Image Edge Enhancing Coherence Filter Toolbox

Advanced 2D/3D noise removal and edge enhancing with anisotropic diffusion filtering ( Weickert )

Description

Introduction:
This toolbox will perform Anisotropic Non-Linear Diffusion filtering on a 2D gray/color or 3D image. This filtering will reduce the image noise while preserving the region edges, and also enhancing the edges by smoothing along them.

This is one of the more advanced image enhancement methods available, and also contains HDCS from october 2009. The result looks like an artist painted the image, with clear brush strokes along the image edges and ridges, see screen-shot.

My paper about the code is included, "Coherence Filtering to Enhance the Mandibular Canal in Cone-Beam CT Data", IEEE-EMBS Benelux Chapter Symposium, 2009.

Method:
The basis of the method used is the one introduced by Weickert.
1, Calculate Hessian from every pixel of the Gaussian smoothed input image
2, Gaussian Smooth the Hessian, and calculate its eigenvectors and values (Image edges give large eigenvalues, and the eigenvectors corresponding to those eigenvalues describe the direction of the edge)
3, The eigenvectors are used as diffusion tensor directions. The amplitude of the diffusion in those 3 directions is based on the eigen values and determined by Weickerts equation.
4, An Finite Difference scheme is used to do the diffusion
5, Back to step 1, till a certain diffusion time is reached.

Diffusion schemes:
There are several diffusion schemes available: standard, implicit, nonegative discretization, and also a special rotation invariant scheme.

Mex Files:
All 3D files are not only available as Matlab but also as C-code /MEX files, to increase speed and reduce the amount of memory used. Compile the c-code by executing compile_c_files.m.

Literature (Full list in the included paper):
- Weickert : "A Scheme for Coherence-Enhancing Diffusion Filtering with Optimized Rotation Invariance"
- Mendrik et al, "Noise Reduction in Computed Tomography Scans Using 3-D Anisotropic Hybrid Diffusion With Continuous Switch", October 2009
- Weickert : "Anisotropic Diffusion in Image Processing", Thesis 1996
- Laura Fritz : "Diffusion-Based Applications for Interactive Medical Image Segmentation"
- Siham Tabik, et al. : "Multiprocessing of Anisotropic Nonlinear Diffusion for filtering 3D image"

Usage:
Read the help of CoherenceFilter, compile the c-code and try the examples in the help.

Please report bugs, successes and questions.

• Required Products: Image Processing Toolbox
• MATLAB release: MATLAB 7.9 (2009b)

Other Files

CoherenceFilter.m,
compile_c_files.m,
functions/derivatives.c,
functions/derivatives.m,
functions/imgaussian.c,
functions/imgaussian.m,
functions/showcs3.fig,
functions/showcs3.m,
functions2D/CoherenceFilterStep2D.c,
functions2D/CoherenceFilterStep2D.m,
functions2D/CoherenceFilterStep2D_functions.c,
functions2D/ConstructDiffusionTensor2D.m,
functions2D/diffusion_scheme_2D_implicit.m,
functions2D/diffusion_scheme_2D_non_negativity.m,
functions2D/diffusion_scheme_2D_rotation_invariant.m,
functions2D/diffusion_scheme_2D_standard.m,
functions2D/EigenVectors2D.m,
functions2D/StructureTensor2D.m,
functions3D/CoherenceFilterStep3D.c,
functions3D/CoherenceFilterStep3D.m,
functions3D/CoherenceFilterStep3D_functions.c,
functions3D/diffusion_scheme_3D_implicit.m,
functions3D/diffusion_scheme_3D_non_negativity.c,
functions3D/diffusion_scheme_3D_non_negativity.m,
functions3D/diffusion_scheme_3D_rotation_invariant.c,
functions3D/diffusion_scheme_3D_rotation_invariant.m,
functions3D/diffusion_scheme_3D_standard.c,
functions3D/diffusion_scheme_3D_standard.m,
functions3D/EigenDecomposition3.c,
functions3D/EigenDecomposition3.h,
functions3D/EigenVectors3D.c,
functions3D/EigenVectors3D.m,
functions3D/StructureTensor2DiffusionTensor3D.c,
functions3D/StructureTensor2DiffusionTensor3D.m,
functions3D/StructureTensor3D.m,
images/sphere.mat,
images/sync.png,
images/sync_noise.png,
license.txt,
Literature/Kroon_CoherenceFiltering.pdf

[Elmar]

Thanks for sharing this tool! works very well and fast, but i'm experiencing some problems:
I'm trying to filter a 3D MRI volume of size 227x227x147. Depending on the value of 'rho' I use I get a variable number of slices in the third dimension that are all 'NaN'. The bigger rho, the more NaN slices are in the output image volume. For every value of T used the number of NaN-slices accumulates, so that after several timesteps the whole image volume consists of NaNs.
What could be the reason for the NaNs in the output?

My original image is single and normalized to a range of 0 to 1 and does not contain any NaNs.
thx, Elmar

[Dirk-Jan Kroon]

* Elmar,

Thank you for your report, I never experienced NaN's my self.
Maybe you can add a small value to rule out division by zero.

If you still have problems, maybe you can share a part of the volume data with me?

Thanx, Dirk-Jan

[Elmar]

I permuted the directions of the volume so that it is 147x227x227, now it works perfectly

[Dirk-Jan Kroon]

*Elmar
Thank you for sharing the solution for your NaN problem.
Now, I know it's probably caused by a boundary check problem.

Dirk-Jan

[Dirk-Jan Kroon]

I uploaded a new version with derivative boundary check bug fixed, probably tomorrow online. thnx Elmar.

[bin yao]

A great code for studying diffusion filtering implementation. Thanks a lot for sharing.

I have two questions about the scheme
1) implicit scheme : does it means using semi-implicit AOS scheme to implementation?
 
2) diffusion_scheme_3D_implicit.m , you said "!! Scheme is unstable, and not ready to use yet." what is the problem?