<html><head></head><body bgcolor="#FFFFFF"><div>Hi Selma,</div><div><br></div><div>I will see if I have anything on thin plate splines (which are related to cubic splines and regularization).</div><div>Wolfram Mathematica has a page on thin plate splines.</div><div>I can answer questions about the involved double integration and partial derivatives from both a mathematical and numerical implementation standpoint.</div><div><br></div><div>Take care,</div><div>John <br><br>Sent from my iPhone 4S</div><div><br>On 2012-05-07, at 7:51 AM, SELMA GÜZEL <<a href="mailto:slm_guzel@hotmail.com">slm_guzel@hotmail.com</a>> wrote:<br><br></div><div></div><blockquote type="cite"><div>
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Hi John,<div><br></div><div>Thank you vey much for your interest. </div><div><br></div><div>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.</div><div>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.</div><div>If you provide, of course I will be so thankful.</div><div><br></div><div>Thank you and best regards,</div><div>Selma</div><div><br><br><div></div><br><br><div><div id="SkyDrivePlaceholder"></div><hr id="stopSpelling">CC: <a href="mailto:insight-users@itk.org">insight-users@itk.org</a><br>From: <a href="mailto:john.drozd@gmail.com">john.drozd@gmail.com</a><br>Subject: Re: [Insight-users] Splines<br>Date: Mon, 7 May 2012 07:11:45 -0400<br>To: <a href="mailto:slm_guzel@hotmail.com">slm_guzel@hotmail.com</a><br><br><div>Hi Selma,</div><div><br></div><div>You're welcome. I am glad I could help.</div><div>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.</div><div><br></div><div>Take care,</div><div>John</div><div><br></div><div>John Drozd, Ph.D.</div><div><br></div><div>Post-Doctoral Scholar (Fellow)</div><div>Robarts Research Institute</div><div>Western University</div><div>London, ON, Canada</div><div><br></div><div>cell: 519-282-3340</div><div><a href="http://publish.uwo.ca/~jdrozd2" target="_blank">http://publish.uwo.ca/~jdrozd2</a></div><div><a href="mailto:jdrozd@imaging.robarts.ca">jdrozd@imaging.robarts.ca</a></div><div><br></div><div>Sent from my iPhone 4S</div><div><br>On 2012-05-07, at 4:57 AM, SELMA GÜZEL <<a href="mailto:slm_guzel@hotmail.com">slm_guzel@hotmail.com</a>> wrote:<br><br></div><div></div><blockquote><div>
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Hi John,<div><br></div><div>I have checked the resource. It seems useful.</div><div><br></div><div>Thank you.</div><div><br></div><div><br><div></div><br><br><div><div id="ecxSkyDrivePlaceholder"></div><hr id="ecxstopSpelling">CC: <a href="mailto:insight-users@itk.org">insight-users@itk.org</a><br>From: <a href="mailto:john.drozd@gmail.com">john.drozd@gmail.com</a><br>Subject: Re: [Insight-users] Splines<br>Date: Sat, 5 May 2012 19:28:52 -0400<br>To: <a href="mailto:slm_guzel@hotmail.com">slm_guzel@hotmail.com</a><br><br><div>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.</div><div><br></div><div>John<br><br>Sent from my iPhone 4S</div><div><br>On 2012-05-05, at 6:20 PM, SELMA GÜZEL <<a href="mailto:slm_guzel@hotmail.com">slm_guzel@hotmail.com</a>> wrote:<br><br></div><div></div><blockquote><div>
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Hello,
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<div>I need a good resource for understanding splines very well. In fact, I studied different resources but something is not clear enough for me.</div>
<div><br></div>
<div>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?</div>
<div>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?</div>
<div><br></div>
<div>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?</div>
<div><br></div>
<div>Thanks in advance.</div>
<div>Best regards,</div>
<div>Selma </div>
<div><br></div>
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