Gaussian filter used to compute Hessian on a 3d image. More...

IPSDKIPLFILTERING_API HessianXYZImg	ipsdk::imaproc::filter::gaussianHessian3dImg (const image::ImageConstPtr &pInImg, const ipReal32 inStdDev)
	wrapper function for Gaussian filter used to compute Hessian on a 3d image More...

IPSDKIPLFILTERING_API HessianXYZImg	ipsdk::imaproc::filter::gaussianHessian3dImg (const image::ImageConstPtr &pInImg, const ipReal32 inStdDevX, const ipReal32 inStdDevY, const ipReal32 inStdDevZ, const attr::GaussianCoverageConstPtr &pInOptHessianGaussianCoverage)
	wrapper function for Gaussian filter used to compute Hessian on a 3d image More...

IPSDKIPLFILTERING_API void	ipsdk::imaproc::filter::gaussianHessian3dImg (const image::ImageConstPtr &pInImg, const ipReal32 inStdDevX, const ipReal32 inStdDevY, const ipReal32 inStdDevZ, const attr::GaussianCoverageConstPtr &pInOptHessianGaussianCoverage, const image::ImagePtr &pOutHxxImg, const image::ImagePtr &pOutHxyImg, const image::ImagePtr &pOutHxzImg, const image::ImagePtr &pOutHyyImg, const image::ImagePtr &pOutHyzImg, const image::ImagePtr &pOutHzzImg)
	wrapper function for Gaussian filter used to compute Hessian on a 3d image More...

Detailed Description

Gaussian filter used to compute Hessian on a 3d image.

The GaussianHessian3dImg algorithm uses separable Gaussian derivarive and smoothing filters to compute the Hessian matrix coefficient on each voxels.

Let's consider the three 1d filters $G(x, \sigma)$ , $G_{\gamma}(x, \sigma)$ and $G_{\gamma \gamma}(x, \sigma)$ along the direction $\gamma \in \left\{ x, y \right\}$ :

$\begin{eqnarray*} G(x, \sigma) & = & \frac{1}{\sigma \sqrt{2 \pi}} \exp \left( - \frac{x^2}{2 \sigma^2} \right)\\ G_{\gamma}(x, \sigma) & = & -\frac{x}{\sigma^3 \sqrt{2 \pi}} \exp \left( - \frac{x^2}{2 \sigma^2} \right)\\ G_{\gamma \gamma}(x, \sigma) & = & \frac{x^2-\sigma^2}{\sigma^5 \sqrt{2 \pi}} \exp \left( - \frac{x^2}{2 \sigma^2} \right) \end{eqnarray*}$

$G(x, \sigma)$ is a smoothing function , $G_{\gamma}(x, \sigma)$ is the first order gaussian derivative and $G_{\gamma \gamma}(x, \sigma)$ is the second order Gaussian derivative along the directon $\gamma$ , $\gamma \in \left\{ x, y \right\}$ .

The kernels used for these filters have a size of $3\sigma$ . The Hessian coefficients are caultulated by a combination of these kernels:

$\begin{eqnarray*} OutHxxImg(x, y, z) & = & \left( \left( InImg(x, y, z) * G_{XX}(x, \sigma) \right) * G(y, \sigma) \right) * G(z, \sigma)\\ OutHxyImg(x, y, z) & = & \left( \left( InImg(x, y, z) * G_{X}(x, \sigma) \right) * G_{Y}(y, \sigma) \right) * G(z, \sigma)\\ OutHxzImg(x, y, z) & = & \left( \left( InImg(x, y, z) * G_{X}(x, \sigma) \right) * G_{Z}(z, \sigma) \right) * G(y, \sigma)\\ OutHyyImg(x, y, z) & = & \left( \left( InImg(x, y, z) * G_{YY}(y, \sigma) \right) * G(x, \sigma) \right) * G(z, \sigma)\\ OutHyzImg(x, y, z) & = & \left( \left( InImg(x, y, z) * G_{Y}(y, \sigma) \right) * G_{Z}(z, \sigma) \right) * G(x, \sigma)\\ OutHzzImg(x, y, z) & = & \left( \left( InImg(x, y, z) * G_{ZZ}(z, \sigma) \right) * G(x, \sigma) \right) * G(y, \sigma) \end{eqnarray*}$

See Gaussian Hessian 2d for an illustration of a 2d Gaussian Hessian result.

See also: https://en.wikipedia.org/wiki/Hessian_matrix

Attributes description

Attribute description for algorithm :

Name	ToolTip	Default Initializer
ipsdk::imaproc::attr::InImg3d	[Input] 3d image for operation	X
ipsdk::imaproc::attr::InStdDevX	[Input] standard deviation used for operation along X axis	X
ipsdk::imaproc::attr::InStdDevY	[Input] standard deviation used for operation along Z axis	X
ipsdk::imaproc::attr::InStdDevZ	[Input] standard deviation used for operation along Z axis	X
ipsdk::imaproc::attr::InOptHessianGaussianCoverage	[Input Optional] Parameter allowing to specify a gaussian distribution coverage for processing	X
ipsdk::imaproc::attr::OutHxxImg	[Output] image of hessian (x-x axis)	promoteUnary (_pOutHxxImg, _pInImg3d, ipsdk::imaproc::ePromoteUnaryType::ePUT_UpperSigned)
ipsdk::imaproc::attr::OutHxyImg	[Output] image of image of hessian (x-y axis)	promoteUnary (_pOutHxyImg, _pInImg3d, ipsdk::imaproc::ePromoteUnaryType::ePUT_UpperSigned)
ipsdk::imaproc::attr::OutHxzImg	[Output] image of hessian (x-z axis)	promoteUnary (_pOutHxzImg, _pInImg3d, ipsdk::imaproc::ePromoteUnaryType::ePUT_UpperSigned)
ipsdk::imaproc::attr::OutHyyImg	[Output] image of hessian (y-y axis)	promoteUnary (_pOutHyyImg, _pInImg3d, ipsdk::imaproc::ePromoteUnaryType::ePUT_UpperSigned)
ipsdk::imaproc::attr::OutHyzImg	[Output] image of image of hessian (y-z axis)	promoteUnary (_pOutHyzImg, _pInImg3d, ipsdk::imaproc::ePromoteUnaryType::ePUT_UpperSigned)
ipsdk::imaproc::attr::OutHzzImg	[Output] image of image of hessian (z-z axis)	promoteUnary (_pOutHzzImg, _pInImg3d, ipsdk::imaproc::ePromoteUnaryType::ePUT_UpperSigned)

Global Rule description

Global rule description for algorithm :
ipsdk::imaproc::matchSize (_pInImg3d,_pOutHxxImg) &&
ipsdk::imaproc::matchSizeAndType (_pOutHxxImg,_pOutHxyImg) &&
ipsdk::imaproc::matchSizeAndType (_pOutHxxImg,_pOutHxzImg) &&
ipsdk::imaproc::matchSizeAndType (_pOutHxxImg,_pOutHyyImg) &&
ipsdk::imaproc::matchSizeAndType (_pOutHxxImg,_pOutHyzImg) &&
ipsdk::imaproc::matchSizeAndType (_pOutHxxImg,_pOutHzzImg)

Example of Python code :

Example imports

import PyIPSDK

import PyIPSDK.IPSDKIPLFiltering as filter

Code Example

    # opening of input images
    inImg = PyIPSDK.loadTiffImageFile(inputImgPath)
    
    # gaussian gradient filter 2d computation
    outHxxImg, outHxyImg, outHxzImg, outHyyImg, outHyzImg, outHzzImg = filter.gaussianHessian3dImg(inImg, 1.5)

Example of C++ code :

Example informations

Associated library

IPSDKIPLFiltering

Header file

#include <IPSDKIPL/IPSDKIPLFiltering/Processor/GaussianHessian3dImg/GaussianHessian3dImg.h>

Code Example

    // opening input image
    ImagePtr pInImg3d = loadTiffImageFile(inputImgPath, eTiffDirectoryMode::eTDM_Volume);
        
    // compute gaussian gradient on input image
    HessianXYZImg hessianXYZ = gaussianHessian3dImg(pInImg3d, inStdDev, inStdDev, inStdDev, createGaussianCoverage(inOptGaussianRatio, minHalfKernelSize));

See also: GaussianHessian3dImgLvl1

Function Documentation

◆ gaussianHessian3dImg() [1/3]

IPSDKIPLFILTERING_API HessianXYZImg ipsdk::imaproc::filter::gaussianHessian3dImg	(	const image::ImageConstPtr &	pInImg,
		const ipReal32	inStdDev
	)

wrapper function for Gaussian filter used to compute Hessian on a 3d image

Exceptions

ipsdk::processor::IPSDKBaseProcessingException on failure

◆ gaussianHessian3dImg() [2/3]

IPSDKIPLFILTERING_API HessianXYZImg ipsdk::imaproc::filter::gaussianHessian3dImg	(	const image::ImageConstPtr &	pInImg,
		const ipReal32	inStdDevX,
		const ipReal32	inStdDevY,
		const ipReal32	inStdDevZ,
		const attr::GaussianCoverageConstPtr &	pInOptHessianGaussianCoverage
	)

wrapper function for Gaussian filter used to compute Hessian on a 3d image

Exceptions

ipsdk::processor::IPSDKBaseProcessingException on failure

◆ gaussianHessian3dImg() [3/3]

IPSDKIPLFILTERING_API void ipsdk::imaproc::filter::gaussianHessian3dImg	(	const image::ImageConstPtr &	pInImg,
		const ipReal32	inStdDevX,
		const ipReal32	inStdDevY,
		const ipReal32	inStdDevZ,
		const attr::GaussianCoverageConstPtr &	pInOptHessianGaussianCoverage,
		const image::ImagePtr &	pOutHxxImg,
		const image::ImagePtr &	pOutHxyImg,
		const image::ImagePtr &	pOutHxzImg,
		const image::ImagePtr &	pOutHyyImg,
		const image::ImagePtr &	pOutHyzImg,
		const image::ImagePtr &	pOutHzzImg
	)

wrapper function for Gaussian filter used to compute Hessian on a 3d image

Exceptions

ipsdk::processor::IPSDKBaseProcessingException on failure