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.