Image Edge Enhancing Coherence Filter Toolbox: u=diffusion_scheme_2D_novel(u,Dxx,Dxy,Dyy,dt,par) - File Exchange

Code covered by the BSD License

Highlights from
Image Edge Enhancing Coherence Filter Toolbox

showcs3(varargin) SHOWCS3 M-file for showcs3.fig
CoherenceFilter(u,Options) This function COHERENCEFILTER will perform Anisotropic Diffusion of a
D=derivatives(I,option) Sobel like derivatives with Scharr rotation invariance stencil notations.
I=imgaussian(I,sigma,siz) IMGAUSSIAN filters an 1D, 2D color/greyscale or 3D image with an
[Dxx,Dxy,Dxz,Dyy,Dyz,Dzz]=Str... From Structure Tensor to Diffusion Tensor
[Dxx,Dxy,Dyy]=ConstructDiffus... Construct the edge preserving diffusion tensor D = [a,b;b,c] such as
[Iout]=ut_gauss(varargin) ut_gauss - 2-D filtering using Gaussian masks
[Jxx, Jxy, Jxz, Jyy, Jyz, Jzz... This function calculates the 3D Structure Tensor
[Jxx, Jxy, Jyy]=StructureTens... This function calculates the 2D
[Lambda1,Lambda2,I2x,I2y,I1x,... This function computes the eigenvectors and eigen values of the 2D image
[mu3,mu2,mu1,v3x,v3y,v3z,v2x,... This function calculates the eigen values and vectors, of the 3D image hessian.
[x,fval,exitflag,output,grad]... FMINLBFGS finds a local minimum of a function of several variables.
[x11,x12,x22]=hessian(x)
a=clmp(a,mina,maxa) Function clmp to boundaries
diffusion_scheme_3D_standard(... Standard Discretization of 3D image diffusion.
err=error_diffusion_scheme_2D... Parameters must be positive. Otherwise the kernels will go to a more
err=error_diffusion_scheme_3D... Parameters must be positive. Otherwise the kernels will go to a more
err=fitgaussian(I,a,t)
optimize_scheme_2D.m This script finds optimized kernel values for in the novel discretization
optimize_scheme_3D.m Initial values for unknowns in optimal derivative kernels
u=diffusion_scheme_2D_implici... Diffusion scheme as introduced by Weickert "Anisotropic Diffusion
u=diffusion_scheme_2D_non_neg... The Basic non_negativity diffusion equation. (Can be found in "A Scheme for
u=diffusion_scheme_2D_novel(u... par=[0.007520981141059, 0.049564810649554, 0.031509665995882, ...
u=diffusion_scheme_2D_rotatio... Most diffusion discretizations are not rotation-invariant, probably
u=diffusion_scheme_2D_standar... The standard diffusion equation. (Can be found in "A Scheme for
u=diffusion_scheme_3D_implici... This 3D Diffusion scheme is based on introduced by Weickert
u=diffusion_scheme_3D_non_neg... This is a basic non_negativity discretization of the 3D diffusion
u=diffusion_scheme_3D_novel(u...
u=diffusion_scheme_3D_novel_g...
u=diffusion_scheme_3D_rotatio... Most diffusion discretizations are not rotation-invariant. This is an
CoherenceFilterStep2D.m
CoherenceFilterStep3D.m
compile_c_files.m
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from Image Edge Enhancing Coherence Filter Toolbox by Dirk-Jan Kroon
Advanced 2D/3D noise removal and edge enhancing with anisotropic diffusion filtering ( Weickert )

u=diffusion_scheme_2D_novel(u,Dxx,Dxy,Dyy,dt,par)

function u=diffusion_scheme_2D_novel(u,Dxx,Dxy,Dyy,dt,par)
Dxx=repmat(Dxx,[1 1 size(u,3)]);
Dxy=repmat(Dxy,[1 1 size(u,3)]);
Dyy=repmat(Dyy,[1 1 size(u,3)]);

if(nargin<6)
%     par=[0.007520981141059, 0.049564810649554, 0.031509665995882, ...
%          0.037869547950557, 0.111394943940548, 0.448053798986724, ...
%          0.081135611356868,	0.333881751894069, 0.936734100573009, ...
%          0.000936487500442,	0.027595332069424, 0.194217089668822, ...
%          0.006184018622016, 0.948352724021832];
par=[0.00549691757211334,4.75686155670860e-10,3.15405721902292e-11,0.00731109320628158,1.40937549145842e-10,0.0876322157772825,0.0256808495553998,5.87110587298283e-11,0.171008417902939,3.80805359553021e-12,9.86953381462523e-12,0.0231020787600445,0.00638922328831119,0.0350184289706385];

end


Mxx =[par(1)  par(2)  par(3)  par(2)  par(1);
      par(4)  par(5)  par(6)  par(5)  par(4); 
     -par(7) -par(8) -par(9) -par(8) -par(7);
      par(4)  par(5)  par(6)  par(5)  par(4); 
      par(1)  par(2)  par(3)  par(2)  par(1)];
Myy=Mxx';

Mxy=[par(10) par(11)   0    -par(11) -par(10);
     par(11) par(12)   0    -par(12) -par(11);
       0        0      0        0       0
    -par(11) -par(12)  0    par(12) par(11);
    -par(10) -par(11)  0    par(11) par(10)];

Mx= [par(13)  par(14)  par(13); 
		0 	    0 	      0; 
	-par(13) -par(14) -par(13)];
My= Mx';

ux=imfilter(u,Mx,'conv','same','replicate');
uy=imfilter(u,My,'conv','same','replicate');
div1=imfilter(Dxx,Mx,'conv','same','replicate')+imfilter(Dxy,My,'conv','same','replicate');
div2=imfilter(Dxy,Mx,'conv','same','replicate')+imfilter(Dyy,My,'conv','same','replicate');
du1= div1.*ux+div2.*uy;

clear ux uy div1 div2

uxx=imfilter(u,Mxx,'conv','same','replicate');
uxy=imfilter(u,Mxy,'conv','same','replicate');
uyy=imfilter(u,Myy,'conv','same','replicate');
du2=uxx.*Dxx+2*uxy.*Dxy + uyy.*Dyy;

clear uxx uxy uyy Dxx Dxy Dyy

du=du1+du2;

u=u+du*dt;

u(~isfinite(u))=0;

Highlights from Image Edge Enhancing Coherence Filter Toolbox

Highlights from
Image Edge Enhancing Coherence Filter Toolbox