Dimensional inspection of 3D objects with complex sculptured surfaces is an important issue, due to the increase in precision manufacturing of dies, patterns, moulds, turbine blades, forged parts, and aerospace structural components. In order to determine the error on a machined surface, the measured points must be located in the design coordinate system of the part. This is called localization. This paper presents an approach which formulates the problem as least squares minimization of distances, with the solution being achieved through self learning neural network. The shortest distance between the measured points and their counterparts on the parametric design surface are determined by solving simultaneous non-linear equations. The neural network is then used to learn the homogeneous transformation matrix. Results obtained from computer simulations performed for both scattered and dense data are presented. The results indicate that the proposed method using neural network is both computationally efficient and robust.