Curve and surface reconstruction method for measurement data

• An Improved Moving Total Least Squares (IMTLS) method is presented.
• Total Least Square (TLS) based on SVD is introduced to local approximants.
• IMTLS uses weight matrix to achieve the parameter estimation.
• Experiments confirm the validity of IMTLS method.

The Moving Total Least Squares (MTLS) method has been developed to fit for the measurement data contaminated with errors. Different from the moving least squares method which only takes into account the error of dependent variable, MTLS method considers the errors of all the variables, which determines the local approximants in the sense of the orthogonal direction. MTLS method is more reasonable than MLS method for dealing with errors-in-variables (EIV) model. But due to the construction way of local approximants, it is time consuming and difficult to change the order of basis function. This paper presents an Improved Moving Total Least Squares (IMTLS) method, in which Total Least Square (TLS) based on singular value decomposition is introduced to the local approximants. IMTLS achieves the parameter estimation of local approximants using weight matrix instead of weight function with compact support in MTLS method. Several examples of curve and surface fitting are given to demonstrate the performance of IMTLS method.