SoMultiscaleStructureEnhancementProcessing2d Class Reference
[Texture Filters]

SoMultiscaleStructureEnhancementProcessing2d engine More...

#include <ImageViz/Engines/ImageFiltering/TextureFilters/SoMultiscaleStructureEnhancementProcessing2d.h>

Inheritance diagram for SoMultiscaleStructureEnhancementProcessing2d:

Public Types
enum	TensorType { HESSIAN = 0, GRADIENT = 1 }
enum	Lightness { BRIGHT = 0, DARK = 1 }
enum	StructureType { ROD = 0, BALL = 1 }
Public Member Functions
	SoMultiscaleStructureEnhancementProcessing2d ()
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). Let $\lambda_1 > \lambda_2$ be the 2 eigenvalues of the extracted tensor.

The score for StructureType2D::ROD corresponds to :

$\text{score}{\text{ROD}} = \exp \left(-\frac{ \big(\frac{ \lambda{ 2 } }{\lambda_{ 1 }} \big)^{ 2 } } {2 \beta^{ 2 } } \right) \left( 1 - \exp \big(-\frac{ S^{ 2 } }{2c ^ {2}} \big) \right)$

This score favors anisotropic tensors.

The score for StructureType2D::BALL structures is computed as follows :

$\text{ score }_{ \text{ BALL } } = \left( 1 - \exp(-\frac{ \big(\frac{ \lambda_{ 2 } }{\lambda_{ 1 }} \big) ^{ 2 } }{2 \beta^{ 2 } }) \right) \left(1 - \exp \big(-\frac{ S^{ 2 } }{2c ^ {2}} \big) \right) \\$

This score favors isotropic tensors.

where $S = \sqrt{ \lambda_{ 1 }^{2}\lambda_{ 2 }^{2} }$ is the tensor norm, $\beta$ 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.

The table below summarizes enhanced feature according to the parameters

Structure Type

$\lambda_1$