Image resizing using thin-plate spline

Abstract

Interpolation of scattered data refers to the problem of passing a smooth surface through a non-uniform distribution of data samples. In many science and engineering fields, where data are often generated or measured at few and irregular positions, this problem is of practical importance. Over the past decades, different methods have been used to yield solutions to the multi-variate scattered data interpolation problem. One of the popular methods that is commonly used is Thin-Plate Spline (TPS). A thin-plate spline is a physically inspired two-dimensional interpolation structure for randomly spaced tabulated data (xi,yi,f(xi,yi)). TPS is the generalization of the natural cubic spline in one dimension. The spline surface represents a thin sheet of metal that is limited not to move at the grid points. Such surfaces are preferred for various modeling and design applications. For decades, TPS had been used in mechanics and engineering, and they were initiated to image analysis community by Bookstein. TPS is practically one of the most frequently used transformation function in non-rigid image registration. In this project, TPS is used for the image resizing purpose and its result shows around 12% improvement in terms of quality compared with Bicubic interpolation method. Furthermore, an approach is proposed to reduce the computational cost drastically for large scale images. The results show that this method speeds up the evaluation of TPS interpolation function up to 16 times, compared with direct evaluation. This approach involves windowing the image in order to implement TPS on smaller data sets rather than applying it to the whole image at once.