Image Deformation With Vector-Field Interpolation Based on MRLS-TPS

Image deformation has been successfully applied in many different kinds of fields. However, how to get an approach with high efficiency and perfect visual effect remains a challenging task. In this paper, we present a vector-field interpolation method for non-rigid image deformation, which is based on moving regularized least squares (MRLS) optimization with a thin-plate spline (TPS). The proposed approach takes user-controlled points as input data and estimates the spatial transformation for each pixel by the control points. In order to achieve a realistic deformation, we formulate the deformation as a novel closed-form transformation estimation problem by MRLS. Unlike moving least squares (MLS), we model the mapping function by a non-rigid TPS function with a regularization coefficient. Therefore, the deformation not only satisfies the global linear affine transformation but also adapts to local non-rigid deformation. In terms of the transformation, we derive a closed-form solution and achieve a fast implementation. Furthermore, the approach can show us a wonderful user experience and can give us a fast and convenient manipulating. Extensive experiments on 2D images and 3D surfaces demonstrated that the proposed method performs better than other state-of-the-art methods like MLS and the commercial software as Adobe PhotoShop CS 6, especially in the case of flexible object motion.