Thin Plate Spline Model

The Thin Plate Spline (TPS) model is a non-rigid interpolation method based on radial basis functions, commonly employed in image registration, surface reconstruction, and similar applications. Its core principle involves constructing smooth deformation fields by minimizing bending energy.

In MATLAB implementation, the TPS model typically involves several key steps: First, establishing control point sets including both source and target point coordinates. Next, computing the radial basis function kernel matrix, frequently utilizing logarithmic or cubic radial basis function forms. Then solving linear equation systems to obtain model weight parameters, and finally generating continuous deformation fields through interpolation functions.

The model's advantage lies in its ability to maintain global smoothness while achieving local deformations, making it particularly effective for non-rigid registration problems. MATLAB's matrix computation capabilities make it exceptionally suitable for implementing such algorithms requiring linear system solutions. When using this approach, attention must be paid to reasonable control point distribution to avoid ill-conditioned matrix issues.