||Airborne LiDAR Point Cloud Fitting With Geometric Constrains
||Department of Geomatics
point cloud reconstruction
由於現今三維城市建模技術的蓬勃發展，三維空間資訊系統可以廣泛的應用在都市計畫、災害管理、交通規劃、觀光導覽、導航系統等用途，而如何進行三維房屋模型的重建，也隨之成為熱門的議題。過往方法多採用空載光達點雲或是航拍影像進行大範圍的三維城市模型的建置，在本研究當中，我們是利用空載光達點雲以及樣版模型進行三維城市建模。在空載光達點雲資料當中，通常含有鄰近物阻擋造成的資料缺口，導致利用空載光達進行三維城市建模時，部分建物表面沒有對應的點雲資訊，進一步導致其表面無法進行重建。為了解決缺少點雲造成模型無法重建的問題，本研究先行使用三維建物模型檢索系統(model retrieval system)，擷取出與點雲資料最相似的三維建物，再利用本研究所提出的方法，將擷取出之模型進行模型重建，使其尺寸及外觀更加擬合真實的建物。
本研究系利用幾何分析、點雲分類及最小二乘擬合三個程序進行三維建物的重建；在幾何分析中，我們將擷取出的模型，利用四元數的方式將每個面之間的資訊紀錄下來，並將這些資訊做為幾合約制條件(geometric constraints)；在點雲分類中，本研究計算點到各個面之間的距離，並將各點分配到與其距離最短的建物表面上；最後透過代數最小二乘擬合(algebraic least squares fitting)計算出最擬合點雲的平面參數式。
Many building models have been created and shared in the website. These user- created models have high-quality appearances. However, the size of these building models would not be suitable for each case. Therefore, a model refinement approach had proposed in this paper to refine building models by using airborne LiDAR data. The proposed approach consists of three steps: data processing, geometric reconstruction, and model refinement. First step is point cloud segmentation to model surface. Second step is to establish the geometric relations and constraints of building models. And the last step is to refine building models with the constraints built in second step. By using the proposed method, the building models can be refined more efficiently and accurately, and the original geometric relations can be also maintained.
Keywords: point cloud reconstruction, building modeling, model refinement.
Point cloud reconstruction is a fundamental step for building and city modeling with a variety of applications, such as urban planning, virtual tourism, real-time emergency response, and navigation. An increasing number of 3D building models have been available in the Internet with the developments of Web 2.0 techniques and scanning equipment. For example, Trimble 3D Warehouse and MakerBot Thingiverse allow users to upload and share their models in their web-based data-sharing platforms. Generally, models from these web platforms are built up manually or processed by semi-automated and complicated procedures. By using model retrieval techniques with an airborne LiDAR point cloud, several models similar to an input point cloud can be extracted from these databases. However, the extracted building models may not well fit the point cloud. Thus, a model refinement method is proposed in this study to fit and refine a building model with its corresponding point cloud. In addition, geometric relationships and geometric constraints of the building models are maintained with the proposed iterative refinement approaches. A set of airborne LiDAR point cloud data is tested to evaluate the proposed method. The experimental results demonstrate that the proposed method can refine building models efficiently and accurately without nontrivial modeling processes in related model reconstruction methods.
MATERIALS AND METHODS
In this study, a model refinement scheme is proposed to reduce the differences between point clouds and building models. Most of the roofs in building models are constructed by planes. Therefore, our refinement scheme is based on plane fitting, which refine a plane by using its corresponding points. The goal of our refinement scheme is to minimize the sum of the squared Euclidean distances between a point cloud and a plane. Figure 1 illustrates the workflow of the proposed approach which consists of three main procedures: geometric analysis, point cloud segmentation, and model refinement.
In previous studies, the process of plane fitting is to find a fitting plane that minimizes the sum of the squared Euclidean distances to given point cloud. However, the geometric relationships of planes do not fully considered in the fitting process. In this study, the geometric relationships are taken to construct building models, including plane normal and angle. These geometric relationships are regarded as geometric constraints in the model fitting and refinement. Besides, these relationships are also used to reconstruct the surfaces of building model after the model refinement.
The proposed refinement approach is based on plane fitting that fits planes by their corresponding points. Region growing is a standard approach to segment the point cloud by using features, e.g., normal and curvature. However, these features are sensitive to noise. In this study, the point cloud is segmented by the surface of the input model. This approach assigns each point to the nearest surface. The nearest surface is determined by using Euclidean distance.
Our reﬁnement procedure combines the geometric relationships and the corresponding points to refine the building model. This procedure is inspired by plane fitting which minimizes the sum of the squared Euclidean distances to the given point cloud. In this part, we used least square fitting to minimize the distance from point to their own plane. When updating the parameters of these plane equations that we can use these updating plane equations to do another least square procedure. The second time least square procedure used to calculate the coordinate of every corner for the candidate model. Therefore, we can get the updating coordinate in this procedure. For more details, please refer to the references . Finally, the solved coordinate are used to reconstruct the surfaces of building model by geometric relationships.
Each point of point cloud data is assigned to the nearest surface. However, some points near the corners of a building model may be assigned to incorrect surface. In order to avoid fail assignment, an iterative optimization procedure is adopted to segment the point cloud and refine the model. After each refinement step, the surface is more close to the point cloud data, the point of point cloud would be re-assigned to the nearest and more correct surface.
RESULTS AND DISCUSSION
To demonstrate the robustness and feasibility of the proposed approach, we use LiDAR point cloud and building model from Trimble 3D Warehouse to verify the geometric constraints. Figure 2 show the refinement result of Technology Building in National Cheng Kung University. Figure 3 show the relation between iterations and root mean-square error (RMSE).
A model refinement method is presented to refine building models by using the newest point cloud data. The experimental results show that our approach can deal with multi-plane fitting by geometric constraints. In addition, the building models can be refined efficiently and accurately, and the original geometric relationships can also be maintained.
第一章 緒論 1
1.1 前言與研究動機 1
1.2 空載光達介紹 3
1.3 研究貢獻 4
1.4 論文架構 6
第二章 相關研究 7
2.1 資料導向建模 7
2.2 模型導向建模 8
第三章 研究方法 10
3.1 點雲分類 10
3.2 平面幾何分析 11
3.3 最小二乘擬合 18
3.4 迭代最佳化處理 25
3.5 額外建物模型偵測與重建 27
第四章 實驗結果與分析 30
4.1 實驗資料與區域 30
4.2 三維建物模型重建實驗成果 32
4.3 附有幾合約制條件之模型重建比較 47
4.4 額外建物模型偵測與重建成果 49
第五章 結論、未來工作以及限制 55
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