Image Reconstruction for Arbitrarily Spaced Data Using Curvature Interpolation

The article is concerned with image reconstruction for arbitrarily spaced data using curvature interpolation. Image reconstruction is a challenging problem when no constraint is imposed on data locations. The problem is illposed and most numerical methods become overly expensive as the number of sample points increases. This article develops an effective partial differential equation (PDE)based algorithm, called the recursive curvature interpolation method (R-CIM). The new method utilizes a curvaturerelated information which is estimated from an intermediate surface of the nonuniform data and plays a role of driving force for the reconstruction of a reliable image surface. The R-CIM is an interpolator, converges to a piecewise smooth image, possesses a minimum oscillatory behavior, and finishes all the computational tasks in O(N) operations, where N is the number of grid points. The new algorithm outperforms the inverse-distance weighting method, one of the most popular surface construction methods for scattered data.