Talk:Thin plate spline

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This is verbatim from "A new point matching algorimth for non-rigid registration" Haili Chui, Anand Rangarajan. I don't know who copied from who. I tried implimenting this algorithm and found numerous mistakes (i.e. dimension mismatch of matrices for multiplication). I've corrected the ones present in this wiki article too.

DRH: This article is horribly written (as are most articles on TPS). The nomenclature is used inconsistently. For example, x and y are used for space coordinates (i.e., the x-coordinate and the y-coordinate of a 2-D space) and as the domain (x) and range (y) of a function (i.e., f:x -> y). There are numerous other problems. Are there supposed to be multiple phi's (script phi and non-script phi)? Is phi a 1-D function or a 3-D function? If it is 1-D, why is it dotted with a 3-D vector? Someone who really knows TPS ought to rewrite this article so that it makes sense. --Darrell

The advantages listed in the Application section are not well expressed: 1. The word "interpolation" is used, but the thin plate spline solutions in general will not interpolate the data points (x_i, y_i), since it is a form of penalised least-squares regression. In the limiting case for an infinite weight parameter lambda the solution will be the same as a simple linear regression through the data points, which will only be an interpolating function if all the data points lie on a plane. 2. It is claimed that "the model has no free parameters that need manual tuning" - my understanding is that the non-negative weight parameter lambda still needs to be set appropriately - from memory Wahba's book explains some ways to do this using cross validation. This certainly sounds like tuning to me! —Preceding unsigned comment added by 138.194.29.10 (talk) 00:47, 5 May 2011 (UTC)

The claim(1) in Applications ("the interpolation is smooth with derivatives of any order") needs to be clarified — Preceding unsigned comment added by Gstat (talk • contribs) 20:13, 21 October 2011 (UTC)