以攝影測量進行水位面及水下物點坐標解算

Abstract

框幅式影像物像對應關係建立於透視投影原理，在單一介質中遵循像點、透視中心及物點共線特性。然而當成像光線行經不同介質環境時會因折射效應產生偏折，惟有正確地描述光線在不同介質中的行經路徑才能獲致良好的物像對應關係。本文旨在清澈且平靜無波的水體環境假設下，在函數模式上考量光線折射效應，並將水位面參數以及水下物點坐標列為前方交會計算之未知參數；在隨機模式上引入虛擬觀測量，使得觀測量或參數誤差能合理及隨資料品質有彈性地在最小二乘平差計算中運作。本文成果包含可解性及解算策略的定性討論，以及在水位面及水下物點坐標解算品質上的定量分析，可作為類似場景及測量任務品質精進之重要參考。

The imaging ray under perspective projection would follow the collinearity property, meaning that the image point, perspective center, and object point are collinear, if single medium of imaging is considered. Yet, the refraction effect would bend the imaging ray when it comes to passing different media. Only by quality object-to-image correspondence could the whole path of imaging ray travelling in varied media be correctly established. Under the assumption of clear and lentic environment, the study aims to determine the underwater object points and the water surface simultaneously when dealing with photogrammetric intersection considering the refraction effect in the function model; besides, the pseudo-observations are drawn into the random model that leads the least square adjustment more reasonable and flexible along with observations or errors from parameters. The results involve not only the qualitative discussions of solvability and the strategies solving for singular geometry, but also the quantitative analysis of the quality of determined underwater object points and the water surface, both ultimately offering tasks of the like effective tools and experiences gained in this study.