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### Highlights from Image Edge Enhancing Coherence Filter Toolbox

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# Image Edge Enhancing Coherence Filter Toolbox

### Dirk-Jan Kroon (view profile)

30 Sep 2009 (Updated )

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

File Information
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 papers about the code are included:
- "Coherence Filtering to Enhance the Mandibular Canal in Cone-Beam CT Data", IEEE-EMBS Benelux Chapter Symposium, 2009.
- "Optimized Anisotropic Rotational Invariant Diffusion Scheme on Cone-Beam CT", MICCAI, 2010

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 rotation invariant scheme, and a novel diffusion scheme with new optimized derivatives.

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.

Acknowledgements
Required Products Image Processing Toolbox
MATLAB release MATLAB 7.9 (R2009b)
10 Jun 2016 Charilaos Mylonas

### Charilaos Mylonas (view profile)

04 May 2016 antonius vandongen

28 May 2015 Aasd

### Aasd (view profile)

good job

20 May 2015 Ilya Belevich

### Ilya Belevich (view profile)

10 Apr 2015 David

### David (view profile)

Nice toolbox but I have two issues:
First your default T value is 2 not 5 as described in the help text.

Second in the main while loop for 3D you compare the Scheme strings and look for R:
if(strcmpi(Options.Scheme,'R'))
u=CoherenceFilterStep3D(u,Options);
else
u=Anisotropic_step3D(u,Options);
end

in Anisotropic_step3D you then look again for R:
switch lower(Options.Scheme)
case 'r'
u=diffusion_scheme_3D_rotation_invariant(u,Dxx,Dxy,Dxz,Dyy,Dyz,Dzz,Options.dt);

So diffusion_scheme_3D_rotation_invariant will actually never be called.
I don't know if this intentional, since for 2D your first comparison looks very different:

if(strcmpi(Options.Scheme,'R')&&(Options.eigenmode==0)&&(exist('CoherenceFilterStep2D')==3))
u=CoherenceFilterStep2D(u,Options);
else
u=Anisotropic_step2D(u,Options);
end

30 Jan 2014 Christopher

### Christopher (view profile)

I'd like to agree with / confirm Michelle's comment. compile_c_files gives an error " mex: no file name given." unless you change "diffusion_scheme_3D_novel_getUpdate" to "diffusion_scheme_3D_novel_getUpdate.c"
Thanks!

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10 May 2013 Michele

### Michele (view profile)

Hi,
there's a little typo in compile_c_files.m.
Last file to be compiled has not the .c extension.
This: "diffusion_scheme_3D_novel_getUpdate.c"
Thanks.

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20 Mar 2013 Sourin

### Sourin (view profile)

solved! it was some mac os problem with gcc!

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20 Mar 2013 Sourin

### Sourin (view profile)

Hi

I am getting the allowing errorâ€¦. any help is greatly appreciated. I am using matlab 2012b on Mac os. thanks

Sourin

derivatives.c:24: warning: incompatible implicit declaration of built-in function 'malloc'
derivatives.c:57: warning: incompatible implicit declaration of built-in function 'malloc'
derivatives.c:110: warning: incompatible implicit declaration of built-in function 'malloc'
derivatives.c:195: warning: incompatible implicit declaration of built-in function 'malloc'
derivatives.c:280: warning: incompatible implicit declaration of built-in function 'malloc'
derivatives.c:364: warning: incompatible implicit declaration of built-in function 'malloc'
derivatives.c:449: warning: incompatible implicit declaration of built-in function 'malloc'
derivatives.c:533: warning: incompatible implicit declaration of built-in function 'malloc'

mex: compile of ' "derivatives.c"' failed.

Error using mex (line 206)
Unable to complete successfully.

Error in compile_c_files (line 8)
mex(filename,'-v');

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18 Mar 2013 Anton Semechko

### Anton Semechko (view profile)

When filtering 3D images I noticed that there is not option to specify the voxel resolution. To me this implies that in creating this function the author assumed that the voxels of the input image have isotropic resolution. Unfortunately this is usually not the case and must be accounted for when discretizing the diffusion equation.

Aside from this, I think this is a great submission. Many thanks!.

27 Sep 2012 Ron

### Ron (view profile)

The original stencel can be found here:
http://www.scribd.com/doc/52387266/Jahne-B-Handbook-of-Computer-Vision-and-Applications-Vol-2-Signal-Processing-and-Pattern-Recognition

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27 Sep 2012 Ron

### Ron (view profile)

Hi,

I have found an error in the code.
The 2D "standard" diffusion algorithm may be incorrect. The stencil shown in Weickertt (2002) is not the same as that referenced (from the handbook volume 2). That stencil has both terms in the top-left and bottom left corners negative. I beleive it is a typo in the Weickertt paper unless I am missing something.

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27 Sep 2012 Ron

### Ron (view profile)

Hi,

I have found an error in the code.
The 2D "standard" diffusion algorithm may be incorrect. The stencil shown in Weickertt (2002) is not the same as that referenced (from the handbook volume 2). That stencil has both terms in the top-left and bottom left corners negative. I beleive it is a typo in the Weickertt paper unless I am missing something.

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06 Jul 2012 leila

### leila (view profile)

I think it is useful to explain how to tune the parameters and constants. The default configuration over-smooth my image. I have a very thin object in a noisy image that disappeared by the filter.
thank you.

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06 Jul 2012 leila

### leila (view profile)

hi, can I request everyone to report run-time of their experiment and size of image volume.
thanks.

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02 Apr 2012 Courosh Mehanian

### Courosh Mehanian (view profile)

where can imresize2 (that's called in hessian) be found?

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28 Mar 2012 xiuhong

### xiuhong (view profile)

it is a useful tool. Thanks the author very much!

23 Nov 2011 ITTelkom

### ITTelkom (view profile)

09 Oct 2011 Sun SHENG

### Sun SHENG (view profile)

it is a elaborate tool. it is very usefull to my research. Thanks the author a lot!

15 Apr 2011 Matthias Schabel

### Matthias Schabel (view profile)

To solve the mex compilation error :

on OSX, add the following as line 3 of diffusion_scheme_3D_novel_getUpdate.c :

#include "string.h"

and re-run the mex script

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17 Feb 2011 Wouter

### Wouter (view profile)

Compliments for this excellent code

I experience the same problem as Anthony Kilburg:

diffusion_scheme_3D_novel_getUpdate.c:126: warning: incompatible implicit declaration of built-in function 'memcpy'

Probably due to OS X or my compiler? (gcc-4.2)

Google 'says' I have to include <String.h>, but this does not seems to solve it.

01 Feb 2011 Ding Yuan

### Ding Yuan (view profile)

Dirk,

Thanks for sharing, your profession in matlab is very impressive. the package is really nonlinear anisotropic diffusion, not only coherence diffusion, so I strongly suggest changing the name. I found a problem in functions2D/EigenVectors2D.m the eigenvectors v1 v2 corresponds to mu2 and mu1, please check it, it can be a serious bug.

18 Jan 2011 Anthony Kilburg

### Anthony Kilburg (view profile)

Hello,

I reached an error while attempting to compile the C-code files. Error message is as follows:

??? Error using ==> mex at 221
Unable to complete successfully.

Error in ==> compile_c_files at 32
mex diffusion_scheme_3D_novel_getUpdate -v;

Upon review of the code I downloaded, I found that all mex funtions call for the function name .c -v for all the except the function I am having trouble with. Is the call in the function meant to be:
mex diffusion_scheme_3D_novel_getUpdate.c -v;

Thank you

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30 Nov 2010 wang ning

### wang ning (view profile)

in diffusion_scheme_3D_standard.c , /* Compute tensor-driven diffusion (as in [1] pp. 80-82) */ which Literature is quoted ? What's [1] ?

23 Mar 2010 nurul

### nurul (view profile)

hi sir,
i just downloaded ur work. i find an error on line 218 . it says
Error in ==> CoherenceFilter at 218
if(size(u,3)<4), u=double(u); else u=single(u);

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22 Nov 2009 bin yao

### bin yao (view profile)

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?

02 Oct 2009 Dirk-Jan Kroon

### Dirk-Jan Kroon (view profile)

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

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02 Oct 2009 Dirk-Jan Kroon

### Dirk-Jan Kroon (view profile)

*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

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01 Oct 2009 Elmar

### Elmar (view profile)

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

01 Oct 2009 Dirk-Jan Kroon

### Dirk-Jan Kroon (view profile)

* 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

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01 Oct 2009 Elmar

### Elmar (view profile)

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

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01 Oct 2009 1.1

Tested Linux Ubuntu

02 Oct 2009 1.2

Fixed boundary check bug in backward derivatives.

19 Oct 2009 1.3

Literature

17 Nov 2009 1.4

Added AdriÃ«nne M. Mendrik et al. "Hybrid Diffusion with Continuous Switch (HDCS)", october 2009 IEEE transactions on medical imaging.

17 Nov 2009 1.5

LCC compiler fix

02 Feb 2010 1.6

Added new Diffusion scheme which uses optimized 5x5 second order derivatives...

06 Sep 2010 1.7

Added paper, some minor changes in values