小波演算法重建點雲覆蓋面

A Wavelet Algorithm for DSM Reconstruction by Using 3D Point Cloud

蔡展榮(Jaan-Rong Tsay) ； 嚴晟瑋(Sheng-Wei Yen)

《航測及遙測學刊》 12卷3期 (2007/09) Pp. 197-216

https://doi.org/10.6574/JPRS.2007.12(3).1

摘要

本文提出一個重建點雲覆蓋面的演算法，它應用具備碎形表達能力的二維三階Daubechies小波之尺度函數來組成每一個點的觀測方程式，運用由粗而細的求解策略，並使用二元格點位置上的虛擬觀測量PHO及POI來解決最小二乘平差求解過程常出現的劣態問題。同時，本文也提出了一個全自動重新給權的模式，來降低改正數絕對值大於兩倍先驗高程精度的光達點高程觀測值之權值；空載光達點雲實驗結果驗證了此法已有效降低「吉布斯效應」之影響，而且當二元格點的點間隔(1.25m)與點雲之平均點間距（約1m）相當時，後驗單位權中誤差為±20~23cm，已相當於點雲的先驗高程精度±25cm。

關鍵字

物面重建 ； 空載光達點雲 ； 小波 ； 劣態條件 ； 吉布斯效應

並列摘要

This paper proposes an algorithm for reconstruction of an object surface covered with 3D points. It utilizes the 2D Daubechies scaling functions of 3(superscript rd) order, which can describe fractal geometry, to derive 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 on dyadic points, called POI (Pseudo Observations by Interpolation) and PHO (Pseudo Height Observations). Moreover, a full-automated weighting model is proposed in order 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. Some tests are done by using airborne LIDAR points. They verify that the artifacts caused by the Gibbs phenomenon can be eliminated to the large extent by combining 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 in our tests are about ±20~23cm which are all to the extents of the a priori height accuracy, ±25cm.

並列關鍵字

object surface reconstruction ； airborne LIDAR point cloud ； wavelets ； ill-posed condition ； Gibbs effect