一個視覺物體或一個三維模型的骨架，是一種可以揭示該物體或模型的拓樸結構的呈現方式，因此骨架可以被應用在諸多場合當中，例如形狀分析和電腦動畫。近年來，有許多針對從一個物體當中抽取骨架的研究工作。然而，大多數的研究著重於完整和乾淨的資料（儘管這些研究當中，有一些有將缺失值考慮在內），但在實務上，我們經常要處理不完整和不潔淨的資料，就像資料裡面可能有缺失值和雜訊。在本論文中，我們研究雜訊處理，而且我們將焦點放在針對帶有雜訊的點雲資料進行前置處理，以便生成相應物體的骨架。在我們提出的方法當中，我們首先識別可能帶有雜訊的資料點，然後降低雜訊值的影響。為了識別雜訊，我們將監督式學習用在以密度和距離作為特徵的資料上。為了降低雜訊值的影響，我們採用三角形表面和投影。這個前置處理方法是有彈性的，因為它可以搭配任何能夠從點雲資料當中抽取出物體的骨架的工具。我們用數個三維模型和多種設定進行實驗，而結果顯示本論文所提出的前置處理方法的有效性。與未經處理的模型（也就是原始模型加上雜訊）相比，在從帶有雜訊的點雲資料當中產生物體的骨架之前，如果我們先使用本論文所提出的前置處理方法，那麼我們可以得到一個包含更多原來的物體的拓撲特徵的骨架。我們的貢獻如下：第一，我們展示了機器學習可以如何協助電腦圖學。第二、針對雜訊識別，我們提出使用距離和密度做為學習過程中要用的特徵。第三、我們提出使用三角表面和投影，以減少在做雜訊削減時所需要花費的時間。第四、本論文提出的方法可以用於改進三維掃描。 / The skeleton of a visual object or a 3D model is a representation that can reveal the topological structure of the object or the model, and therefore it can be used in various applications such as shape analysis and computer animation. Over the years there have been many studies working on the extraction of the skeleton of an object. However, most of those studies focused on complete and clean data (even though some of them took missing values into account), while in practice we often have to deal with incomplete and unclean data, just as there might be missing values and noise in data. In this thesis, we study noise handling, and we put our focus on preprocessing a noisy point cloud for the generation of the skeleton of the corresponding object. In the proposed approach, we first identify data points that might be noise and then lower the impact of the noisy values. For identifying noise, we use supervised learning on data whose features are density and distance. For lowering the impact of the noisy values, we use triangular surfaces and projection. The preprocessing method is flexible, because it can be used with any tool that can extract skeletons from point clouds. We conduct experiments with several 3D models and various settings, and the results show the effectiveness of the proposed preprocessing approach. Compared with the unprocessed model (which is the original model with the added noise), if we apply the proposed preprocessing approach to a noisy point cloud before using a tool to generate the skeleton, we can obtain a skeleton that contains more topological characteristics of the model. Our contributions are as follows: First, we show how machine learning can help computer graphics. Second, we propose to use distance and density as features in learning for noise identification. Third, we propose to use triangular surfaces and projection to save execution time in noise reduction. Fourth, the proposed approach could be used to improve 3D scanning.

近年來諸多學者專家致力於從多視角影像獲取精確的點雲資訊，並藉由點雲資訊進行三維模型重建等研究，然而透過多視角影像求取三維資訊的精確度仍然有待提升，其中萃取影像對應與重建三維資訊方法，是多視角影像重建三維資訊的關鍵核心，決定點雲資訊的形成方式與成效。 本論文中，我們提出了一套新的方法，由多視角影像之間的幾何關係出發，萃取多視角影像對應與重建三維點，可以有效地改善對應點與三維點的精確度。首先，在萃取多視角影像對應的部份，我們以相互支持轉換、動態高斯濾波法與綜合性相似度評估函數，改善補綴面為基礎的比對方法，提高相似度測量值的辨識力與可信度，可從多視角影像中獲得精確的對應點。其次，在重建三維點的部份，我們使用K均值分群演算法與線性內插法發掘潛在的三維點，讓求出的三維點更貼近三維空間真實物體表面，能在多視角影像中獲得更精確的三維點。 實驗結果顯示，採用本研究所提出的方法進行改善後，在對應點精確度的提升上有很好的成效，所獲得的點雲資訊存在數萬個精確的三維點，而且僅有少數的離群點。 / Recently, many researchers pay attentions in obtaining accurate point cloud data from multi-view images and use these data in 3D model reconstruction. However, this accuracy still needs to be improved. Among these researches, the methods in extracting the corresponding points as well as computing the 3D point information are the most critical ones. These methods practically affect the final results of the point cloud data and the 3D models so constructed. In this thesis, we propose new approaches, based on multi-view geometry, to improve the accuracy of corresponding points and 3D points. Mutual support transformation, dynamic Gaussian filtering, and similarity evaluation function were used to improve the patch-based matching methods in multi-view image correspondence. Using these mechanisms, the discrimination ability and reliability of the similarity function and, hence, the accuracy of the extracted corresponding points can be greatly improved. We also used K-mean algorithms and linear interpolations to find the better 3D point candidates. The 3D point so computed will be much closer to the surface of the actual 3D object. Thus, this mechanism will produce highly accurate 3D points. Experimental results show that our mechanism can improve the accuracy of corresponding points as well as the 3D point cloud data. We successfully generated accurate point cloud data that contains tens of thousands 3D points, and, moreover, only has a few outliers.

點雲（point cloud）為以大量三維坐標描述地表實際情形的資料形式，其中包含其三維坐標及相關屬性。通常點雲資料取得方式為光達測量，其以單一波段雷射光束掃描獲取資料，以光達獲取點雲，常面臨掃描時間差、缺乏多波段資訊、可靠邊緣線及角點資訊、大量離散點雲又缺乏語意資訊（semantic information）難以直接判讀及缺乏多餘觀測量等問題。 攝影測量藉由感測反射自太陽光或地物本身放射之能量，可記錄為二維多光譜影像，透過地物在不同光譜範圍表現之特性，可輔助分類，改善分類成果。若匹配多張高重疊率的多波段影像，可以獲取包含多波段資訊且位於明顯特徵點上的點雲，提供光達以外的點雲資料來源。 傳統空中三角測量平差解算地物點坐標及產製數值表面模型（Digital Surface Model, DSM）時，多採用可見光影像為主；而目前常見之高空間解析度數值航照影像，除了記錄可見光波段之外，亦可蒐集近紅外光波段影像。但較少採用近紅外光波段影像，以求解地物點坐標及建立DSM。 因此本研究利用多波段影像所蘊含的豐富光譜資訊，以取像方式簡易及低限制條件的近景攝影測量方式，匹配多張可見光、近紅外光及紅外彩色影像，分別建立可見光、近紅外光及紅外彩色之DSM，其目的在於探討加入近紅外光波段後，所產生的近紅外光及紅外彩色DSM，和可見光DSM之異同；並比較該DSM是否更能突顯植被區。 研究顯示，以可見光點雲為檢核資料，計算近紅外光與紅外彩色點雲的均方根誤差為其距離門檻值之相對檢核方法，可獲得約21%的點雲增加率；然而使用近紅外光或紅外彩色影像，即使能增加點雲資料量，但對於增加可見光影像未能匹配的資料方面，其效果仍屬有限。 / Point cloud represents the surface as mass 3D coordinates and attributes. Generally, these data are usually collected by LIDAR (LIght Detection And Ranging), which acquires data through single band laser scanning. But the data collected by LIDAR could face problems, such as scanning process is not instantaneous, lack of multispectral information, breaklines, corners, semantic information and redundancies. However, photogrammetry record the electromagnetic energy reflected or emitted from the surface as 2D multispectral images, via ground features with different characteristics differ in spectrum, it can be classified more efficiently and precisely. By matching multiple high overlapping multispectral images, point cloud including multispectral information and locating on obvious feature points can be acquired. This provides another point cloud source aparting from LIDAR. In most studies, visible light (VIS) images are used primarily, while calculating ground point coordinates and generating digital surface models （DSM） through aerotriangulation. Although nowadays, high spatial resolution digital aerial images can acquire not only VIS channel, but also near infrared (NIR) channel as well. But there is lack of research doing the former procedures by using NIR images. Therefore, this research focuses on the rich spectral information in multispectral images, by using easy image collection and low restriction close range photogrammetry method. It matches several VIS, NIR and color infrared (CIR) images, and generate DSMs respectively. The purpose is to analyze the difference between VIS, NIR and CIR data sets, and whether it can emphasize the vegetation area, after adding NIR channel in DSM generation. The result shows that by using relative check points between NIR, CIR data with VIS one. First, VIS point cloud was set as check point data, then, the RMSE (Root Mean Square Error) of NIR and CIR point cloud was calculated as distance threshold. Its data increment is 21% ca. However, the point cloud data amount can be increased, by matching NIR and CIR images. But the effect of increasing data, which was not being matched from VIS images are limited.

在植被覆蓋的山區中，由於空載雷射掃描可穿透植被間縫隙的特性，有較高機會收集到植被下的地面資訊，因此適合作為製作植被覆蓋地區數值高程模型的資料來源，而在過濾過程中，一般僅利用點雲間的三維位置關係進行幾何過濾，而全波形空載雷射掃描可另外提供點位的波形寬、振幅值、散射截面積以及散射截面積數等波形資料，本研究將透過波形資料分析進行點雲過濾。 首先經最低點採樣後，本研究利用貝氏定理自動分析並計算得到地面點的波形資料的特徵區間範圍，採用振幅值、散射截面積以及散射截面積係數得到的特徵區間範圍開始第一階段的波形資料過濾，完成後再以第二階段的一般幾何過濾濾除剩餘之非地面點，最後的成果將與航測以及只採用幾何過濾時的成果比較。 由研究成果中顯示，不同的植被覆蓋間的單一回波波形資料的差異較明顯，最後回波類似。同一植被覆蓋下的單一回波及最後回波反應不同。而在成果的比較中，本實驗的成果與不採用波形資料輔助的成果大致相同本研究的成果在部分植被覆蓋的區域成果稍差，但透過波形過濾，可將幾何過濾所需計算的點雲數減少許多，可以增進整理過濾的效率。本研究的成果與航測相比時，在植被覆蓋區域較航測成果貼近實際的地面起伏，數值高程模型成果較為正確。 / In mountain areas covered with vegetation, discrete airborne laser scanning is an appropriate technique to produce DEMs for its laser signal is able to reach the ground beneath the vegetation. Once the scanned data was derived, point cloud filtering was performed based on the geometry relationship between the points at the processing stage. With the development of the advanced full-waveform laser scanning system, the additional waveform data has been proved useful for improving the performance of point cloud filtering. This research therefore focused on using the waveform data to extract DEM over vegetation covered area. The amplitude, backscatter cross-section and backscatter cross-section coefficient were the waveform parameters used to do the filtering. After initial waveform analysis was accomplished, an automated method to determine threshold range of each parameter representing ground points was proposed. By applying the thresholds, the original point cloud was filtered. Geometric filtering method was then used to eliminate the remained non-ground points. As a result, the DEM over the target vegetated area was derived. With the comparison against photogrammetric DEM and DEM derived from traditional filtering method, it was demonstrated that the quality of the resultant DEM was improved.

空載光達系統於建置國土測繪基本資料扮演關鍵角色，依國土測繪法，為確保測繪成果品質，應依測量計畫目的及作業精度需求辦理儀器校正。國土測繪中心已於102年度建置航遙測感應器系統校正作業中，提出矩形建物之平屋頂面做為空載光達系統校正之可行性，而其所稱之校正，是以點雲精度評估待校件空載光達系統所得最終成果品質，並不對儀器做任何參數改正，但其校正成果可能因不同人員操作而有差異，因此本研究嘗試建立一套空載光達點雲半自動化精度評估程序，此外探討以山形屋脊線執行點雲精度評估之可行性。 由於光達點雲為離散的三維資訊，不論是以山形屋脊線或矩形建物之平屋頂面作為標物執行點雲精度評估，均須先萃取屋頂面上之點，為避免萃取成果受雜訊影響，本研究引入粗差偵測理論，發展最小一乘法結合李德仁以後驗變方估計原理導出的選擇權迭代法(李德仁法)將非屋頂點視為粗差排除。研究中分別對矩形建物之平屋頂面及山形屋脊線進行模擬及真實資料實驗，其中山形屋脊線作為點雲精度評估之可行性實驗中發現不適合用於評估點雲精度，因此後續實驗僅以萃取矩形建物之平屋頂面點雲過程探討粗差比率對半自動化點雲精度評估程序之影響。模擬實驗成果顯示最小一乘法有助於提升李德仁法偵測粗差數量5%至10%；真實資料實驗，以含有牆面點雲的狀況為例，則有助提升5%的偵測粗差數量。本研究由逐步測試結果提出能夠適用於真實狀況的半自動化之點雲精度評估程序，即使由不同人員操作，仍能獲得一致的成果，顯示本研究半自動化精度評估程序之可信度。 / The airborne LiDAR system plays a crucial role in building land surveying data. Based on the Land Surveying and Mapping Act, to ensure the quality of surveying, instrument calibration is required. The approach proposed by National Land Surveying and Mapping Center (NLSC) in 2013 was confirmed the feasibility for airborne LiDAR system calibration using rectangular horizontal roof plane. The calibration mean to assess the final quality of airborne LiDAR system based on the assessment of the accuracy of the point cloud, and do not adjust the instrument. But the results may vary according to different operators. This study attempts to establish a semi-automatic procedure for the accuracy assessment of point clouds from airborne LiDAR system. In addition, the gable roof ridge lines is discussed for its feasibility for the accuracy assessment of point cloud. No matter that calibration is performed using rectangular horizontal roof plane or gable roof ridge line, point clouds located on roof planes need to be extracted at first. Therefore, Least Absolute Deviation (LAD) combined with the Iteration using Selected Weights (Deren Li method) is developed to exclude the non-roof points which regarded as gross errors and eliminate their influences. The simulated test and actual data test found that gable roof ridge lines are not suitable for accuracy assessment. As for the simulated test using horizontal roof planes, LAD combined with Deren Li method prompts the rate of gross error detection about 5% to 10% than that only by Deren Li method. In actual test, data contains wall points, LAD combined with Deren Li method can prompt about 5%. Meanwhile, a semi-automatic procedure for real operations is proposed by the step-by-step test. Even different operators employ this semi-automatic procedure, consistent results will be obtained and the reliability can achieve.