Thin-plate smoothing spline
Thin plate splines (TPS) are a spline-based technique for data interpolation and smoothing. They were introduced to geometric design by Duchon. They are an important special case of a polyharmonic spline. Robust Point Matching (RPM) is a common extension and shortly known as the TPS-RPM algorithm. See more The name thin plate spline refers to a physical analogy involving the bending of a thin sheet of metal. Just as the metal has rigidity, the TPS fit resists bending also, implying a penalty involving the smoothness of the … See more TPS has been widely used as the non-rigid transformation model in image alignment and shape matching. An additional application is the … See more • Explanation for a simplified variation problem • TPS at MathWorld • TPS in C++ See more The thin plate spline has a natural representation in terms of radial basis functions. Given a set of control points $${\displaystyle \{c_{i},i=1,2,\ldots ,K\}}$$, a radial basis function defines a spatial mapping which maps any location $${\displaystyle x}$$ in … See more • Elastic map (a discrete version of the thin plate approximation for manifold learning) • Inverse distance weighting • Polyharmonic spline (the thin plate spline is a special case of a … See more WebThin plate regression splines are constructed by starting with the basis and penalty for a full thin plate spline and then truncating this basis in an optimal manner, to obtain a low rank …
Thin-plate smoothing spline
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Webst = tpaps(x,y) is the stform of a thin-plate smoothing spline f for the given data sites x(:,j) and the given data values y(:,j). The x(:,j) must be distinct points in the plane, the values … WebMar 6, 2024 · A thin plate spline would smooth through/across the boundary between the two arms of the rotated U; the low values of the lower arm of the U would leak across the …
Webful that cubic smoothing splines would have achieved their current popularity. (Furthermore, although not generally critical, thin plate spline fitting problems can have condition numbers in excess of 109, which has the potential to cause problems if a thin plate spline is embedded in a non-linear model, for example.)
WebSpline smo othing has been previously generalized to the plane, at torus, and standard sphere, b y replacing the single in tegral in Equation 1.1 with a so-called \thin-plate" energy term, whic h is a measure of roughness (Duc hon 1977; Meinguet 1979; W ah ba 1981; 1990). The theory of spline smo othing has b een extended to arbitrary ... Webplate smoothing splines, and partial thin plate smoothing splines, to incorporate varying degrees of topographic dependence. Partial thin plate splines, as described by Bates et al.
WebTitle A Suite of R Functions Implementing Spline Smoothing Techniques Version 3.1.8 Description Fit various smoothing spline models. Includes an ssr() function for smoothing ... Return a matrix evaluating reproducing kernels for thin plate splines at observed points. Usage tp.pseudo(s, u=s, order=2) tp(s, u=s, order=2) tp.linear(s, u=s) Thin 77 ...
WebEnter the email address you signed up with and we'll email you a reset link. r22 head pressure chartWebThin plate regression splines are constructed by starting with the basis and penalty for a full thin plate spline and then truncating this basis in an optimal manner, to obtain a low rank smoother. Details are given in Wood (2003). shivaji song lyricsWebthin plate smoothing spline when there is no parametric sub-model (i.e., when p = 0). The smoothing. -. parameter p determines a trade-off between data infidelity and surface … r22 helicopter manualWebJan 1, 1991 · Thin plate smoothing splines are widely used to spatially interpolate surface climate, however, their application to large data sets is limited by computational efficiency. r22 height velocity diagramWebApr 11, 2008 · Thin plate splines are a type of smoothing spline used for the visualization of complex relationships between continuous predictors and response variables. Thin plate … shivaji science college websiteWebThe effect of mean excessive pressure on the cylindrical bending of a plate is studied. An increase in this pressure leads to a decrease in deflection and vice 掌桥科研 一站式科研服务平台 r22 jntuh working days of btechWebThe thin-plate smoothing spline f is the unique minimizer of the weighted sum p E ( f) + ( 1 − p) R ( f) with E ( f) the error measure E ( f) = ∑ j y (:, j) − f ( x (:, j)) 2 and R ( f) the roughness measure R ( f) = ∫ ( D 1 D 1 f 2 + 2 D 1 D 2 f 2 + D 2 D 2 f 2) shivajirao s. jondhale college of engineering