單像滅點解算姿態角與內方位參數之幾何與誤差分析

The Geometry and Error Analysis of Solving Pose and Interior Orientation Parameters by Vanishing Point Geometry through Single View

陳韋彤(Wei-Tong Chen)

指導教授 ： 趙鍵哲

國立臺灣大學/工學院/土木工程學研究所/碩士(2021年)

https://doi.org/10.6342/NTU202100418

摘要

利用滅點幾何解算內方位參數與姿態角，在電腦視覺與攝影測量領域中已是常見的方法。然而，回顧過往的文獻，鮮少有對於此方法解算的成果進行概括性的誤差分析。本研究的目標為探討滅點幾何於內方位參數與姿態角解算時的誤差影響因子，利用誤差傳播詳細分析攝影時的條件對於解算精度的影響；結合滅點與內方位參數和姿態角間之幾何關係，視覺化分析各因子對整體幾何結構之影響，以便於更直覺的理解誤差傳播分析的結果。本文滅點幾何課題研究不受限於單一特定之攝影環境，針對不同攝影條件下所歸納誤差之定性定量分析有助於釐清攝像幾何對於姿態角及內方位參數估值之品質影響及各影響因子之相關性，能提供參數解算分析及取像姿態設計任務更全貌的參考。
本研究課題解析成果之具體成效如下:(1)於內方位參數與姿態角誤差特性之相互影響方面，當姿態角ω、φ接近0°、90°時，內方位參數誤差越大，但因同時受幾何交互作用的影響，誤差極小值不會出現在特定位置。(2)姿態角的部分，ω角和φ角的誤差分別與|sin2ω|和|tanφ|有正向關係，但三角函數在接近0°時會急遽變化，使反算的姿態角對於誤差相當敏感。至於κ角則與Y、Z方向滅點距離成反比。(3)以模擬實驗驗證前述誤差特性，並定量分析各影響因子對品質之影響。

關鍵字

滅點幾何 ； 內方位參數 ； 姿態角 ； 誤差分析 ； 單像

並列摘要

Using vanishing point geometry to solve interior orientation parameters and pose is common in computer vision and photogrammetry. However, reviewing the literature, the general error analyses of the results for this method are scarce. Therefore, the purpose of this research is to explore the influential factors of the accuracy of these parameters and uses error propagation to analyze the accuracy of the solution under different photographic conditions. Furthermore, visualizing the influence of each factor on the overall geometric structure makes the error analysis more intuitive. The study of vanishing point geometry in this article is not limited to a specific photographic condition. Qualitative and quantitative analysis of accuracy summarized under different photographic conditions helps to clarify the influence between the estimation of pose and interior orientation parameters.
The significances of this study can be summarized as follow: (1) In terms of the mutual influence of error between the interior orientation parameters and pose, when ω and φ are close to 0° or 90°, the error of interior orientation parameters will be larger. However, the occurrence of minimal error is hard to be located. (2) The errors of ω and φ are positively related to |sin2ω| and |tanφ|, respectively. However, the trigonometric function will change rapidly when it is close to 0 degrees, which makes the inverse operation of pose very sensitive to error. As for κ, it is inversely proportional to the vanishing point distance in Y and Z directions. (3) Verify the aforementioned error characteristics and quantitatively analyze the impact of each influence factor on the quality with simulation experiments.

並列關鍵字

single view ； vanishing point geometry ； error analysis ； interior orientation parameters ； pose

參考文獻

Barnard, S.T., 1983. Interpreting perspective images, Artificial Intelligence, 21(4):435-462.

Brown, D.C., 1971. Close-range camera calibration, Photogrammetric Engineering, 37:855-866.

Chang, H., 2017. Single View Reconstruction Using Refined Vanishing Point Geometry, Ph.D. dissertation, National Central University, Taoyuan, 193 p.

Fryer, J.G., 1996. Camera Calibration, Close-range photogrammetry and machine vision, (K.B. Atkinson, editor), Whittles Publishing, UK, pp. 156-179.

Fan, Y.C., Chen, Y.C., and Chou, S.Y., 2014. Vanishing point based depth cue measurement scheme for 3DTV system, 2014 International Conference on Information Science, Electronics and Electrical Engineering, Vol. 3, Sapporo, Japan, pp. 1775-1778.