利用衛星影像以有理函數物像對應解算水位面高程及水下物點三維坐標

Simultaneously Determining Water Surface and Underwater Object Points based on Rational Function Model by Using Satellite Images

張雅博(Ya-Po Chang) ； 趙鍵哲(Jen-Jer Jaw)

《航測及遙測學刊》 24卷2期 (2019/06) Pp. 89-110

https://doi.org/10.6574/JPRS.201906_24(2).0002

摘要

現今衛星影像大多利用有理函數模式進行物像對應，但是當衛星攝影取像對象為水下可視場景時，成像光線會因為折射效應而產生偏移，此時衛星影像帶有的有理函數係數並無法正確描述雙介質的物像對應關係。為此，本研究提出一調變模式，在有理函數模式下仿擬成像路徑，並考慮折射效應，建構帶有約制的廣義最小二乘平差模式進行水位面高程及水下物點三維坐標解算。基於幾何本質，受到折射效應的成像路徑，在水位面為完全未知的情況下，水下折射向量會隨著水位面位置的迭代解算而改變，此時水位面及水下物點定位具有很大的可接受解算範圍，無法獲得良好的定位成效。因此，本文除揭櫫此物像對應的特質外，並探討倘若具有額外物空間之觀測值，例如：水位面高程、高程控制點、全控點及水深等，其如何助益於水位面及水下物點的定位解算。除此之外，聯合多點解算之效益也一併納入考量。實驗資料部分，則以模擬資料與實際資料驗證所提模式之適用性並完成成果之定性及定量分析。成果上，水位面品質為此定位模式之關鍵，故須採用可資使用的物空間約制來進行，在絕對條件具有良好品質時，以水位面約制效果最佳；另一方面，高品質之水深資訊約制解算可獲致水位面定位品質達1～2 pixels，聯合多點位水深約制效果又會更佳。除此之外，在高品質水深約制模式下，水下物點高程分量品質更勝於水位面完全已知時之解算成效。

關鍵字

有理函數模式 ； 折射效應 ； 水下物點 ； 水位面高程 ； 約制

並列摘要

Nowadays, most satellite imagery vendors offer rational polynomial coefficients (RPCs) to users for processing geometric information. Although known RPCs in rational function model (RFM) would give explicit object-to-image correspondence, the physical meaning of the parameters is hard to be interpreted. Especially, when faced with underwater object points, the object-to-image correspondence cannot be directly realized by these RPCs due to the refraction effect. To cope with this situation, this study proposes an alternative way in the imaging rays under RFM and refraction effect to determine both the water surface and underwater object points. A generalized least-squares adjustment with constraints is developed to well handle functional and stochastic models. To its essence provided that the water surface is totally unknown, the refraction vectors under the water varying with estimated water surface through each iteration results in a weak geometry and leads to unstable solutions. In addition to revealing the characteristics of aforementioned object-to-image correspondence, this study explores how the underwater object point and water surface determination would benefit from the prior observations of water surface, vertical control point, full control point, and even water depth. The effect of using multiple points is also investigated in this study. In experiment part, this study uses not only simulation data but also real satellite imagery to verify the feasibility of the proposed model. And it can be summarized that the quality of water surface, either through priori information or derived from control information, is crucial to the positioning performance of underwater object points. The accuracy of water depth better than 2m, under employed satellite imagery, would supply water surface with 1-2 pixels positioning quality, and even bring about superior underwater object point coordinates as compared to when they are to be determined through perfect water surface.

並列關鍵字

Rational function model ； Refraction effect ； Underwater object points ； Water surface ； Constraints