單張框幅式影像後方交會危險配置解析及因應

Analysis and Solutions for the Singular Problem under Single Frame Photo Resection

李慧娟(Hui-Chuan Lee)

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(2015年)

https://doi.org/10.6342/NTU.2015.01542

摘要

儘管影像外方位參數獲取方式漸趨多元，單張框幅式影像後方交會仍是攝影測量常見任務，當滿足最小求解條件之控制特徵物像對應，便可解算影像的外方位參數。然而，當控制特徵及透視中心呈現危險配置，將面臨數值解算困難。為免除危險配置對單張框幅式影像後方交會解算的限制，必須剖析其特性。本研究工作包含解析及因應兩部分，並以控制點、控制直線及綜合兩者的混合特徵為對象進行探討。
於解析的部分，確立危險配置類型後，遵循攝影測量後方交會及物像對應之原則，以幾何方法論證透視中心幾何不唯一與外方位參數解算系統數值奇異兩者間的對應性，過程中引用線性代數方法輔助分析；於因應的部分，以控制特徵、透視中心間的相對關係定義坐標軸向，分析組合有效的地面簡易觀測量類型，透過像點量測與外方位參數解算系統進行連結，消弭危險配置並獲致穩定解。
本研究工作完成十一種危險配置的幾何解析及十三種危險配置的因應方式。結果顯示，在幾何解析階段，數值奇異有其對應之透視中心幾何不定軌跡，此部分學理性之探討拓展了此課題之完整性及周延性；於因應階段，所施作之有效觀測量以解除幾何缺失考量進行布設，較之傳統以控制點或控制線補強之作法更開創實務應用價值。

關鍵字

單張框幅式影像後方交會 ； 外方位參數 ； 危險配置 ； 線性代數 ； 控制點 ； 控制線

並列摘要

Despite the various ways of acquiring exterior orientation parameters developed in recent years, single photo resection has not diminished its importance in many photogrammetric applications. The exterior orientation parameters of single photo can be resolved when provided with minimal number of control data. However, when faced with critical configurations, solving exterior orientation parameters would be difficult, if not impossible, in numerical manipulation and/or unreliable in getting solutions.
This study aimed at analyzing critical configurations of single frame photo resection when employing control points, control lines, or the mixture of both and offered effective ways of adding observations both in image space and object space to satisfy the geometric condition. Techniques of linear algebra have been applied to confirm and quantify the critical configurations. The trajectories of perspective center under critical configurations, if any, were found analytically.
In total, 11 critical configurations have been thoroughly analyzed and 13 treatments of overcoming rank deficiency have been proposed. The analysis of critical configurations of single photo resection using control points, control lines, or both has strengthened as well as expanded the domain knowledge in this subfield. On the other hand, the configured angle and distance measurements convenient to take in site to satisfy the geometric condition obviously offer alternatives more favoring the practical applications, as compared to the traditional way of adding control points or control lines for overcoming rank deficiency.

並列關鍵字

Single Frame Photo Resection ； Exterior Orientation Parameters ； Critical Configurations ； Linear Algebra ； Control Point ； Control Line

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