- 期刊
有理函式秩虧處理
Alternative Treatment of Rank Deficiency When Solving Rational Function Model
摘要
應用衛星影像進行物空間定位及測圖任務須依賴可靠之物像對應關係，其中，有理函數模式（Rational Function Model, RFM）具有不需引入感測器物理模式並能在某些條件具足下呈現近乎等同於嚴密感測器模式的物像幾何對應品質，並深具使用上的透明性及便利性，遂成為一通用的物像對應數學工具。然而，實務作業中，引用控制點方式進行高階有理函式物像對應之參數解算受制於過度參數化影響，為一秩虧（Rank Deficiency）方程，現行作業常以加入微小常數方式使求解系統穩定，然作業上仍有諸多不便之處。本研究探討以消除相依參數之概念處理上述問題，經由初步之測試成果驗證，本文引用之方法為能夠選用獨立參數組且能達提升工作效能之益。
並列摘要
Among models sufficiently employed for positioning and mapping tasks by using satellite imagery, rational function model (RFM) performs almost as equally well as rigorous sensor model when fulfilling some restrictions, and has gained increasing popularity due to its transparency and convenience on application side. One disadvantage of RFM is the issue of rank deficiency when estimating high-order RFM coefficients by exclusively using ground control points with insufficient geometry as referring to RFM. Although the approach of regularizing normal matrix by adding a small multiplication of the identity matrix has been commonly used to stabilize the system and obtain the solution, non-smoothing processing still gets bothered and suggests that more efficient methods are welcome and expected. To this end, the authors proposed a method in which correlated parameters are to be eliminated. The preliminary result shows that effectiveness of the proposed method towards the solution is highly performed. Apart from that, identifying the correlations among the parameters highlights the very unique contribution as compared to other alternatives.