Thin Plate Spline Model for Image Registration

The Thin Plate Spline (TPS) model serves as a powerful image registration technique that performs non-rigid transformations to convert source images into desired target images. Widely adopted in image processing, particularly for registration tasks, the TPS model employs radial basis functions to achieve smooth deformations while minimizing bending energy. From an implementation perspective, the algorithm typically involves: 1) Establishing correspondence points between images, 2) Constructing a kernel matrix using radial basis functions φ(r) = r²log(r), 3) Solving a linear system to determine transformation parameters, and 4) Applying the deformation field to warp the source image. This approach enables precise image alignment and distortion correction, making TPS an essential tool in computer vision and medical imaging where accurate spatial transformations are critical. The model's mathematical foundation ensures smooth interpolations while preserving local structures during deformation processes.