What is thin plate spline interpolation?

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.

How does thin plate spline work?

Thin Plate Splines is one such technique. It interpolates a surface that passes through each control point. A set of 3 points will thus generate a flat plane. It is easy to think of the control points as position constraints on a bending surface.

What is a spline R?

Spline is a special function defined piece-wise by polynomials. The term “spline” is used to refer to a wide class of functions that are used in applications requiring data interpolation and/or smoothing. The data may be either one-dimensional or multi-dimensional.

What is the purpose of a smoothing spline?

Smoothing splines are related to, but distinct from: Regression splines. In this method, the data is fitted to a set of spline basis functions with a reduced set of knots, typically by least squares. No roughness penalty is used.

Why are spline plates thin?

Thin plate splines are a type of smoothing spline used for the visualization of complex relationships between continuous predictors and response variables.

What is a thin plate?

A plate is a structural element which is thin and flat. By “thin,” it is meant that the plate’s transverse dimension, or thickness, is small compared to the length and width dimensions. Plates might be classified as very thin if Łt > 100, moderately thin if 20 < Łt < 100, thick if 3 < Łt < 20, and very thick if Łt < 3.

What is a natural spline?

‘Natural Cubic Spline’ — is a piece-wise cubic polynomial that is twice continuously differentiable. In mathematical language, this means that the second derivative of the spline at end points are zero.

What is thin plate spline transformation?

The term “thin-plate spline” refers to the bending of a thin sheet of metal [1][3][4][5][6]. The process of using thin- plate splines in image warping involves miminizing a bending energy function for a transformation over a set of given nodes or landmark points.

What is a thin flat plate called?

LAMINA. a thin plate or layer (especially of bone or mineral)

What do you mean by thin plate spline?

Thin plate spline. Thin plate splines (TPS) are a spline-based technique for data interpolation and smoothing.

How are thin plate splines represented in regression?

Rather than a single curve, thin plate splines are represented as a bendable surface. Each continuous variable is plotted on an individual x-axis, creating a bivariate, two-dimensional surface. The outcome is then plotted on a y-axis, continuously across that bivariate surface in three-dimensions (Fig 1).

How to fit thin plate to irregularly spaced data?

Fits a thin plate spline surface to irregularly spaced data. The smoothing parameter is chosen by generalized cross-validation. The assumed model is additive Y = f (X) +e where f (X) is a d dimensional surface.

Why is the TPS-RPM algorithm called thin plate spline?

Robust Point Matching (RPM) is a common extension and shortly known as the TPS-RPM algorithm. 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 fitted surface.