version 1.7.0.0 (10.1 MB) by
Dirk-Jan Kroon

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

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.

Dirk-Jan Kroon (2021). Image Edge Enhancing Coherence Filter Toolbox (https://www.mathworks.com/matlabcentral/fileexchange/25449-image-edge-enhancing-coherence-filter-toolbox), MATLAB Central File Exchange. Retrieved .

Created with
R2009b

Compatible with any release

**Inspired:**
Microscopy Image Browser (MIB), Anisotropic Diffusion with Memory based on Speckle Statistics for Ultrasound Images, CSKMorphometrics

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Daniel TofinoHello, I'm experiencing the same problem as Christian Sanders and rui gao both in Matlab 2018b AND 2019B. I already tried to change the C functions as Christian Sanders but the error remains. I don't understand C and i would deeply appreciate if you can help me solve this problem as right now it's impossible to use the filter.

Error using CoherenceFilterStep2D

Requested 2379411882152x1 (17728.0GB) array exceeds maximum array size preference. Creation of arrays greater

than this limit may take a long time and cause MATLAB to become unresponsive. See array size limit or

preference panel for more information.

Error in CoherenceFilter (line 249)

u=CoherenceFilterStep2D(u,Options);

Error in Untitled (line 22)

filter_coherence=CoherenceFilter(image_original);

rui gaorui gao(My MATLAB version is MATLAB R2018b)

Every time when I call the function which relates to C files, I will always meet the error which said something about memory and something else.

The functions are 'imgaussian.m', derivatives.m' and 'CoherenceFilterStep2D.m'.

If I changed the name of those files, like 'imgaussian_works.m', I can run the example successfully. Only the example - Rotation Invariant - cannot be gained since 'CoherenceFilterStep2D.m' contains nothing.

I just started learning Matlab and no backgrounds about C, any helpful information for me would be appreciated!

rui gaoI have also met a similar problem with Christian Sanders, and the hint from my MATLAB R2018b is:

Error using CoherenceFilterStep2D

Requested 1103806595329x1 (8224.0GB) array exceeds maximum array size preference. Creation of arrays greater than this limit may take a long time and cause MATLAB to become unresponsive. See array size limit or preference panel for more information.

Some default values in 'Options' are not the same as the description in the comments. Does that mean that the values in the 'Options' result in this undesirable feedback?

Another question is the thing which relates to compiling. If I compile the file, 'compile_c_files.m', directly, I got the hint:

"Error in compile_c_files (line 32)

mex diffusion_scheme_3D_novel_getUpdate -v;"

But if I modify the 32nd line with "mex diffusion_scheme_3D_novel_getUpdate.c -v", it would be compilied successfully. Just like Christopher's comment on 30 Jan 2014.

Christian SandersFor any of the examples (this is the last one of the list), the program is requesting an extensively large amount of memory. I'm using the 2018b version.

Error using imgaussian

Requested 279172874305x11547402067903512641x2483235742355800016 (17179869184.0GB) array

exceeds maximum array size preference. Creation of arrays greater than this limit may

take a long time and cause MATLAB to become unresponsive. See array size limit or

preference panel for more information.

Error in CoherenceFilter>Anisotropic_step3D (line 314)

usigma=imgaussian(u,Options.sigma,4*Options.sigma);

Error in CoherenceFilter (line 258)

u=Anisotropic_step3D(u,Options);

Error in examples (line 43)

JS = CoherenceFilter(V,struct('T',5,'dt',0.15,'Scheme','S','eigenmode',4));

Fixed by changing the following in each c file:

mxCreateNumericArray(3, dims, mxDOUBLE_CLASS, mxREAL) --TO--> mxCreateNumericArray(3, dimsu_const, mxDOUBLE_CLASS, mxREAL)

I assumed the interface has changed after all these years

chen jianjiangThank you for sharing the codes.

LONG LIAOsupriya sumansir i am beginner ,plz tell me how to run this code for 2d fundus image for image enhancement

Siva YedithiI keep having an access violation exception whenever I try to run the 2d example. Has anyone else had this problem? I've run the compile script and I don't see any errors.

Abdullahnow the compiler can run how can I apply it on random images ???

Charilaos Mylonasantonius vandongenAasdgood job

Ilya BelevichDavidNice 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

ChristopherI'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!

MicheleHi,

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.

Sourinsolved! it was some mac os problem with gcc!

SourinHi

I am getting the allowing error…. any help is greatly appreciated. I am using matlab 2012b on Mac os. thanks

Sourin

derivatives.c: In function 'gradient2Dx':

derivatives.c:24: warning: incompatible implicit declaration of built-in function 'malloc'

derivatives.c: In function 'gradient2Dy':

derivatives.c:57: warning: incompatible implicit declaration of built-in function 'malloc'

derivatives.c: In function 'gradient3Dx_double':

derivatives.c:110: warning: incompatible implicit declaration of built-in function 'malloc'

derivatives.c: In function 'gradient3Dx_float':

derivatives.c:195: warning: incompatible implicit declaration of built-in function 'malloc'

derivatives.c: In function 'gradient3Dy_float':

derivatives.c:280: warning: incompatible implicit declaration of built-in function 'malloc'

derivatives.c: In function 'gradient3Dz_float':

derivatives.c:364: warning: incompatible implicit declaration of built-in function 'malloc'

derivatives.c: In function 'gradient3Dy_double':

derivatives.c:449: warning: incompatible implicit declaration of built-in function 'malloc'

derivatives.c: In function 'gradient3Dz_double':

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');

Anton SemechkoWhen 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!.

RonThe 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

RonHi,

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.

RonHi,

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.

leilaI 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.

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

thanks.

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

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

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

Matthias SchabelTo 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

WouterCompliments 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.

Ding YuanDirk,

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.

Anthony KilburgHello,

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

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

nurulhi 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);

bin yaoA 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?

Dirk-Jan KroonI uploaded a new version with derivative boundary check bug fixed, probably tomorrow online. thnx Elmar.

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

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

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

ElmarThanks 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