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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal>Dear all,<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>I have two corresponding 3D point sets and tried to map one domain towards the other using <o:p></o:p></p><p class=MsoNormal>“itkThinPlateSplineKernelTransform”. Since I want to allow small landmark localization errors, I set<o:p></o:p></p><p class=MsoNormal>the stiffness parameter > 0. However, the results do not make sense at all (I also have a Matlab<o:p></o:p></p><p class=MsoNormal>implementation where I can compare it with).<o:p></o:p></p><p class=MsoNormal>Having a look at the code I noticed, that the G matrix is computed as r i.e. the Euclidean distance<o:p></o:p></p><p class=MsoNormal>between landmarks. Shouldn’t that be –r instead? While for the interpolation case it shouldn’t <o:p></o:p></p><p class=MsoNormal>matter (since u(x) = A*x + B + I* sum_i=1_N(wi * ri) and if ri is –ri, the warping coefficients wi <o:p></o:p></p><p class=MsoNormal>become –wi as well), it does matter for the approximation case.<o:p></o:p></p><p class=MsoNormal>To give it a try, I changed r to –r and the results are already much better, however still not <o:p></o:p></p><p class=MsoNormal>correct. Finally I tried m_Stiffness = 0 for –r and I saw that the result is different from the result<o:p></o:p></p><p class=MsoNormal>using r, which shouldn’t be the case (see above).<o:p></o:p></p><p class=MsoNormal>Could anyone comment on this? Did anyone use the TPS mapping with setting m_Stiffness > 0<o:p></o:p></p><p class=MsoNormal> in the past? I tried to step through “itkKernelTransform” but couldn’t find an error so far. However<o:p></o:p></p><p class=MsoNormal>I also have to admit that I had quite some trouble getting through the code…<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>One further remark: What is in the current implementation is a smoothing TPS rather than a TPS<o:p></o:p></p><p class=MsoNormal>approximation since m_Stiffness has to be specified as being the same for all landmarks. For the<o:p></o:p></p><p class=MsoNormal>approximation case, as demonstrated in the Rohr et al. paper, it should be possible to set <o:p></o:p></p><p class=MsoNormal>m_Stiffness for all landmarks individually.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Thanks in advance.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Greetings,<o:p></o:p></p><p class=MsoNormal>Martin<o:p></o:p></p></div></body></html>