本論文描述如何在單一視角的平面影像中，藉由透視投影所隱含之幾何資訊，量測與重建場景特徵物的三維模型。
單影像量測所依據的是物空間三個彼此正交軸向的平行線，在影像上所交集的滅點，藉由滅點重新推論出成像時的物像關係與相機參數及姿態。
此演算法具有低操作門檻、低成本與可靠精度等特性，並能針對已遭拆遷或破壞之歷史建物進行三維重建。

本研究提出之演算流程，可在無先驗資訊，例如相機內外方位參數、透鏡畸變等環境下，在具有透視投影的照片或是圖畫中，以層疊霍式轉換自動化地萃取與分類通過三方向滅點的直線特徵。
在初始滅點與估算特徵投影點的迭代過程中，利用投影點的誤差分析以O(1)計算複雜度的階層式微調機制修正滅點的位置，降低滅點幾何的隨機與系統性誤差。
平面模型藉由滅點幾何即可推估特徵點的相對坐標，而針對三種常見的曲面結構：橢圓柱型、旋轉曲面、自由曲面，則進行不同策略性的三維幾何特徵參數重建。
圓柱結構萃取其長短軸長度與起迄點位置，旋轉曲面尋找其中心軸與邊界曲線，自由曲面則決定取樣點數與建立邊界參數後，內插出曲面參數模型。

本研究使用之測試例影像來源包含低誤差之電腦模擬輸出影像、近景攝影之非量測型相機與視訊擷取、真實畫作與數化歷史影像等。
電腦模擬輸出影像在規則與非平面模型的建置誤差皆低於1\%。
近景攝影建置之規則與非平面模型，相較於地面光達與航測立體對的模型誤差則各低於2\%與3\%。
滅點微調機制能給重建後三維模型的均方根誤差由2\%降至0.6\%。
建置成果與現地量測等資料進行量化驗証與視覺化之比較，同時也針對視角條件進行了誤差分析。
此技術能應用於三維數位典藏、虛擬實境、數位城市、畫作三維視覺化與構圖分析等多方領域。

This study developed algorithms to measure and reconstruct three-dimentional (3D) objects and scenes from a single-perspective image based on its geometric cues.
Single view metrology relies on the 3 vanishing points that converge by parallel lines along 3 mutually orthogonal axes.
Vanishing points can be used to estimate not only the camera pose but also internal parameters; thus, the 3D measurement of monocular vision can obtain a partial or complete 3D reconstruction of a scene.
Advantages of the proposed method include low cost, reliable accuracy and flexibility, and the potential to reconstruct buildings and other architecture that are heavily damaged or even no longer exist.

The presented algorithms employ uncalibrated images; therefore, no prior camera information is needed.
Exterior and interior orientation parameters can be calibrated directly from the vanishing points.
The proposed scheme began with line segment extraction and classification using cascade Hough transform from photographs or paintings with fine-perspective projection, and a fully automated base point searching algorithm is then used to locate the projection of feature points on the referenced plane.
The systematic and random errors of the vanishing points and base points are minimized iteratively during the vanishing point refinement process based on the diversity of each projection group with an O(1) computational complexity.
Three-dimensional coordinates of feature points are computed based on the single-view metrology.
In addition, 3 types of non-planar structures including elliptic cylinder shapes, surfaces of revolution, and free-form surfaces are extracted separately for reconstruction based on their significant parameters.
Finally, regular and curved models are merged based on their shared feature points.

The output imagery of a computer-simulated model, video frame cut, consumer camera, and real paintings are used in this study to test the performance of the algorithms.
The proposed vanishing point refinement process is able to reduce the differences between the images with and without lens distortion.
Quantitative evaluations of the results compared with ground-based surveying and visualized comparison with raw images indicate that the algorithms can successfully extract 3D information and reconstruct 3D models of specific non-planar structures.
Estimation errors of regular and non-planar parameters are less than 1\% compared to the ground truth using computer simulated imagery.
For close range photograph, the average regular and non-planar errors are less than 2\% and 3\%, respectively, compared to the ground truth measured by ground-based LIDAR and stereo photo pairs.
The proposed vanishing point refinement process improves the RMSE of the 3D model from about 2\% error to about 0.6\%.
The accuracy of the proposed methods are related to the viewing angles based on the vanishing point geometry, and validation of viewing angle tolerance is also provided by given random errors during vanishing point calculation.

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