摘 要 近年來光達掃瞄儀已廣泛的使用在量測領域上，光達可快速獲取高精度且高解析度點雲資料，因此 相關點雲模型建置的技術也越來越受到重視。點雲資料模型重建面臨到的共同問題是如何處理點雲資料 隱含的誤差，此外模型的邊角特徵突顯也會是一個重要的挑戰與問題。本研究提出一新的點雲建模技術， 本技術是以階層式模型樣版為基礎對三維點雲資料進行模型重建，此樣版是由三個主要基本幾何元件構 成，分別為平面、圓球以及圓柱，基本幾何元件皆以代數式描述。階層式模型樣版的第一層為自訂的基 本幾何元件，接著利用基本幾何元件組合出下一層簡單形狀的模型樣版，然後進一步結合前層模型樣版 以建立更高階複雜模型。其作法首先從點雲資料萃取出數個基本幾何點雲群集，再利用模型樣版進行點 雲擬合，此模型樣版以線性代數式描述來取代非線性函式，因此在計算效率與演算法的強鈍性上有十足 提升。此外，在每一模型樣版階層加入幾何約制條件以提高建模品質。實驗結果顯示本方法比利用隱性 面函式建模方法在資料誤差的抵擋與建模品質上有更佳的表現，且比一般最小二乘法相關的重建方法在 視覺上擁有更佳的建模品質。

ABSTRACT Digital scanning devices such as LiDAR have recently become affordable and available. They are capable of acquiring high-accuracy and high-resolution point clouds. Thus, the techniques for point cloud modeling have received increasingly attentions in the last decade. As the approaches reconstruct the point clouds, they face a common problem: how to handle point clouds with inherent noises. Moreover, it will be especially challenge in handing point clouds that contains sharp features, e.g., city buildings. In the paper, a novel template-based modeling approach for 3D point clouds sampled from unknown city buildings is introduced. A hierarchy algebraic template, comprising of three types of primitive geometries (that is, plane, sphere, and cylinder), is used to fit point clouds. The algebraic template is organized in a hierarchical manner. The first-level, i.e., the lowest-level, consists of the primitive geometries which are represented in algebra form. These primitive geometries are merged into 3D objects with simple shapes in the next level. These 3D objects are further joined to form the final template model in the last level. After the point clouds are partitioned into several geometric sets, the constructed template model is used to fit them. The point cloud fitting is archived by solving a least-square linear system instead of solving a non-linear one, making the approach efficient and robust in the modeling. The experimental results show that the approach is better, in terms of sharp feature fitting and noise withstanding, than the approaches based on implicit surfaces. In addition, comparing to the general least-square fitting approaches, the template-based fitting with geometry constraints improves modeling quality with respect to human visual system.