二維形式的資料在過去很長一段時間內被用於描述空間資訊，然而隨著技術的演進，以三維形式表達空間資訊的需求也日益提高，促使三維場景重建技術蓬勃發展。在都會地區，建築物為常見的主要地物，因此自動化產製三維建物模型成為了重要的研究議題。在眾多建模技術中，點雲已逐漸成為自動化建模的主要資料來源；點雲建模的關鍵在於從離散的點群萃取出所需的幾何資訊，以產製真實地物的三維模型。本文將體元法應用於航測影像密匹配點雲之三維山形屋頂房屋模型建置，並提出一套依據點座標精度給定觀測量權重之加權模式，其中座標精度的估算將考量匹配像點紋理複雜度及物點交會幾何強度，進行加權體元平差建模。
體元法的基本概念為將點雲資料以最小二乘方式套合至事先定義好的房屋模型上。首先，山形屋頂房屋模型以一地面角點A座標X_A、Y_A、Z_A，兩相鄰邊長w_1、w_2，高h、屋脊高r、屋脊線相對於平行牆面之水平偏移量s，以及水平面上旋轉角θ共九個參數所定義。接著將實驗用的航測影像輸入軟體Metashape進行密匹配而得到建模所需之點雲資料。利用九參數所定義出的平面方程式，以點到模型面距離作為虛擬觀測量而建立觀測方程式，將建物點雲以最小二乘平差方式套合，即可求解模型參數並產製三維房屋模型。
為了得到精度較高之房屋模型，故透過各點誤差橢球計算出沿著建物面法方向上的精度，作為觀測量的給權依據，以加權體元平差進行建模運算。為求得各點誤差橢球，本文提出一個考量了匹配像點紋理複雜度及物點交會幾何強度的方式，以估算各點之座標精度。像點紋理複雜度是採用Haralick等人（1973）提出之灰階共生矩陣計算一物點之對應匹配像點熵值後，再取其平均作為代表；交會幾何強度則是透過物點倒投影之方式求得前方交會光線所構成之法矩陣，取其主對角元素而得。接著將熵平均值倒數與三個主對角元素相乘，分別作為X、Y、Z座標之精度大小指標，建物點雲將依據指標被分為由小到大共三個精度等級點群，同等級點群內各點視為具有一致的精度大小，最後利用點群內各點到近似房屋模型面的垂距分量來估算座標精度。
實驗內容則分為模擬點雲及真實點雲測試兩部分。首先透過模擬點雲的實驗檢視體元模型的幾何約制力及平差模式的穩定性，實驗項目包括最少點數建模、初始近似值誤差測試及不同密度點雲建模測試。最少點數之建模結果顯示，當所有面上均有點分布，或是其中一面含有至少三個不共線點時較有利於平差解算。初始近似值誤差測試結果顯示體元平差對參數w_1、w_2的初始值誤差容忍度較高，可達到±〖10〗^14~〖10〗^15m；X_A、Y_A、Z_A及h次之，誤差可達到±〖10〗^7m；r、s最小，可容許誤差不超過10m；至於θ誤差在±68°內均能收歛至正確解，超出此範圍後平差解算將變得不穩定。不同點密度建模測試則顯示，實驗中產製的模擬點雲在點密度超過0.1點/地元的情況下，解算所得之模型參數誤差不再顯著地降低；參數最或是值的後驗精度則在點密度超過0.6點/地元後不再明顯改善。
真實點雲實驗則是從航測影像密匹配點雲中挑選兩棟建物之點雲進行等、加權體元平差建模測試。建物一周圍遮蔽少而牆面點雲分佈較為完整；建物二坐落於建物密集地區，牆面點雲受鄰近房屋遮蔽而相對缺乏。為了解嚴重遮蔽以及點雲內含有粗差時的建模情形，故基於建物一點雲再設計兩個延伸測試例。延伸測試例1是篩除建物一部分屋頂及牆面點雲後所得，用於測試嚴重遮蔽下之建模成果；延伸測試例2則是將原本不屬於建物一主體結構之附屬構造物點群加入建物一點雲中，進行點雲含有粗差時之建模測試。
比較四個案例的等、加權體元套合精度，其中只有延伸測試例1在加權計算下之精度比等權計算小1cm；其餘案例之等、加權套合精度差異均在毫米等級，差異並不明顯。將四個案例等、加權計算所得之模型參數與檢核資料相比，以公尺為單位之參數在等、加權計算下的誤差大小差值大部分小於1cm，各案例至多2〜3個參數超過1cm。參數θ之等、加權誤差差異則以建物一最大，其加權計算下之誤差大小高出等權計算約113倍，但誤差大小不超過0.0001rad。延伸測試例2亦為加權所得之θ誤差大小較大，接近0.002rad，且高出等權計算之誤差大小約6.6倍。建物二及延伸測試例1等、加權解算所得之θ則無明顯差異，不過建物二之θ誤差大小較大，接近0.02rad，延伸測試例1較小，不超過0.002rad。
為了檢視本文提出之精度指標是否能發揮效用，故人工挑選適合的密匹配像對產製建物點雲，額外再進行一補充實驗。補充實驗例的結果證實了在掌握密匹配像對的方位資訊下，本文提出之加權模式確實能達到優於等權模式之模型套合精度。等權計算下的精度為0.167m，加權計算則為0.116m，加權模式的模型套合精度較等權模式提升了5.1cm。此外，各等級點群座標精度估值之大小關係大致上與實際精度吻合，也因此發揮了加權平差的效果，提升了模型成果精度。不過仍有部分等級點群之實際精度與對應等級的大小關係不符，因此後續研究工作仍有待改良精度指標分類點雲資料的方式。
綜觀目前之實驗結果，等、加權體元建模之間的成果差異並不明顯。進一步分析加權模式下的精度估值、所提出之精度指標以及依據指標分級之點群實際座標精度，可發現用以估算座標精度之點群樣本容易遇到精度指標一致性偏低、樣本點數不足、點到近似模型面之垂距分量不符合隨機誤差分布特性等問題，代表目前之點雲分群方式有待調整，需提升座標精度估值之代表性，才能發揮加權計算的效果。
依據本文的實驗結果，後續之研究方向可聚焦於如何善用所提出之精度指標而尋找出座標精度相近的點群，使精度估值能更接近實際精度。未來建議可嘗試以K-means演算法（K-means clustering）應用於點雲精度指標分群，此外應結合可評估樣本隨機性質的之統計檢定方式，以確保計算座標精度所使用之垂距分量服從常態分佈，同時點群之點數是否足夠亦應納入考量。

In this research, a weighting model for Voxel Method(VM) is designed and proposed for the construction of 3D gable-roof building models from dense matching point clouds of aerial images. VM defines a set of unknown parameters for a building in advance, and then the point cloud data of this building is introduced to fit with the pre-defined building model through least square manner. This article aims at the generation of gable-roof 3D building model, which can be described by 9 parameters, along with a proposed weighting model that considers both the matching accuracy and geometry strength of the point data. Simulated point cloud data is produced to investigate some basic characteristics of VM least square model, including the geometric constraint and adjustment robustness. Finally, point data sets of two gable-roof buildings are extracted from dense matching point clouds to test the weighting VM. One of the building point sets is used to design two extensional tests which investigate VM’s performance while facing occlusions and outliers. The results suggest that the current method for estimating point coordinates’ accuracy still needs improvement so that the effect of the weighting model can be fully exploited.

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