在计算机视觉以及CAD/CAM等领域都涉及到基于离散观测数据的目标图象或三维曲面图形的重建问题，为此，将最佳逼近与数据平滑理论相结合，提出了一种基于有限元技术的图形与图象重建方法，该方法首先采用Lagrange乘子方法建立正定泛函，进而应用有限元技术及Wewton失代方法求得函极值解，然后通过有限元解的插值计算，重新构造出图形或图象，由于结合了数据平滑处理，因此该方法不仅消除了数据上噪声的影响，而且提高了重建的精度，实验结果证明了方法的有效性和实用性。

In the areas of computer vision and CAD/CAM, it is often needed to represent an image or a 3D surface from discrete measured data. A novel algorithm for the shape representation and image reconstruction is presented in this paper, which integrates the theories of optimal approximation and data smoothing. A positive definite functional is set up according to Lagrange multiplier method, and solved by finite element method and Newton iteration method. The shape or image is then constructed on the basis of finite element interpolation. This algorithm combines the smoothing processing technique with finite element method, the influence of the noise in input data is eliminated and reconstructing precision is improved. The formulations to calculate Lagrange multiplier and the relevant equations of eight-node isoparametric finite element were dervied. Effects of the variations in smoothing factor, in the finite element mesh and in the amount of imput data on the reconstructed results were investigated. A Gauss surface and two images of sphere and saddle surface were represented from discrete data with imposed noise, the results show the effectiveness of presented method. To illustrate the applicability of the method, a Morie fringes image of a tensile composite plate containing a hole was reconstructed. The method is conceptually simple and relatively easy and expedient to apply. The number of input data required in the presented method is less than that in numerical interpolation and fitting and the method can be used to the problem of irregular region with coved boundary.