A wavelet approach for determining a surface covered with airborne LiDAR points

This paper presents a new approach for reconstructing object surface covered with 3D points. It utilizes the 2D Daubechies scaling functions of 3 ^rd order, which can describe fractal geometry, to formulate the observation equation for each point. The linear system is then solved by the least-squares adjustment (LSA) and the reconstructed surface can then be generated. To overcome the ill-posed problem which often emerges in LSA, we employ a from-coarse-to-fine strategy and use the pseudo observations designed on dyadic points, called PHO (Pseudo Height Observations) and POI (Pseudo Observations by Interpolation). Moreover, a full-automated weighting model is proposed to eliminate the so-called Gibbs effect. It reduces the weights of the points whose absolute residuals are larger than twice the a priori height accuracy of the LiDAR point. Tests are done by using airborne LiDAR points. They verify that the artifacts can be completely eliminated by adopting the pseudo observations and the weighting model. While the dyadic points have approximately the point interval of LiDAR points, the a posteriori standard deviations of unit weight of our tests are about ±20∼23cm which are all to the extents of the a priori height accuracy, ±25cm.