利用衛星影像以有理函數物像對應同時求解水位面及水下物點三維坐標

Abstract

現今衛星影像多利用有理函數模式進行物像對應，然而，當衛星攝影取像對象為水下可視場景時，成像光線會受到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。面對這樣雙介質的攝影任務，本研究提出一調變方式，在有理函數模式下模擬出成像路徑，並考慮折射效應同時求解水位面及水下物點三維坐標，建構帶有約制的廣義最小二乘平差模式進行解算。幾何本質上，受折射影響的成像路徑，在水位面為完全未知的解算系統下，水下折射向量隨水位面的迭代解算位置調變，水位面及水下物點之定位具很大的解算可接受範圍，無法獲致品質良好的水下物點及水位面的定位成效。本文除揭櫫此物像對應特質之外，並探討倘有額外物空間之觀測值(如:水位面、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，像點量測精度及聯合多點解算之效益也一併納入考量。同時，也探討當異軌衛星影像帶有各自的水位面時，如何在前述模式下完成水位面及水下物點定位及分析其品質。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。

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 benefits of increasing the accuracy of measured image points and using multiple points are also investigated in this study. Moreover, the situation of having different water surfaces with across-track image acquisition is analyzed together with the estimation quality on water surfaces and underwater object points. In experiment part, this study uses not only simulation data but also real satellite imagery to verify the feasibility of the proposed model.