Insight Journal - Implementation of local structure tensor and enhancement anisotropic diffusion filters in ITK

Implementation of local structure tensor and enhancement anisotropic diffusion filters in ITK

Please use this identifier to cite or link to this publication: http://hdl.handle.net/10380/3199

Published in The Insight Journal - 2010 July-December.

Submitted by Andinet Enquobahrie on 08-17-2010.

This paper describes implementation of local structure tensor and anisotropic enhancement diffusion filters using the Insight Toolkit. The anisotropic diffusion filters are implemented using ITK's finite difference solver framework. The filters are used to implement the 3D edge-enhancing diffusion ( EED), coherence-enhancing diffusion (CED) and hybrid diffusion with continuous switch(HDCS) noise filtering algorithms described in Mendrik et al[1].

The most up-to-date version of the code presented in this paper is distributed with the TubeTK project:
http://public.kitware.com/Wiki/TubeTK

Data

3 Datasets (298Kb)

PrimitiveObjects.mha (244Kb)
CroppedWholeLungCTScan.mhd (350b)
CroppedWholeLungCTScan.raw (54Kb)

Code

Automatic Testing Results by Insight-Journal Dashboard on Tue Jan 29 16:07:53 2013 for revision #3

expertise: 5 sensitivity: 3

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Automatic Testing Results by Insight-Journal Dashboard on Thu Aug 19 03:36:47 2010 for revision #1

expertise: 5 sensitivity: 3.3

Reviews

Working ITK3 and ITK4 version Anisotropic Diffusion Filters by Adrienne Mendrik on 2013-12-18 09:54:30 for revision #3

expertise: 5 sensitivity: 4

Summary:

I made some more changes to the ITK3 version (AnisotropicFilters-itk3.20.0) of the anisotropic diffusion filters and also adjusted the code to work in ITK4 (AnisotropicFilters-itk4.4.2). I think they work properly now.

AnisotropicDiffusionFilters.zip (158Kb)

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Adjusted code by Adriënne Mendrik on 2012-09-27 04:39:14 for revision #3

expertise: 5 sensitivity: 4

Summary:

I adjusted the itk code, such that it gives similar results as my implementation of the HDCS, EED and CED filter that I used for my paper Mendrik et al [1].

Below a list of changes:

Parameter rho added to files (used to smooth structure tensor): itkAnisotropicHybridDiffusionImageFilterTest, itkAnisotropicHybridDiffusionImageFilter (.h and .txx), itkStructureTensorRecursiveGaussianImageFilter (.h and .txx), itkAnisotropicCoherenceEnhancingDiffusionImageFilterTest, itkAnisotropicCoherenceEnhancingDiffusionImageFilter (.h and .txx)

Smoothing of the structure tensor components added by Fethallah only smoothed in one direction, which is incorrect. Therefore I changed the smoothing filter to "DiscreteGaussianImageFilter" which smoothes in all three directions (isotropic), otherwise filtering results are incorrect. Probably another filter can also be used, but just make sure that filtering is performed in all three directions using rho as the scale parameter. Changed in: itkStructureTensorRecursiveGaussianImageFilter

Text adjusted in itkAnisotropicCoherenceEnhancingDiffusionImageFilterTest: Edge_Enhanced_Output_Image --> Coherence_Enhanced_Output_Image

The third eigenvalue of the diffusion tensor in the CED filter should be set according to the paper of Weickert. In the hybrid filter I used an alternative equation, but in my opinion the CED filter should be implemented according to the original version of CED by Weickert: Joachim Weickert, "Coherence-Enhancing Diffusion Filtering", International Journal of Computer Vision 31(2/3), 111–127 (1999). So I changed the setting of lambda3 in the file: itkAnisotropicCoherenceEnhancingDiffusionImageFilter.txx

Correct sorting of the eigenvectors in "UpdateDiffusionTensorImage()" of all three filters: itkAnisotropicCoherenceEnhancingDiffusionImageFilter.txx, itkAnisotropicEdgeEnhancementDiffusionImageFilter.txx, itkAnisotropicHybridDiffusionImageFilter.txx

AdjustedAnDiffCode.zip (24Kb)

Error: Eigenvectors of the structure tensor are not sorted! by Adriënne Mendrik on 2011-12-09 06:20:22 for revision #1

expertise: 5 sensitivity: 4.3

Summary:

Dear authors,

Thanks for implementing these filters in ITK. However, I agree with Fethallah Benmansour that there was a loss of precision in the structure tensor code and the outer product components of the structure tensor needed to be smoothed using an additional parameter rho.

I found another error in the function "UpdateDiffusionTensorImage()" of all three filters: itkAnisotropicCoherenceEnhancingDiffusionImageFilter.txx, itkAnisotropicEdgeEnhancementDiffusionImageFilter.txx, itkAnisotropicHybridDiffusionImageFilter.txx.

The eigenvalues of the structure tensor are neatly ordered in decreasing order, however the corresponding eigenvectors of the structure tensor are not! This will cause all diffusion filters (EED, CED, HDCS) to work incorrectly...

Hypothesis:

The diffusion tensor is based on the orientation of the structure tensor. The first eigenvector of the structure tensor is assumed to point into the direction with the highest contrast (largest eigenvalue), however, in the current version of the code, the first eigenvector points into the direction of the lowest contrast (still sorted in ascending order). Because the eigenvalues are sorted, the largest eigenvalue is 'coupled' to the eigenvector with originally the lowest eigenvalue, therefore filtering across edges will take place instead of along edges...

Evidence:

The eigenvectors can be ordered after ordering the eigenvalues in the function UpdateDiffusionTensorImage(), by for example adding the following code:

    unsigned int vectorLength = 3; // Eigenvector length
    EigenVectorMatrixType eigenVectorMatrix;
    eigenVectorMatrix = eigenVectorImageIterator.Get();

    itk::VariableLengthVector<double> firstEigenVector( vectorLength );
    itk::VariableLengthVector<double> secondEigenVector( vectorLength );
    itk::VariableLengthVector<double> thirdEigenVector( vectorLength );
    for ( unsigned int i=0; i < vectorLength; i++ ) {
      // Get eigenvectors belonging to eigenvalue order
      firstEigenVector[i] = eigenVectorMatrix[largestEigenValueIndex][i];
      secondEigenVector[i] = eigenVectorMatrix[middleEigenValueIndex][i];
      thirdEigenVector[i] = eigenVectorMatrix[smallestEigenValueIndex][i];

      // Set eigenVectorMatrix in correct order
      eigenVectorMatrix[0][i] = firstEigenVector[i];
      eigenVectorMatrix[1][i] = secondEigenVector[i];
      eigenVectorMatrix[2][i] = thirdEigenVector[i];
    }

A couple of errors by Fethallah Benmansour on 2011-01-21 11:58:22 for revision #1

expertise: 5 sensitivity: 2.7

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Quick Comments

Comment by Andinet Enquobahrie

Adrienne and Fethallah,

Thanks for your feedback. We have uploaded a revised version of the source code incorporating your bug fixes.

Let us know if you have any more questions.

Andinet

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Paper Id:	748
Categories:	Anisotropic blurring filters, Blurring filters, Filtering
Keywords:	Noise filtering, Diffusion, Anisotropic, Tensor
Toolkits:	ITK
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Status:	Open for public review

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