Feature guided non-rigid image/surface deformation via moving least squares with manifold regularization

In this paper, a novel closed-form transformation estimation method based on feature guided moving least squares together with manifold regularization is proposed for nonrigid image/surface deformation. The method takes the user-controlled point-offset-vectors and the feature points of the image/surface as input, and estimates the spatial transformation between the two control point sets for each pixel/voxel. To achieve a detail-preserving and realistic deformation, the transformation estimation is formulated as a vector-field interpolation problem using a feature guided moving least squares method, where a manifold regularization is imposed as a prior on the transformation to capture the underlying intrinsic geometry of the input image/surface. The non-rigid transformation is specified in a reproducing kernel Hilbert space. We derive a closed-form solution of the transformation and adopt a sparse approximation to achieve a fast implementation, which largely reduces the computation complexity without performance sacrifice. In addition, the proposed method can give a wonderful user experience, fast and convenient manipulating. Extensive experiments on both 2D and 3D data demonstrate that the proposed method can produce more natural deformations compared with other state-of-the-art methods.