[Insight-users] Insight-users Digest, Vol 52, Issue 49 needs help for "Gaussian Curvature" (Kun)

Thu Aug 28 13:25:59 EDT 2008

Dear Khun,

the formula for computing the Gaussian curvature of a surface given its
implicit representation
\phi is given by (I use LaTex notation)

\begin{eqnarray}
K_\textnormal{\scriptsize Gauss} & = & \frac{\phi_x^2(\phi_{yy}\phi_{zz}
- \phi_{yz}^2) +
\phi_y^2(\phi_{xx}\phi_{zz} - \phi_{xz}^2) +
\phi_z^2(\phi_{xx}\phi_{yy} - \phi_{xy}^2)}
{(\phi_x^2 + \phi_y^2 + \phi_z^2)^2}  \\
& + & 2 \phantom{c} \frac{\phi_x\phi_y(\phi_{xz} \phi_{yz} - \phi_{xy}
\phi_{zz}) +
\phi_y\phi_z(\phi_{xy} \phi_{xz} - \phi_{yz} \phi_{xx}) +
\phi_x\phi_z(\phi_{xy} \phi_{yz} - \phi_{xz} \phi_{yy})}
{(\phi_x^2 + \phi_y^2 + \phi_z^2)^2} \nonumber
\end{eqnarray}

The computation of Gaussian curvature is used in the computation of
minimum curvature.As far
as I know, either Gaussian or minimum curvature are not currently
implemented at ITK. Anyway,
it is quite easy to extend the mean curvature filter at ITK in order to
compute Gaussian and minimum
curvatures using this formula.

The level set method uses the implicit representation \phi for all the
computations. Therefore, the
Gaussian curvature given in the formula is not just the curvature at the
surface but at all the level
sets of the surface in the whole computation domain. In order to recover
the Gaussian curvature
at the points of the surface you have to seek for the values of K_Gauss
at \phi = 0.

Best,
Monica.

insight-users-request at itk.org wrote:
> Send Insight-users mailing list submissions to
> 	insight-users at itk.org
>
> To subscribe or unsubscribe via the World Wide Web, visit
> 	http://www.itk.org/mailman/listinfo/insight-users
> or, via email, send a message with subject or body 'help' to
> 	insight-users-request at itk.org
>
> You can reach the person managing the list at
> 	insight-users-owner at itk.org
>
> When replying, please edit your Subject line so it is more specific
> than "Re: Contents of Insight-users digest..."
>
>
> Today's Topics:
>
>    1. needs help for "Gaussian Curvature" (Kun)
>    2. need help with my Code (Nadia Alvi)
>    3. which version of FLTK must be uesd with Itk ? (Martine Lefevre)
>    4. ITK -TCON 2.0 : Second Life (Luis Ibanez)
>    5. How to concatenate itk transformations (Jian Yang)
>
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Thu, 28 Aug 2008 06:01:26 +0800 (CST)
> From: Kun <kun_ch at 163.com>
> Subject: [Insight-users] needs help for "Gaussian Curvature"
> To: "insight-users at itk.org" <insight-users at itk.org>
> Message-ID:
> 	<27132818.509911219874486411.JavaMail.coremail at bj163app121.163.com>
> Content-Type: text/plain; charset="gbk"
>
>  Hi, all
>
>     I meet a problem these days, and need help.
>     I try to use Gaussian Curvature in the Level Set Method. Suppose the Level Set Function phi = f(x,y,z), and the zero-level-set-surface is phi=0, then how can I calculate the Gaussian Curvature of the surface?
>
> And I think the curvature should be calculated using phi, is it right?
>
> Or is there any existing code to do this? Currently, I only find the "Mean Curvature" code in ITK, but can't  find the "Gaussian Curvature" Code.
>
>     Could anybody help me?
>
> Thanks all.
>
> Kun
>
>
>  
>  
>  
> -------------- next part --------------
> An HTML attachment was scrubbed...
> URL: <http://www.itk.org/pipermail/insight-users/attachments/20080828/df5ecea6/attachment-0001.htm>
>
> ------------------------------
>
> Message: 2
> Date: Thu, 28 Aug 2008 01:14:49 -0700 (PDT)
> From: Nadia Alvi <nadiaalvi at yahoo.com>
> Subject: [Insight-users] need help with my Code
> To: insight-users at itk.org
> Message-ID: <410155.11425.qm at web31006.mail.mud.yahoo.com>
> Content-Type: text/plain; charset="iso-8859-1"
>
>
>
>
>
>
>
>
>
> Hi All,
> ?
> Please see the code attached. 
> It should read the 3 slices and write them as a tiff file but it only reads the 2nd slice and write it 3 times in a tiff file. Apparently it is incrementing the start index by 1 and reading that slice 3 times. 
> Can some body please help me in finding what i m doing wrong?
> Many many thanks
> Nadia
> ?
> ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
>
> typedef unsigned char?????????????????????? PixelType;
> ? const unsigned int Dimension = 3;
> ? 
> ? typedef itk::Image< PixelType, Dimension >? ImageType;
> ? 
> ? typedef itk::ImageSeriesReader< ImageType >? ReaderType;
> ? typedef itk::ImageFileWriter<ImageType> WriterType;
>
> ? WriterType::Pointer writer = WriterType::New();
> ? ReaderType::Pointer reader1 = ReaderType::New();
> ? typedef itk::NumericSeriesFileNames??? NameGeneratorType;
> ? NameGeneratorType::Pointer nameGenerator = NameGeneratorType::New();
> ? nameGenerator->SetSeriesFormat( "clint_binary_080320_noDescription%04d.tiff" );
> ? nameGenerator->SetStartIndex(1);
> ? nameGenerator->SetEndIndex(3);
> ? nameGenerator->SetIncrementIndex(1);
>
> ? reader1->SetImageIO( itk::TIFFImageIO::New() );
> ? reader1->SetFileNames( nameGenerator->GetFileNames()? );
>
> ? writer->SetFileName("labeledImage.tif");
> ? writer->SetInput(reader1->GetOutput());
> ? try 
> ??? { 
> ??
> ??writer->Update(); 
> ??? } 
>
>
>
>       
> -------------- next part --------------
> An HTML attachment was scrubbed...
> URL: <http://www.itk.org/pipermail/insight-users/attachments/20080828/3f5fe742/attachment-0001.htm>
>
> ------------------------------
>
> Message: 3
> Date: Thu, 28 Aug 2008 10:30:59 +0000 (GMT)
> From: Martine Lefevre <martine_lef at yahoo.fr>
> Subject: [Insight-users] which version of FLTK must be uesd with Itk ?
> To: insight itk <insight-users at itk.org>
> Message-ID: <246756.49418.qm at web28311.mail.ukl.yahoo.com>
> Content-Type: text/plain; charset="utf-8"
>
> Hi
> I?try to build InsightApplications-3.8.0 and as I have read there is some application which need FLTK.
> For this reason I have downloded FLTK version 1.1.6 since based on the mailing list its the best to use with itk. I configure it using Cmake and when I try to build it using VC Net, I get a lot of errors and one fatal error related to some library.
> So my questions are:
> Is it relay the?version to be used with itk ? if yes, am I wrong to configure it using Cmake ? 
> What's the way to configure and built such package? I have read in?readme file of this package that we need?just? to open the solution FLTK (in the visualc folder) and built it using the compiler ....please could you give me more suggestions on how to built and integrate FLTK especialy wich version should be used with itk ?
> Waiting for your reply !
> Many thanks
> Martine
>
>
>       _____________________________________________________________________________ 
> Envoyez avec Yahoo! Mail. Une boite mail plus intelligente http://mail.yahoo.fr
> -------------- next part --------------
> An HTML attachment was scrubbed...
> URL: <http://www.itk.org/pipermail/insight-users/attachments/20080828/1eeadbb0/attachment-0001.htm>
>
> ------------------------------
>
> Message: 4
> Date: Thu, 28 Aug 2008 11:47:53 -0400
> From: Luis Ibanez <luis.ibanez at kitware.com>
> Subject: [Insight-users] ITK -TCON 2.0 : Second Life
> To: Insight Users <insight-users at itk.org>
> Message-ID: <48B6C8A9.9030406 at kitware.com>
> Content-Type: text/plain; charset=ISO-8859-1; format=flowed
>
>
> Just a reminder that tomorrow we will hold again the
> ITK Tcon 2.0 in Second Life at 1pm EST.
>
> You can teleport to the Tcon site (the "Linden Open Source Project HQ")
> by using the following link:
> http://slurl.com/secondlife/Hippotropolis/238/14/24/?img=http%3A//public.kitware.com/Insight/Doxygen/html/itkLogo.jpg&title=ITK%20Tcon&msg=Insight%20Toolkit%20%28ITK%29%20Tcon
>
>
>     Luis
>
>
>
>
>
>
> ------------------------------
>
> Message: 5
> Date: Thu, 28 Aug 2008 11:51:55 -0400
> From: "Jian Yang" <yaland1977 at gmail.com>
> Subject: [Insight-users] How to concatenate itk transformations
> To: insight-users at itk.org
> Message-ID:
> 	<a17c5eac0808280851l175da73fp32e7c09dc94c7b6 at mail.gmail.com>
> Content-Type: text/plain; charset=ISO-8859-1
>
> Hi all, I have serials of itk transformations, which includes Affine
> and BSpline transformations, I am wondering how to concatenate them
> together and get a combined transformation?
>
> I checked the insight journal and find two classes related to my
> topic: Combining
> Transforms(http://www.insight-journal.org/dspace/view_item.php?itemid=438)
> and Serial Transformations
> (http://www.insight-journal.org/dspace/view_item.php?itemid=1080).
> However it seems both of them doing the transformations in sequence
> instead of combining them together to get a final form of
> transformation. If the number of the transformations is very big, the
> sequence transformation of image will no doubt downgrade the image
> qualities.
>
> Your help will greatly appreciated.
>
> Jian
>
>
> ------------------------------
>
> _______________________________________________
> Insight-users mailing list
> Insight-users at itk.org
> http://www.itk.org/mailman/listinfo/insight-users
>
>
> End of Insight-users Digest, Vol 52, Issue 49
> *********************************************
>
>   