## Why thin plate spline?

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

What is thin plate spline transformation?

The term “thin-plate spline” refers to the bending of a thin sheet of metal . 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.

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. The surface is forced to pass through all these 7 control points.

### 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.

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 thin flat plate called?

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

## What are the assumptions made in pure bending of thin plates?

Assumptions made in the theory of Pure Bending The material of the beam is homogeneous1 and isotropic2. The value of Young’s Modulus of Elasticity is same in tension and compression. The transverse sections which were plane before bending, remain plane after bending also.

How are principal warps related to the decomposition of a spline?

The spline maps decompose, in the same way as the spline surfaces, into a linear part (an affine transformation) together with the superposition of principal warps, which are geometrically in- dependent, affine-free deformations of progressively smaller geomet- rical scales.

Can a thin plate be warped to make a face look different?

Given two sets of facial landmarks in two images, one face could be warped to make it look like the other face. Before introducing the Thin Plate Spline warping algorithm, we will quickly go through the radial basis function interpolation, which is the general form of the thin plate spline interpolation problem.

### How are thin plate splines used to model shape change?

When these splines are paired, one representing the x-coordinate of another form and the other the y-coordinate, they aid greatly in the modeling of biological shape change as deformation. In this context, the pair becomes an interpolation map from RZ to R2 relating two sets of landmark points.

How is the thin plate warping algorithm used?

Before introducing the Thin Plate Spline warping algorithm, we will quickly go through the radial basis function interpolation, which is the general form of the thin plate spline interpolation problem. We will just focus on explaining the 1 D 1 D example introduced in the last section.