The Research On New Interpolation Methods In Graphics And Image Processing

Interpolation technology is an important method for curve/surface modeling,and digital image processing,which play an important role in engineering design,animation,video and image processing.In order to improve the interpolation methods used in graphics and image processing,in this paper we investigate the interpolation problems for graphics and image processing,and then propose several new interpolation methods.According to the spatial dimension of interpolation data,our contribution mainly includes the following:1)Energy-minimizing B-spline curve interpolation method by discrete masks.This discrete mask algorithm firstly establishes linear relationship between the control points by different minimal energy.From the expression,its coefficient matrix is a symmetric pentadiagonal and sparse matrix,which greatly improves the computational efficiency.The key idea is: given a number of ending control points,then the remaining control points can be determined by the corresponding discrete mask such that the constructed B-spline curve has minimal stretch or bending energy.2)Image interpolation method based on Gaussian-Sinc interpolation function.On the basis of graphical interpolation,we propose a new image interpolation method with Gaussian-Sinc interpolation function.This paper firstly introduces the Gaussian-Sinc interpolation function and its geometric properties,then restores the image from the low resolution images by interpolating,finally calculates the PSNR and SSIM between the reconstruction image and the original image,and compare the proposed method with other classical image interpolation algorithms.3)Mesh editing method with interpolation constraints based on angle-representation.We firstly proposed an angle representation form for triangle mesh models to describe the mesh geometric details.The angle information is invariant under the translation,rotation,and uniform scaling.And only three sparse linear systems are solved for mesh interpolation reconstruction,which improves computation efficiency.The experiment results show that the proposed method can preserve angle information and geometric details on the mesh model,which can achieve natural deformation results.