SoMultiscaleStructureEnhancementProcessing3d Class Reference
[Texture Filters]

SoMultiscaleStructureEnhancementProcessing2d engine More...

#include <ImageViz/Engines/ImageFiltering/TextureFilters/SoMultiscaleStructureEnhancementProcessing3d.h>

Inheritance diagram for SoMultiscaleStructureEnhancementProcessing3d:

Public Types
enum	TensorType { HESSIAN = 0, GRADIENT = 1 }
enum	Lightness { BRIGHT = 0, DARK = 1 }
enum	StructureType { ROD = 0, BALL = 1, PLANE = 2 }
Public Member Functions
	SoMultiscaleStructureEnhancementProcessing3d ()
Public Attributes
SoSFImageDataAdapter	inImage
SoSFEnum	tensorType
SoSFVec2f	standardDeviationRange
SoSFFloat	standardDeviationStep
SoSFEnum	lightness
SoSFEnum	structureType
SoImageVizEngineOutput < SoSFImageDataAdapter, SoImageDataAdapter * >	outImage

Detailed Description

SoMultiscaleStructureEnhancementProcessing2d engine

Overview

The purpose of this algorithm is to enhance structures of interest from an image using a multi scale analysis. The result of this algorithm is a score image that can be used with the goal of segmenting the input image.

The SoMultiscaleStructureEnhancement filters compute a score between 0 and 1 for each pixel, 1 representing a good matching with a structure model and 0 a background pixel. This provides a powerful technique for automatically identifying structures such as blood vessels. The score can be computed either on an Hessian matrix to detect ridge structures or on a Gradient tensor for object edges and corners. The structure models available are:

Balls (circular structures with Hessian in 2D, spherical in 3D, object corners with Gradient tensor)
Rods (linear structures)
Plates (only available in 3D)

The principle of the algorithm can be summarized as follows :

A set of tensor fields is extracted from the image by filtering the image at different scales.
A score image is extracted from each tensor field by analyzing the eigenvalues of tensors.
The final score is obtained by selecting the maximum of all score images.

The following publication describes this algorithm when applied to detect Rod structures with the Hessian matrix: A.F.Frangi, W.J.Niessen, K.L.Vincken, M.A.Viergever, "Multiscale vessel enhancement filtering", Lecture Notes in Computer Science(MICCAI), vol. 1496, pp. 130-137, 1998.

Tensor Extraction

2 modes are available for computing the tensor field; the GRADIENT mode and the HESSIAN mode. The first one is based on the gradient tensor the second one on the hessian matrix.

GRADIENT mode

In the GRADIENT mode, the gradient tensor is extracted. This tensor also referred to as structure tensor or second order moment matrix, is a matrix derived from the gradient of the image. This matrix summarizes the predominant directions of the gradient around the voxel of interest.

$S_w(p) = \left( \begin{array}{cc} \int w(r) (I_x(p - r)) ^ 2\, d r & \int w(r) I_x(p - r)I_y(p - r)\, d r \\ \int w(r) I_x(p - r)I_y(p - r)\, d r & \int w(r) (I_y(p - r)) ^ 2\, d r \end{array} \right)$

Where $w(r)$ is a gaussian kernel controlling the scale of analysis.

HESSIAN mode

In this mode, the tensor field is based on the extraction of the hessian matrix of the image. This hessian matrix is computed by filtering the image with the derivative of a gaussian kernel.The standard deviation of the kernel controls the scale of analysis.

Feature extraction

The parameter structureType controls the type of structure that is extracted from the tensor field(ROD/BALL/PLANE). The computation is based on eigen values $\lambda_{1}$ , $\lambda_{2}$ and $\lambda_{3}$ where $\mid \lambda_{1} \mid \geq \mid \lambda_{2} \mid \geq \mid \lambda_{3} \mid$ .

Let first introduce

$\mathcal{R}_b = \frac{ \lambda_1 }{ \sqrt{ \lambda_2 \lambda_3 } }$ , and

$\mathcal{R}_a = \frac{ \lambda_2 }{ \lambda_3 }$

The first ratio attains its maximum for blob-like structure. The second ratio distinguishes plate-like and line-like structures.

The score for StructureType3D::ROD corresponds to :

$\text{score}_{\text{ROD}} = (1-\exp(-\frac{\mathcal{R}_a^2}{2\alpha^2}))\exp(-\frac{\mathcal{R}_b^2}{2\beta^2})(1-\exp(-\frac{S^2}{2c^2}))$

The score for StructureType3D::BALL is computed as follow :

$\text{score}_{\text{BALL}} = (1-\exp(-\frac{\mathcal{R}_a^2}{2\alpha^2}))(1-\exp(-\frac{\mathcal{R}_b^2}{2\beta^2}))(1-\exp(-\frac{S^2}{2c^2}))$

The score for StructureType3D::PLANE is computed as follow :

$\text{score}_{\text{PLANE}} = \exp(-\frac{\mathcal{R}_a^2}{2\alpha^2})\exp(-\frac{\mathcal{R}_b^2}{2\beta^2})(1-\exp(-\frac{S^2}{2c^2}))$

where $S$ is the tensor norm $S = \sqrt{\sum \lambda_i^2}$ , $\alpha$ is a threshold which controls the flatness sensitivity, $\beta$ is a threshold which controls the blobness sensitivity, and $ c $ is a sensitivity threshold which controls the noise influence. $c = \text{noiseCutoff} \times S_{max}$ with $S_{max}$ the maximum Hessian norm in the image.

In the HESSIAN mode, the lightness parameter limits the feature extraction to dark or bright objects by analyzing the sign of eigenvalues. This parameter is ignored in GRADIENT mode where tensors are positive definite matrices.

FILE FORMAT/DEFAULT

inImage	NULL
tensorType	HESSIAN
standardDeviationRange	1.0f 3.0f
standardDeviationStep	1.0f
lightness	BRIGHT
structureType	ROD

Library references: structureenhancementfilter3d

Member Enumeration Documentation

enum SoMultiscaleStructureEnhancementProcessing3d::Lightness

Enumerator:

BRIGHT	Extracts bright structures from dark background.
DARK	Extracts dark structures from bright background.

enum SoMultiscaleStructureEnhancementProcessing3d::StructureType

Enumerator:

ROD	Extracts tubular structures.
BALL	Extracts blob-like structures.
PLANE	Extracts plate-like structures.

enum SoMultiscaleStructureEnhancementProcessing3d::TensorType

Enumerator:

HESSIAN	Extracts the Hessian matrix.
GRADIENT	Extracts the gradient tensor.

Constructor & Destructor Documentation

SoMultiscaleStructureEnhancementProcessing3d::SoMultiscaleStructureEnhancementProcessing3d ( )

Constructor.

Member Data Documentation

SoSFImageDataAdapter SoMultiscaleStructureEnhancementProcessing3d::inImage

Input image.

Type of the image can be integer or floating. Default value is NULL. Supported types include: grayscale image.

SoSFEnum SoMultiscaleStructureEnhancementProcessing3d::lightness

The lightness type of structures to enhance.

Use enum Lightness. Default is BRIGHT

SoImageVizEngineOutput<SoSFImageDataAdapter,SoImageDataAdapter*> SoMultiscaleStructureEnhancementProcessing3d::outImage

Output image.

Type of the output image is forced to float. Default value is NULL. Supported types include: grayscale image.

SoSFVec2f SoMultiscaleStructureEnhancementProcessing3d::standardDeviationRange

Standard deviation of the Gaussian kernel at the minimum and maximum scale.

Default value is SbVec2f(1.0f,3.0f).

SoSFFloat SoMultiscaleStructureEnhancementProcessing3d::standardDeviationStep

Standard deviation step.

Structures will be detected from min to max standard deviation at a pitch of this value. Default value is 1.0f.

SoSFEnum SoMultiscaleStructureEnhancementProcessing3d::structureType

Shape of structures to extract.

Use enum StructureType. Default is ROD

SoSFEnum SoMultiscaleStructureEnhancementProcessing3d::tensorType

Defines whether the command will use the gradient tensor or the hessian matrix.

Use enum TensorType. Default is HESSIAN

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

ImageViz/Engines/ImageFiltering/TextureFilters/SoMultiscaleStructureEnhancementProcessing3d.h

SoMultiscaleStructureEnhancementProcessing3d Class Reference [Texture Filters]

Public Types

Public Member Functions

Public Attributes

Detailed Description

SEE ALSO

FILE FORMAT/DEFAULT

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Data Documentation

SoMultiscaleStructureEnhancementProcessing3d Class Reference
[Texture Filters]