SoMultiscaleStructureEnhancementProcessing3d Class Reference
[Texture Filters]

ImageViz SoMultiscaleStructureEnhancementProcessing2d engine More...

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

Inheritance diagram for SoMultiscaleStructureEnhancementProcessing3d:
SoImageVizEngine SoEngine SoFieldContainer SoBase SoRefCounter SoTypedObject

List of all members.

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

ImageViz 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:

The principle of the algorithm can be summarized as follows :

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.

SEE ALSO

SoMultiscaleStructureEnhancementProcessing2d.

FILE FORMAT/DEFAULT


Library references: structureenhancementfilter3d


Member Enumeration Documentation

Enumerator:
BRIGHT 

Extracts bright structures from dark background.

DARK 

Extracts dark structures from bright background.

Enumerator:
ROD 

Extracts tubular structures.

BALL 

Extracts blob-like structures.

PLANE 

Extracts plate-like structures.

Enumerator:
HESSIAN 

Extracts the Hessian matrix.

GRADIENT 

Extracts the gradient tensor.


Constructor & Destructor Documentation

SoMultiscaleStructureEnhancementProcessing3d::SoMultiscaleStructureEnhancementProcessing3d (  ) 

Constructor.


Member Data Documentation

Input image.

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

The lightness type of structures to enhance.

Use enum Lightness. Default is BRIGHT

Output image.

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

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

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

Standard deviation step.

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

Shape of structures to extract.

Use enum StructureType. Default is ROD

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:

Open Inventor Toolkit reference manual, generated on 11 Nov 2019
Copyright © Thermo Fisher Scientific All rights reserved.
http://www.openinventor.com/