template<class TFixedImage, class TMovingImage>
class itk::AdvancedNormalizedCorrelationImageToImageMetric< TFixedImage, 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:
![\[
\mathrm{NC} = \frac{\sum_x f(x) * m(x+u(x,p))}{\sqrt{ \sum_x f(x)^2 * \sum_x m(x+u(x,p))^2}}
= \frac{\mathtt{sfm}}{\sqrt{\mathtt{sff} * \mathtt{smm}}}
\]](form_51.png)
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:
![\[
\frac{\partial \mathrm{NC}}{\partial p} = \frac{\partial \mathrm{NC}}{\partial m}
\frac{\partial m}{\partial x} \frac{\partial x}{\partial p}
= \frac{\partial \mathrm{NC}}{\partial m} * \mathtt{gradient} * \mathtt{jacobian},
\]](form_52.png)
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:
![\[
\frac{\partial \mathrm{NC}}{\partial p}
= \frac{\sum_x[ f(x) * \mathtt{differential} ] - ( \mathtt{sfm} / \mathtt{smm} )
* \sum_x[ m(x+u(x,p)) * \mathtt{differential} ]}{\sqrt{\mathtt{sff} * \mathtt{smm}}}
\]](form_53.png)
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:
![\[
\mathrm{NC} = \frac{\sum_x ( f(x) - \mathtt{Af} ) * ( m(x+u(x,p)) - \mathtt{Am})}
{\sqrt{\sum_x (f(x) - \mathtt{Af})^2 * \sum_x (m(x+u(x,p)) - \mathtt{Am})^2}}
= \frac{\mathtt{sfm} - \mathtt{sf} * \mathtt{sm} / N}
{\sqrt{(\mathtt{sff} - \mathtt{sf} * \mathtt{sf} / N) * (\mathtt{smm} - \mathtt{sm} *\mathtt{sm} / N)}},
\]](form_54.png)
where Af and Am are the average of f and m, respectively.
Definition at line 90 of file itkAdvancedNormalizedCorrelationImageToImageMetric.h.
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| typedef SmartPointer< const Self > | ConstPointer |
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| typedef Superclass::CoordinateRepresentationType | CoordinateRepresentationType |
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| typedef Superclass::DerivativeType | DerivativeType |
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| typedef Superclass::DerivativeValueType | DerivativeValueType |
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| typedef Superclass::FixedImageConstPointer | FixedImageConstPointer |
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| typedef Superclass::FixedImageLimiterOutputType | FixedImageLimiterOutputType |
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| typedef Superclass::FixedImageLimiterType | FixedImageLimiterType |
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| typedef Superclass::FixedImageMaskPointer | FixedImageMaskPointer |
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| typedef Superclass::FixedImageMaskType | FixedImageMaskType |
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| typedef Superclass::FixedImagePixelType | FixedImagePixelType |
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| typedef Superclass::FixedImageRegionType | FixedImageRegionType |
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| typedef Superclass::FixedImageType | FixedImageType |
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| typedef Superclass::GradientImageFilterPointer | GradientImageFilterPointer |
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| typedef Superclass::GradientImageFilterType | GradientImageFilterType |
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| typedef Superclass::GradientImagePointer | GradientImagePointer |
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| typedef Superclass::GradientImageType | GradientImageType |
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| typedef Superclass::GradientPixelType | GradientPixelType |
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| typedef Superclass::ImageSampleContainerPointer | ImageSampleContainerPointer |
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| typedef Superclass::ImageSampleContainerType | ImageSampleContainerType |
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| typedef Superclass::ImageSamplerPointer | ImageSamplerPointer |
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| typedef Superclass::ImageSamplerType | ImageSamplerType |
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| typedef Superclass::InputPointType | InputPointType |
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| typedef Superclass::InterpolatorPointer | InterpolatorPointer |
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| typedef Superclass::InterpolatorType | InterpolatorType |
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| typedef Superclass::MeasureType | MeasureType |
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| typedef Superclass::MovingImageConstPointer | MovingImageConstPointer |
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| typedef Superclass::MovingImageDerivativeScalesType | MovingImageDerivativeScalesType |
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| typedef Superclass::MovingImageLimiterOutputType | MovingImageLimiterOutputType |
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| typedef Superclass::MovingImageLimiterType | MovingImageLimiterType |
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| typedef Superclass::MovingImageMaskPointer | MovingImageMaskPointer |
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| typedef Superclass::MovingImageMaskType | MovingImageMaskType |
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| typedef Superclass::MovingImagePixelType | MovingImagePixelType |
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| typedef Superclass::MovingImageRegionType | MovingImageRegionType |
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| typedef Superclass::MovingImageType | MovingImageType |
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| typedef Superclass::NumberOfParametersType | NumberOfParametersType |
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| typedef Superclass::OutputPointType | OutputPointType |
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| typedef Superclass::ParametersType | ParametersType |
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| typedef SmartPointer< Self > | Pointer |
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| typedef Superclass::RealType | RealType |
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| typedef AdvancedNormalizedCorrelationImageToImageMetric | Self |
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| typedef AdvancedImageToImageMetric< TFixedImage, TMovingImage > | Superclass |
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| typedef Superclass::ThreaderType | ThreaderType |
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| typedef Superclass::ThreadInfoType | ThreadInfoType |
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| typedef Superclass::TransformJacobianType | TransformJacobianType |
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| typedef Superclass::TransformParametersType | TransformParametersType |
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| typedef Superclass::TransformPointer | TransformPointer |
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| typedef Superclass::TransformType | TransformType |
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| typedef AdvancedTransform< ScalarType, FixedImageDimension, MovingImageDimension > | AdvancedTransformType |
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| typedef BSplineOrder1TransformType::Pointer | BSplineOrder1TransformPointer |
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| typedef AdvancedBSplineDeformableTransform< ScalarType, FixedImageDimension, 1 > | BSplineOrder1TransformType |
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| typedef BSplineOrder2TransformType::Pointer | BSplineOrder2TransformPointer |
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| typedef AdvancedBSplineDeformableTransform< ScalarType, FixedImageDimension, 2 > | BSplineOrder2TransformType |
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| typedef BSplineOrder3TransformType::Pointer | BSplineOrder3TransformPointer |
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| typedef AdvancedBSplineDeformableTransform< ScalarType, FixedImageDimension, 3 > | BSplineOrder3TransformType |
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| typedef AdvancedCombinationTransform< ScalarType, FixedImageDimension > | CombinationTransformType |
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| typedef SmartPointer< const Self > | ConstPointer |
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| typedef Superclass::CoordinateRepresentationType | CoordinateRepresentationType |
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| typedef Superclass::DerivativeType | DerivativeType |
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| typedef DerivativeType::ValueType | DerivativeValueType |
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| typedef Superclass::FixedImageConstPointer | FixedImageConstPointer |
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| typedef FixedImageLimiterType::OutputType | FixedImageLimiterOutputType |
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| typedef FixedImageLimiterType::Pointer | FixedImageLimiterPointer |
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| typedef LimiterFunctionBase< RealType, FixedImageDimension > | FixedImageLimiterType |
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| typedef Superclass::FixedImageMaskPointer | FixedImageMaskPointer |
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| typedef ImageMaskSpatialObject< itkGetStaticConstMacro(FixedImageDimension) > | FixedImageMaskSpatialObject2Type |
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| typedef Superclass::FixedImageMaskType | FixedImageMaskType |
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| typedef FixedImageType::PixelType | FixedImagePixelType |
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| typedef FixedImageType::Pointer | FixedImagePointer |
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| typedef Superclass::FixedImageRegionType | FixedImageRegionType |
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| typedef Superclass::FixedImageType | FixedImageType |
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| typedef Superclass::GradientImageFilterPointer | GradientImageFilterPointer |
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| typedef Superclass::GradientImageFilterType | GradientImageFilterType |
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| typedef Superclass::GradientImagePointer | GradientImagePointer |
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| typedef Superclass::GradientImageType | GradientImageType |
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| typedef Superclass::GradientPixelType | GradientPixelType |
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| typedef vnl_sparse_matrix< HessianValueType > | HessianType |
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| typedef DerivativeType::ValueType | HessianValueType |
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| typedef ImageSamplerType::OutputVectorContainerPointer | ImageSampleContainerPointer |
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| typedef ImageSamplerType::OutputVectorContainerType | ImageSampleContainerType |
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| typedef ImageSamplerType::Pointer | ImageSamplerPointer |
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| typedef ImageSamplerBase< FixedImageType > | ImageSamplerType |
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| typedef Superclass::InputPointType | InputPointType |
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| typedef Superclass::InterpolatorPointer | InterpolatorPointer |
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| typedef Superclass::InterpolatorType | InterpolatorType |
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| typedef Superclass::MeasureType | MeasureType |
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| typedef Superclass::MovingImageConstPointer | MovingImageConstPointer |
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| typedef FixedArray< double, Self::MovingImageDimension > | MovingImageDerivativeScalesType |
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| typedef MovingImageLimiterType::OutputType | MovingImageLimiterOutputType |
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| typedef MovingImageLimiterType::Pointer | MovingImageLimiterPointer |
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| typedef LimiterFunctionBase< RealType, MovingImageDimension > | MovingImageLimiterType |
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| typedef Superclass::MovingImageMaskPointer | MovingImageMaskPointer |
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| typedef ImageMaskSpatialObject< itkGetStaticConstMacro(MovingImageDimension) > | MovingImageMaskSpatialObject2Type |
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| typedef Superclass::MovingImageMaskType | MovingImageMaskType |
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| typedef Superclass::MovingImagePixelType | MovingImagePixelType |
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| typedef MovingImageType::Pointer | MovingImagePointer |
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| typedef MovingImageType::RegionType | MovingImageRegionType |
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| typedef Superclass::MovingImageType | MovingImageType |
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| typedef AdvancedTransformType::NumberOfParametersType | NumberOfParametersType |
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| typedef Superclass::OutputPointType | OutputPointType |
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| typedef Superclass::ParametersType | ParametersType |
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| typedef SmartPointer< Self > | Pointer |
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| typedef Superclass::RealType | RealType |
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| typedef TransformType::ScalarType | ScalarType |
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| typedef AdvancedImageToImageMetric | Self |
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| typedef ImageToImageMetric< TFixedImage, TMovingImage > | Superclass |
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| typedef itk::PlatformMultiThreader | ThreaderType |
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| typedef ThreaderType::WorkUnitInfo | ThreadInfoType |
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| typedef Superclass::TransformJacobianType | TransformJacobianType |
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| typedef Superclass::TransformParametersType | TransformParametersType |
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| typedef Superclass::TransformPointer | TransformPointer |
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| typedef Superclass::TransformType | TransformType |
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|
| virtual const char * | GetClassName () const |
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| void | GetDerivative (const TransformParametersType ¶meters, DerivativeType &derivative) const override |
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| virtual const bool & | GetSubtractMean () |
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| MeasureType | GetValue (const TransformParametersType ¶meters) const override |
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| void | GetValueAndDerivative (const TransformParametersType ¶meters, MeasureType &value, DerivativeType &derivative) const override |
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| void | GetValueAndDerivativeSingleThreaded (const TransformParametersType ¶meters, MeasureType &value, DerivativeType &derivative) const |
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| | itkStaticConstMacro (FixedImageDimension, unsigned int, FixedImageType::ImageDimension) |
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| | itkStaticConstMacro (MovingImageDimension, unsigned int, MovingImageType::ImageDimension) |
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| virtual void | SetSubtractMean (bool _arg) |
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| virtual void | SubtractMeanOff () |
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| virtual void | SubtractMeanOn () |
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| virtual void | BeforeThreadedGetValueAndDerivative (const TransformParametersType ¶meters) const |
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| virtual const char * | GetClassName () const |
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| virtual const FixedImageLimiterType * | GetFixedImageLimiter () |
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| virtual double | GetFixedLimitRangeRatio () const |
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| virtual ImageSamplerType * | GetImageSampler (void) const |
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| virtual const MovingImageDerivativeScalesType & | GetMovingImageDerivativeScales () |
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| virtual const MovingImageLimiterType * | GetMovingImageLimiter () |
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| virtual double | GetMovingLimitRangeRatio () const |
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| virtual double | GetRequiredRatioOfValidSamples () const |
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| virtual bool | GetScaleGradientWithRespectToMovingImageOrientation () const |
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| virtual void | GetSelfHessian (const TransformParametersType ¶meters, HessianType &H) const |
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| const AdvancedTransformType * | GetTransform (void) const override |
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| virtual bool | GetUseFixedImageLimiter () const |
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| virtual bool | GetUseImageSampler () const |
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| virtual const bool & | GetUseMetricSingleThreaded () |
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| virtual bool | GetUseMovingImageDerivativeScales () const |
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| virtual bool | GetUseMovingImageLimiter () const |
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| virtual const bool & | GetUseMultiThread () |
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| void | Initialize (void) override |
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| | itkStaticConstMacro (FixedImageDimension, unsigned int, TFixedImage::ImageDimension) |
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| | itkStaticConstMacro (MovingImageDimension, unsigned int, TMovingImage::ImageDimension) |
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| virtual void | SetFixedImageLimiter (FixedImageLimiterType *_arg) |
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| virtual void | SetFixedLimitRangeRatio (double _arg) |
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| virtual void | SetImageSampler (ImageSamplerType *_arg) |
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| virtual void | SetMovingImageDerivativeScales (MovingImageDerivativeScalesType _arg) |
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| virtual void | SetMovingImageLimiter (MovingImageLimiterType *_arg) |
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| virtual void | SetMovingLimitRangeRatio (double _arg) |
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| virtual void | SetNumberOfWorkUnits (ThreadIdType numberOfThreads) |
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| virtual void | SetRequiredRatioOfValidSamples (double _arg) |
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| virtual void | SetScaleGradientWithRespectToMovingImageOrientation (bool _arg) |
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| virtual void | SetTransform (AdvancedTransformType *arg) |
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| virtual void | SetUseMetricSingleThreaded (bool _arg) |
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| virtual void | SetUseMovingImageDerivativeScales (bool _arg) |
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| virtual void | SetUseMultiThread (bool _arg) |
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| virtual void | UseMetricSingleThreadedOff () |
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| virtual void | UseMetricSingleThreadedOn () |
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| virtual void | UseMultiThreadOff () |
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| virtual void | UseMultiThreadOn () |
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| | AdvancedNormalizedCorrelationImageToImageMetric () |
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| void | AfterThreadedGetValueAndDerivative (MeasureType &value, DerivativeType &derivative) const override |
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| void | InitializeThreadingParameters (void) const override |
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| void | PrintSelf (std::ostream &os, Indent indent) const override |
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| void | ThreadedGetValueAndDerivative (ThreadIdType threadID) override |
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| void | UpdateDerivativeTerms (const RealType &fixedImageValue, const RealType &movingImageValue, const DerivativeType &imageJacobian, const NonZeroJacobianIndicesType &nzji, DerivativeType &derivativeF, DerivativeType &derivativeM, DerivativeType &differential) const |
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| | ~AdvancedNormalizedCorrelationImageToImageMetric () override |
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| | AdvancedImageToImageMetric () |
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| virtual void | AfterThreadedGetValue (MeasureType &value) const |
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| virtual void | AfterThreadedGetValueAndDerivative (MeasureType &value, DerivativeType &derivative) const |
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| virtual void | CheckForAdvancedTransform (void) |
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| virtual void | CheckForBSplineInterpolator (void) |
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| virtual void | CheckForBSplineTransform (void) const |
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| virtual void | CheckNumberOfSamples (unsigned long wanted, unsigned long found) const |
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| virtual bool | EvaluateMovingImageValueAndDerivative (const MovingImagePointType &mappedPoint, RealType &movingImageValue, MovingImageDerivativeType *gradient) const |
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| virtual bool | EvaluateTransformJacobian (const FixedImagePointType &fixedImagePoint, TransformJacobianType &jacobian, NonZeroJacobianIndicesType &nzji) const |
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| virtual void | EvaluateTransformJacobianInnerProduct (const TransformJacobianType &jacobian, const MovingImageDerivativeType &movingImageDerivative, DerivativeType &imageJacobian) const |
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| virtual void | InitializeImageSampler (void) |
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| virtual void | InitializeLimiters (void) |
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| virtual void | InitializeThreadingParameters (void) const |
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| virtual bool | IsInsideMovingMask (const MovingImagePointType &point) const |
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| | itkAlignedTypedef (ITK_CACHE_LINE_ALIGNMENT, PaddedGetValueAndDerivativePerThreadStruct, AlignedGetValueAndDerivativePerThreadStruct) |
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| | itkAlignedTypedef (ITK_CACHE_LINE_ALIGNMENT, PaddedGetValuePerThreadStruct, AlignedGetValuePerThreadStruct) |
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| | itkPadStruct (ITK_CACHE_LINE_ALIGNMENT, GetValueAndDerivativePerThreadStruct, PaddedGetValueAndDerivativePerThreadStruct) |
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| | itkPadStruct (ITK_CACHE_LINE_ALIGNMENT, GetValuePerThreadStruct, PaddedGetValuePerThreadStruct) |
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| void | LaunchGetValueAndDerivativeThreaderCallback (void) const |
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| void | LaunchGetValueThreaderCallback (void) const |
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| void | PrintSelf (std::ostream &os, Indent indent) const override |
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| virtual void | SetUseFixedImageLimiter (bool _arg) |
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| virtual void | SetUseImageSampler (bool _arg) |
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| virtual void | SetUseMovingImageLimiter (bool _arg) |
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| virtual void | ThreadedGetValue (ThreadIdType threadID) |
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| virtual void | ThreadedGetValueAndDerivative (ThreadIdType threadID) |
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| virtual bool | TransformPoint (const FixedImagePointType &fixedImagePoint, MovingImagePointType &mappedPoint) const |
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| | ~AdvancedImageToImageMetric () override |
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Inheritance diagram for itk::AdvancedNormalizedCorrelationImageToImageMetric< TFixedImage, TMovingImage >:
1.9.4 