template<class TFixedImage, class TMovingImage>
Computes normalized correlation between two images, based on AdvancedImageToImageMetric ...
This metric computes the correlation between pixels in the fixed image and pixels in the moving image. The spatial correspondence between fixed and moving image is established through a Transform. Pixel values are taken from the fixed image, their positions are mapped to the moving image and result in general in non-grid position on it. Values at these non-grid position of the moving image are interpolated using a user-selected Interpolator. The correlation is normalized by the autocorrelations of both the fixed and moving images.
This implementation of the NormalizedCorrelation is based on the AdvancedImageToImageMetric , which means that:
It uses the ImageSampler-framework
It makes use of the compact support of B-splines, in case of B-spline transforms.
Image derivatives are computed using either the B-spline interpolator's implementation or by nearest neighbor interpolation of a precomputed central difference image. A minimum number of samples that should map within the moving image (mask) can be specified.
The normalized correlation NC is defined as:
where x a voxel in the fixed image f, m the moving image, u(x,p) the deformation of x depending on the transform parameters p. sfm, sff and smm is notation used in the source code. The derivative of NC to p equals:
where gradient is the derivative of the moving image m to x, and where Jacobian is the derivative of the transformation to its parameters. gradient * Jacobian is called the differential. This yields for the derivative:
This class has an option to subtract the sample mean from the sample values in the cross correlation formula. This typically results in narrower valleys in the cost function NC. The default value is false. If SubtractMean is true, the NC is defined as:
where Af and Am are the average of f and m, respectively.
Definition at line 91 of file itkAdvancedNormalizedCorrelationImageToImageMetric.h .
using ConstPointer = SmartPointer< const Self > using DerivativeValueType = typename DerivativeType::ValueType using FixedImageLimiterOutputType = typename FixedImageLimiterType::OutputType using FixedImageLimiterType = LimiterFunctionBase < RealType, FixedImageDimension > using FixedImagePixelType = typename FixedImageType::PixelType using ImageSampleContainerPointer = typename ImageSamplerType::OutputVectorContainerPointer using ImageSampleContainerType = typename ImageSamplerType::OutputVectorContainerType using ImageSamplerPointer = typename ImageSamplerType::Pointer using ImageSamplerType = ImageSamplerBase < FixedImageType > using MovingImageDerivativeScalesType = FixedArray< double , Self::MovingImageDimension > using MovingImageLimiterOutputType = typename MovingImageLimiterType::OutputType using MovingImageLimiterType = LimiterFunctionBase < RealType, MovingImageDimension > using MovingImageRegionType = typename MovingImageType::RegionType using NumberOfParametersType = typename AdvancedTransformType::NumberOfParametersType using Pointer = SmartPointer< Self > using Self = AdvancedNormalizedCorrelationImageToImageMetric using Superclass = AdvancedImageToImageMetric < TFixedImage, TMovingImage > using ThreaderType = itk::PlatformMultiThreader using ThreadInfoType = typename ThreaderType::WorkUnitInfo using AdvancedTransformType = AdvancedTransform < ScalarType , FixedImageDimension, MovingImageDimension > using BSplineOrder1TransformPointer = typename BSplineOrder1TransformType::Pointer using BSplineOrder1TransformType = AdvancedBSplineDeformableTransform < ScalarType , FixedImageDimension, 1 > using BSplineOrder2TransformPointer = typename BSplineOrder2TransformType::Pointer using BSplineOrder2TransformType = AdvancedBSplineDeformableTransform < ScalarType , FixedImageDimension, 2 > using BSplineOrder3TransformPointer = typename BSplineOrder3TransformType::Pointer using BSplineOrder3TransformType = AdvancedBSplineDeformableTransform < ScalarType , FixedImageDimension, 3 > using CombinationTransformType = AdvancedCombinationTransform < ScalarType , FixedImageDimension > using ConstPointer = SmartPointer< const Self > using DerivativeValueType = typename DerivativeType::ValueType using FixedImageLimiterOutputType = typename FixedImageLimiterType::OutputType using FixedImageLimiterPointer = typename FixedImageLimiterType::Pointer using FixedImageLimiterType = LimiterFunctionBase < RealType, FixedImageDimension > using FixedImageMaskSpatialObject2Type = ImageMaskSpatialObject< Self::FixedImageDimension > using FixedImagePixelType = typename FixedImageType::PixelType using FixedImagePointer = typename FixedImageType::Pointer using HessianType = vnl_sparse_matrix< HessianValueType > using HessianValueType = typename DerivativeType::ValueType using ImageSampleContainerPointer = typename ImageSamplerType::OutputVectorContainerPointer using ImageSampleContainerType = typename ImageSamplerType::OutputVectorContainerType using ImageSamplerPointer = typename ImageSamplerType::Pointer using ImageSamplerType = ImageSamplerBase < FixedImageType > using MovingImageDerivativeScalesType = FixedArray< double , Self::MovingImageDimension > using MovingImageLimiterOutputType = typename MovingImageLimiterType::OutputType using MovingImageLimiterPointer = typename MovingImageLimiterType::Pointer using MovingImageLimiterType = LimiterFunctionBase < RealType, MovingImageDimension > using MovingImageMaskSpatialObject2Type = ImageMaskSpatialObject< Self::MovingImageDimension > using MovingImagePointer = typename MovingImageType::Pointer using MovingImageRegionType = typename MovingImageType::RegionType using NumberOfParametersType = typename AdvancedTransformType::NumberOfParametersType using Pointer = SmartPointer< Self > using ScalarType = typename TransformType::ScalarType using Self = AdvancedImageToImageMetric using Superclass = ImageToImageMetric< TFixedImage, TMovingImage > using ThreaderType = itk::PlatformMultiThreader using ThreadInfoType = typename ThreaderType::WorkUnitInfo
virtual const char * GetClassName () const void GetDerivative (const TransformParametersType ¶meters, DerivativeType &derivative) const override virtual const bool & GetSubtractMean () MeasureType GetValue (const TransformParametersType ¶meters) const override void GetValueAndDerivative (const TransformParametersType ¶meters, MeasureType &value, DerivativeType &derivative) const override void GetValueAndDerivativeSingleThreaded (const TransformParametersType ¶meters, MeasureType &value, DerivativeType &derivative) const ITK_DISALLOW_COPY_AND_MOVE (AdvancedNormalizedCorrelationImageToImageMetric ) itkStaticConstMacro (FixedImageDimension, unsigned int , FixedImageType::ImageDimension) itkStaticConstMacro (MovingImageDimension, unsigned int , MovingImageType::ImageDimension) virtual void SetSubtractMean (bool _arg) virtual void SubtractMeanOff () virtual void SubtractMeanOn () virtual void BeforeThreadedGetValueAndDerivative (const TransformParametersType ¶meters) const virtual const char * GetClassName () const virtual const FixedImageLimiterType * GetFixedImageLimiter () virtual double GetFixedLimitRangeRatio () const virtual ImageSamplerType * GetImageSampler () const virtual const MovingImageDerivativeScalesType & GetMovingImageDerivativeScales () virtual const MovingImageLimiterType * GetMovingImageLimiter () virtual double GetMovingLimitRangeRatio () const virtual double GetRequiredRatioOfValidSamples () const virtual bool GetScaleGradientWithRespectToMovingImageOrientation () const virtual void GetSelfHessian (const TransformParametersType ¶meters, HessianType &H) const const AdvancedTransformType * GetTransform () const override virtual bool GetUseFixedImageLimiter () const virtual bool GetUseImageSampler () const virtual const bool & GetUseMetricSingleThreaded () virtual bool GetUseMovingImageDerivativeScales () const virtual bool GetUseMovingImageLimiter () const virtual const bool & GetUseMultiThread () void Initialize () override ITK_DISALLOW_COPY_AND_MOVE (AdvancedImageToImageMetric ) itkStaticConstMacro (FixedImageDimension, unsigned int , TFixedImage::ImageDimension) itkStaticConstMacro (MovingImageDimension, unsigned int , TMovingImage::ImageDimension) virtual void SetFixedImageLimiter (FixedImageLimiterType *_arg) virtual void SetFixedLimitRangeRatio (double _arg) virtual void SetImageSampler (ImageSamplerType *_arg) virtual void SetMovingImageDerivativeScales (MovingImageDerivativeScalesType _arg) virtual void SetMovingImageLimiter (MovingImageLimiterType *_arg) virtual void SetMovingLimitRangeRatio (double _arg) virtual void SetNumberOfWorkUnits (ThreadIdType numberOfThreads) virtual void SetRequiredRatioOfValidSamples (double _arg) virtual void SetScaleGradientWithRespectToMovingImageOrientation (bool _arg) virtual void SetTransform (AdvancedTransformType *arg) virtual void SetUseMetricSingleThreaded (bool _arg) virtual void SetUseMovingImageDerivativeScales (bool _arg) virtual void SetUseMultiThread (bool _arg) virtual void UseMetricSingleThreadedOff () virtual void UseMetricSingleThreadedOn () virtual void UseMultiThreadOff () virtual void UseMultiThreadOn ()
using BSplineInterpolatorType = BSplineInterpolateImageFunction< MovingImageType, CoordinateRepresentationType, double > using CentralDifferenceGradientFilterType = GradientImageFilter< MovingImageType, RealType, RealType > using FixedImageIndexType = typename FixedImageType::IndexType using FixedImageIndexValueType = typename FixedImageIndexType::IndexValueType using FixedImagePointType = typename TransformType::InputPointType using MovingImageContinuousIndexType = typename InterpolatorType::ContinuousIndexType using MovingImageDerivativeType = typename BSplineInterpolatorType::CovariantVectorType using MovingImageIndexType = typename MovingImageType::IndexType using MovingImagePointType = typename TransformType::OutputPointType using NonZeroJacobianIndicesType = typename AdvancedTransformType::NonZeroJacobianIndicesType using BSplineInterpolatorFloatPointer = typename BSplineInterpolatorFloatType::Pointer using BSplineInterpolatorFloatType = BSplineInterpolateImageFunction< MovingImageType, CoordinateRepresentationType, float > using BSplineInterpolatorPointer = typename BSplineInterpolatorType::Pointer using BSplineInterpolatorType = BSplineInterpolateImageFunction< MovingImageType, CoordinateRepresentationType, double > using CentralDifferenceGradientFilterPointer = typename CentralDifferenceGradientFilterType::Pointer using CentralDifferenceGradientFilterType = GradientImageFilter< MovingImageType, RealType, RealType > using FixedImageIndexType = typename FixedImageType::IndexType using FixedImageIndexValueType = typename FixedImageIndexType::IndexValueType using FixedImagePointType = typename TransformType::InputPointType using LinearInterpolatorPointer = typename LinearInterpolatorType::Pointer using LinearInterpolatorType = AdvancedLinearInterpolateImageFunction < MovingImageType, CoordinateRepresentationType > using MovingImageContinuousIndexType = typename InterpolatorType::ContinuousIndexType using MovingImageDerivativeType = typename BSplineInterpolatorType::CovariantVectorType using MovingImageIndexType = typename MovingImageType::IndexType using MovingImagePointType = typename TransformType::OutputPointType using NonZeroJacobianIndicesType = typename AdvancedTransformType::NonZeroJacobianIndicesType using ReducedBSplineInterpolatorPointer = typename ReducedBSplineInterpolatorType::Pointer using ReducedBSplineInterpolatorType = ReducedDimensionBSplineInterpolateImageFunction < MovingImageType, CoordinateRepresentationType, double >
AdvancedNormalizedCorrelationImageToImageMetric () void AfterThreadedGetValueAndDerivative (MeasureType &value, DerivativeType &derivative) const override void InitializeThreadingParameters () const override void PrintSelf (std::ostream &os, Indent indent) const override void ThreadedGetValueAndDerivative (ThreadIdType threadID) override void UpdateDerivativeTerms (const RealType &fixedImageValue, const RealType &movingImageValue, const DerivativeType &imageJacobian, const NonZeroJacobianIndicesType &nzji, DerivativeType &derivativeF, DerivativeType &derivativeM, DerivativeType &differential) const ~AdvancedNormalizedCorrelationImageToImageMetric () override=default AdvancedImageToImageMetric () virtual void AfterThreadedGetValue (MeasureType &value) const virtual void AfterThreadedGetValueAndDerivative (MeasureType &value, DerivativeType &derivative) const virtual void CheckForAdvancedTransform () virtual void CheckForBSplineInterpolator () virtual void CheckForBSplineTransform () const virtual void CheckNumberOfSamples (unsigned long wanted, unsigned long found) const virtual bool EvaluateMovingImageValueAndDerivative (const MovingImagePointType &mappedPoint, RealType &movingImageValue, MovingImageDerivativeType *gradient) const virtual bool EvaluateTransformJacobian (const FixedImagePointType &fixedImagePoint, TransformJacobianType &jacobian, NonZeroJacobianIndicesType &nzji) const virtual void EvaluateTransformJacobianInnerProduct (const TransformJacobianType &jacobian, const MovingImageDerivativeType &movingImageDerivative, DerivativeType &imageJacobian) const bool FastEvaluateMovingImageValueAndDerivative (const MovingImagePointType &mappedPoint, RealType &movingImageValue, MovingImageDerivativeType *gradient, const ThreadIdType threadId) const virtual void InitializeImageSampler () virtual void InitializeLimiters () virtual void InitializeThreadingParameters () const virtual bool IsInsideMovingMask (const MovingImagePointType &point) const itkAlignedTypedef (ITK_CACHE_LINE_ALIGNMENT, PaddedGetValueAndDerivativePerThreadStruct, AlignedGetValueAndDerivativePerThreadStruct) itkAlignedTypedef (ITK_CACHE_LINE_ALIGNMENT, PaddedGetValuePerThreadStruct, AlignedGetValuePerThreadStruct) itkPadStruct (ITK_CACHE_LINE_ALIGNMENT, GetValueAndDerivativePerThreadStruct , PaddedGetValueAndDerivativePerThreadStruct) itkPadStruct (ITK_CACHE_LINE_ALIGNMENT, GetValuePerThreadStruct , PaddedGetValuePerThreadStruct) void LaunchGetValueAndDerivativeThreaderCallback () const void LaunchGetValueThreaderCallback () const void PrintSelf (std::ostream &os, Indent indent) const override virtual void SetUseFixedImageLimiter (bool _arg) virtual void SetUseImageSampler (bool _arg) virtual void SetUseMovingImageLimiter (bool _arg) virtual void ThreadedGetValue (ThreadIdType threadID) virtual void ThreadedGetValueAndDerivative (ThreadIdType threadID) MovingImagePointType TransformPoint (const FixedImagePointType &fixedImagePoint) const ~AdvancedImageToImageMetric () override=default
![\[
\mathrm{NC} = \frac{\sum_x f(x) * m(x+u(x,p))}{\sqrt{ \sum_x f(x)^2 * \sum_x m(x+u(x,p))^2}}
= \frac{\mathtt{sfm}}{\sqrt{\mathtt{sff} * \mathtt{smm}}}
\]](form_51_dark.png)
![\[
\frac{\partial \mathrm{NC}}{\partial p} = \frac{\partial \mathrm{NC}}{\partial m}
\frac{\partial m}{\partial x} \frac{\partial x}{\partial p}
= \frac{\partial \mathrm{NC}}{\partial m} * \mathtt{gradient} * \mathtt{jacobian},
\]](form_52_dark.png)
![\[
\frac{\partial \mathrm{NC}}{\partial p}
= \frac{\sum_x[ f(x) * \mathtt{differential} ] - ( \mathtt{sfm} / \mathtt{smm} )
* \sum_x[ m(x+u(x,p)) * \mathtt{differential} ]}{\sqrt{\mathtt{sff} * \mathtt{smm}}}
\]](form_53_dark.png)
![\[
\mathrm{NC} = \frac{\sum_x ( f(x) - \mathtt{Af} ) * ( m(x+u(x,p)) - \mathtt{Am})}
{\sqrt{\sum_x (f(x) - \mathtt{Af})^2 * \sum_x (m(x+u(x,p)) - \mathtt{Am})^2}}
= \frac{\mathtt{sfm} - \mathtt{sf} * \mathtt{sm} / N}
{\sqrt{(\mathtt{sff} - \mathtt{sf} * \mathtt{sf} / N) * (\mathtt{smm} - \mathtt{sm} *\mathtt{sm} / N)}},
\]](form_54_dark.png)
Public Types inherited from itk::AdvancedImageToImageMetric< TFixedImage, TMovingImage >
1.9.6