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Topic: measured boundary conditions with pde toolbox
Replies: 17   Last Post: Apr 8, 2014 6:00 AM

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Tony Kittler

Posts: 105
Registered: 2/5/11
Re: measured boundary conditions with pde toolbox
Posted: Nov 17, 2012 9:02 AM
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"Carl S." wrote in message <k879vh$k4n$1@newscl01ah.mathworks.com>...
> "Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <h5rf05$nb8$1@fred.mathworks.com>...
> > Doug, I have a hard time to explain why using pointwise Neumann condition is dangerous in a simple term. So I continue to provide indication, and hope one of them will speak to you. If you are familiarize with boundary single layer potential, you will see that the normal derivative have a jump relation related to the local value of the potential (see Colton & Kress book). This show that we can set pointwise Neumann bc at any values, though the Banach L^p norm (1<=p<infinity) of the "trace" can be anything else. There are an infinity harmonic functions that meet the *point-wise* Neumann condition.
> >
> > I might not fully understand where your Neumann data are from (I understand from measurement), but you have to be careful about how to plug them into the PDE, even if you think you can define it in the boundary.m.
> >
> > Bruno

>
> Hi, I think this is the correct place to ask my question that is about Sobolev. The codes are ;
>
> u=NeumannBoundCond(u);
> [u_x,u_y]=gradient(u);
> s=sqrt(u_x.^2 + u_y.^2);
> smallNumber=1e-10;
> Nx=u_x./(s+smallNumber); % add a small positive number to avoid division by zero
> Ny=u_y./(s+smallNumber);
> curvature=div(Nx,Ny);
>
> diracPhi=Dirac(u,epsilon);
> areaTerm=diracPhi.*g; % balloon/pressure force
>
> edgeTerm=diracPhi.*(vx.*Nx+vy.*Ny) + diracPhi.*g.*curvature;
> % u=u + timestep*(lambda*EdgeTerm + alfa*areaTerm);
>
> SobolevGradEdgeTerm = (1./(Img-gradient(u).^2)).*edgeTerm;
> u=u + timestep*(lambda*SobolevGradEdgeTerm + alfa*areaTerm);
>
> When I multiply the edgeTerm and lambda then I can see the evoluation of the active contour. But I want to use Sobolev gradient. (So, I have added the last two code lines.) In this case, when I multiply the lambda with SobolevGradEdgeTerm then the active contour disappears in the figure. What is the mistake ?


I tried this
SobolevGradEdgeTerm = (1./(eye(256)-gradient(u).^2)).*edgeTerm;
but I have still the same problem :(



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