Abstract: 3D object reconstruction based on point clouds is an important field in computer graphics
which have been used in computer animation, medical image processing and so on. Many good
algorithms have been developed to solve this problem such as Levenberg-Marquart algorithm based
on least squares and M-Estimator based on maximum likelihood estimation. But all of these
algorithms are sensitive to noise and the data number of too lager or too little. And the result of these
algorithms would have a larger error, which can influence the effect of reconstruction. In order to
solve these problems, we propose a new algorithm which is based on Levenberg-Marquart algorithm
and M-Estimator. Our algorithm takes advantage of high convergence of Levenberg-Marquart
algorithm and noise proof of M-Estimator, so it can solve two problems mentioned above. And we
improved the weighting function of M-Estimator which replaces the constant value with the flexible
and adaptive value. This way makes our algorithm to behave very well in large number of points and high level of noise. We apply our algorithm on ball and cylinder and compare with the latest research
results. From the experimental data we can see that our algorithm behaves much well than the others.

Key words: Levenberg-Marquart, M-Estimato, adaptive weighting function, point cloud;
reconstruction