[Insight-users] Splines

[John Drozd]

Hi Selma,

I will see if I have anything on thin plate splines (which are related to cubic splines and regularization).
Wolfram Mathematica has a page on thin plate splines.
I can answer questions about the involved double integration and partial derivatives from both a mathematical and numerical implementation standpoint.

Take care,
John 

Sent from my iPhone 4S

On 2012-05-07, at 7:51 AM, SELMA GÜZEL <slm_guzel at hotmail.com> wrote:

> Hi John,
> 
> Thank you vey much for your interest. 
> 
> I have been studying on image registration. However, due to the fact that my mathematical background is not sufficient enough, I prefer to fill the gaps firstly.
> In fact the method I will have to use is TPS. I've studied some resources, but the formulas are not clear enough for me to use. I need some examples including TPS.
> If you provide, of course I will be so thankful.
> 
> Thank you and best regards,
> Selma
> 
> 
> 
> 
> CC: insight-users at itk.org
> From: john.drozd at gmail.com
> Subject: Re: [Insight-users] Splines
> Date: Mon, 7 May 2012 07:11:45 -0400
> To: slm_guzel at hotmail.com
> 
> Hi Selma,
> 
> You're welcome.  I am glad I could help.
> I also have a nice Numerical Analysis textbook and instructor's solutions manual in my office. I was a TA for this course on numerical analysis that my Ph.D. Supervisor taught.  When I get to my office, I will scan the pertinent pages on Splines and email you a PDF attachment. I am an Applied  Mathematician & Theoretical Physicist with a Computer Science background so I have a lot of this information.  I have included my contact information below.
> 
> Take care,
> John
> 
> John Drozd, Ph.D.
> 
> Post-Doctoral Scholar (Fellow)
> Robarts Research Institute
> Western University
> London, ON, Canada
> 
> cell: 519-282-3340
> http://publish.uwo.ca/~jdrozd2
> jdrozd at imaging.robarts.ca
> 
> Sent from my iPhone 4S
> 
> On 2012-05-07, at 4:57 AM, SELMA GÜZEL <slm_guzel at hotmail.com> wrote:
> 
> Hi John,
> 
> I have checked the resource. It seems useful.
> 
> Thank you.
> 
> 
> 
> 
> CC: insight-users at itk.org
> From: john.drozd at gmail.com
> Subject: Re: [Insight-users] Splines
> Date: Sat, 5 May 2012 19:28:52 -0400
> To: slm_guzel at hotmail.com
> 
> A nice resource for splines is Numerical Recipies in C. It briefly describes the theory and gives the C code.  The PDF is available free online.
> 
> John
> 
> Sent from my iPhone 4S
> 
> On 2012-05-05, at 6:20 PM, SELMA GÜZEL <slm_guzel at hotmail.com> wrote:
> 
> Hello,
> 
> I need a good resource for understanding splines very well. In fact, I studied different resources but something is not clear enough for me.
> 
> For example, when we use piecewise cubic splines, we find an equation for each curve segment corresponding the local segments of a shape, am I correct?
> Then, how can we calculate a general function that we can use for any segment at the end? Or, do we transform each part separately, namely use each curve segment equation for a point within that local part? Are the weighted mean approach used for this problem? If yes, how can we calculate the weights for each part?
> 
> My mathematical background is not sufficient to comprehend all aspects, could you explain splines including TPS a bit? And/or could you recommend some good resources to understand splines from the point of image registration?
> 
> Thanks in advance.
> Best regards,
> Selma
> 
>  
> 
> 
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