typedef typename PointSetType::PointType PointType;
typedef typename PointSetType::Pointer PointSetPointer;
typedef typename PointSetType::PixelType PointDataType;
typedef typename PointSetType::PointDataContainer PointDataContainerType;
/** Other typedefs. */
typedef float RealType;
typedef VectorContainer<unsigned, RealType> WeightsContainerType;
/** Image types. */
typedef Image<PointDataType,
itkGetStaticConstMacro( ImageDimension )> PointDataImageType;
typedef Image<RealType,
itkGetStaticConstMacro( ImageDimension )> RealImageType;
typedef typename RealImageType::Pointer RealImagePointer;
typedef typename PointDataImageType::Pointer PointDataImagePointer;
typedef FixedArray<unsigned,
itkGetStaticConstMacro( ImageDimension )> ArrayType;
typedef FixedArray<RealType,
itkGetStaticConstMacro( ImageDimension )> RealArrayType;
/** Interpolation kernel type (default spline order = 3). */
typedef CoxDeBoorBSplineKernelFunction<3> KernelType;
typedef BSplineKernelFunction<0> KernelOrder0Type;
typedef BSplineKernelFunction<1> KernelOrder1Type;
typedef BSplineKernelFunction<2> KernelOrder2Type;
typedef BSplineKernelFunction<3> KernelOrder3Type;
/** Set the spline order assuming it is the same in all parametric dimensions.
* The spline order determines the continuity between B-spline elements and
* the degree of polynomial used to construct the B-spline elements. Default
* = 3. */
void SetSplineOrder( unsigned int );
/** Set the spline order for each parametric dimension separately. The spline
* order determines the continuity between B-spline elements and the degree of
* polynomial used to construct the B-spline elements. Default = 3. */
void SetSplineOrder( const ArrayType & );
/** Get the spline order for all parametric dimensions. The spline order
* determines the continuity between B-spline elements and the degree of
* polynomial used to construct the B-spline elements. Default = 3. */
itkGetConstReferenceMacro( SplineOrder, ArrayType );
/** Set/Get the number of control points for each parametric dimension at the
* initial fitting level. The B-spline mesh size is equal to the number
* of control points minus the spline order. Default = 4 in each dimension.
*/
itkSetMacro( NumberOfControlPoints, ArrayType );
itkGetConstReferenceMacro( NumberOfControlPoints, ArrayType );
/** Get the number of current control points for each parametric dimension at
* the current fitting level. The B-spline mesh size is equal to the number
* of control points minus the spline order. Default = 4 in each dimension.
*/
itkGetConstReferenceMacro( CurrentNumberOfControlPoints, ArrayType );
/** Set the number of fitting levels assuming the number of fitting levels is
* the same for each parametric dimension. Starting with the mesh size
* implied by setting the number of control points, the mesh size is doubled
* at each fitting level. Default = 1 in all parametric dimensions. */
void SetNumberOfLevels( unsigned int );
/** Set the number of fitting levels in each parametric dimension separately.
* Starting with the mesh size implied by setting the number of control
* points, the mesh size is doubled at each fitting level. Default = 1 in all
* parametric dimensions. */
void SetNumberOfLevels( const ArrayType & );
/** Get the number of fitting levels for all parametric dimensions. Starting
* with the mesh size implied by setting the number of control points, the
* mesh size is doubled at each fitting level. Default = 1 in all parametric
* dimensions. */
itkGetConstReferenceMacro( NumberOfLevels, ArrayType );
/** Set/Get the epsilon used for B-splines. The B-spline parametric domain in
* 1-D is defined on the half-closed interval [a,b). Extension to n-D is
* defined similarly. This presents some difficulty for defining the
* the image domain to be co-extensive with the parametric domain. We use
* the B-spline epsilon to push the edge of the image boundary inside the
* B-spline parametric domain. */
itkSetMacro( BSplineEpsilon, RealType );
itkGetConstMacro( BSplineEpsilon, RealType );
/** Set/Get the array to define the periodicity of the dimensions in the
* parametric space is to be.
* This array of 0/1 values defines whether a particular dimension of the
* parametric space is to be considered periodic or not. For example, if you
* are using interpolating along a 1D closed curve, the array type will have
* size 1, and you should set the first element of this array to the value
* "1". In the case that you were interpolating in a planar surface with
* cylindrical topology, the array type will have two components, and you
* should set to "1" the component that goes around the cylinder, and set to
* "0" the component that goes from the top of the cylinder to the bottom.
* This will indicate the periodity of that parameter to the filter.
* Internally, in order to make periodic the domain of the parameter, the
* filter will reuse some of the points at the beginning of the domain as if
* they were also located at the end of the domain. The number of points to
* be reused will depend on the spline order. As a user, you don't need to
* replicate the points, the filter will do this for you. */
itkSetMacro( CloseDimension, ArrayType );
itkGetConstReferenceMacro( CloseDimension, ArrayType );
/** A weighted fitting is possible where each input point is assigned a
* relative weighting. */
void SetPointWeights( WeightsContainerType *weights );
/** Set/Get whether or not the sampled output B-spline object is constructed.
* The result of the fitting process is an n-D grid of control points which
* describe the continuous B-spline object. */
itkSetMacro( GenerateOutputImage, bool );
itkGetConstReferenceMacro( GenerateOutputImage, bool );
itkBooleanMacro( GenerateOutputImage );
/** Get the control point lattice produced by the fitting process. */
PointDataImagePointer GetPhiLattice()
{
return static_cast<PointDataImageType *>( this->ProcessObject::GetOutput( 1 ) );
}
protected:
BSplineScatteredDataPointSetToImageFilter();
virtual ~BSplineScatteredDataPointSetToImageFilter() ITK_OVERRIDE;
void PrintSelf(std::ostream & os, Indent indent) const ITK_OVERRIDE;
void ThreadedGenerateData( const RegionType &, ThreadIdType ) ITK_OVERRIDE;
void BeforeThreadedGenerateData() ITK_OVERRIDE;
void AfterThreadedGenerateData() ITK_OVERRIDE;
unsigned int SplitRequestedRegion( unsigned int, unsigned int, RegionType & ) ITK_OVERRIDE;
void GenerateData() ITK_OVERRIDE;
private:
ITK_DISALLOW_COPY_AND_ASSIGN(BSplineScatteredDataPointSetToImageFilter);
/** Function used to propagate the fitting solution at one fitting level
* to the next level with the mesh resolution doubled. */
void RefineControlPointLattice();
/** Determine the residuals after fitting to one level. */
void UpdatePointSet();
/** This function is not used as it requires an evaluation of all
* (SplineOrder+1)^ImageDimensions B-spline weights for each evaluation. */
void GenerateOutputImage();
/** Function used to generate the sampled B-spline object quickly. */
void ThreadedGenerateDataForFitting( const RegionType &, ThreadIdType );
/** Function used to generate the sampled B-spline object quickly. */
void ThreadedGenerateDataForReconstruction( const RegionType &, ThreadIdType );
/** Sub-function used by GenerateOutputImageFast() to generate the sampled
* B-spline object quickly. */
void CollapsePhiLattice( PointDataImageType *, PointDataImageType *,
const RealType, const unsigned int );
/** Set the grid parametric domain parameters such as the origin, size,
* spacing, and direction. */
void SetPhiLatticeParametricDomainParameters();
/** Convert number to index given a size of image. Used to index
* the local control point neighborhoods. */
IndexType NumberToIndex( const unsigned int, const SizeType );
bool m_DoMultilevel;
bool m_GenerateOutputImage;
bool m_UsePointWeights;
unsigned int m_MaximumNumberOfLevels;
unsigned int m_CurrentLevel;
ArrayType m_NumberOfControlPoints;
ArrayType m_CurrentNumberOfControlPoints;
ArrayType m_CloseDimension;
ArrayType m_SplineOrder;
ArrayType m_NumberOfLevels;
typename WeightsContainerType::Pointer m_PointWeights;
typename PointDataImageType::Pointer m_PhiLattice;
typename PointDataImageType::Pointer m_PsiLattice;
vnl_matrix<RealType> m_RefinedLatticeCoefficients[ImageDimension];
typename PointDataContainerType::Pointer m_InputPointData;
typename PointDataContainerType::Pointer m_OutputPointData;
typename KernelType::Pointer m_Kernel[ImageDimension];
typename KernelOrder0Type::Pointer m_KernelOrder0;
typename KernelOrder1Type::Pointer m_KernelOrder1;
typename KernelOrder2Type::Pointer m_KernelOrder2;
typename KernelOrder3Type::Pointer m_KernelOrder3;
std::vector<RealImagePointer> m_OmegaLatticePerThread;
std::vector<PointDataImagePointer> m_DeltaLatticePerThread;
RealType m_BSplineEpsilon;
bool m_IsFittingComplete;
};
} // end namespace itk
#ifndef ITK_MANUAL_INSTANTIATION
#include "itkBSplineScatteredDataPointSetToImageFilter.hxx"
#endif
#endif
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