以多項式取代共線式在SPOT立體像對匹配及前方交會上之應用

Using Polynomials Instead of Collinearity Equations for Matching and Space Intersection of SPOT Stereo Images

王嵐威(Lan-Wei Wang) ； 王蜀嘉(Shue-Chia Wang)

《航測及遙測學刊》 2卷2期 (1997/06) Pp. 65-79

https://doi.org/10.6574/JPRS.1997.2(2).4

摘要

本文針對SPOT立體像對，研究利用多項式代替共線式，配合近似的高程資訊，建立一套以影像匹配的方式自動化產生數值地形模型的模式。由於SPOT影像屬於線列式投影的影像，投影中心為時間的函數，以嚴密的共線式作計算，計算量比一般的航測像片大。Kratky提出了多項式投影函數（polynomial mapping functions，以下簡稱PMFs）的構想，以解決SPOT影像在解析製圖上即時（Real-Time）定位的問題。本文嘗試將PMFs應用到用數位式SPOT立體像對的處理上。利用影像到影像的PMFs可以用來定義在影像匹配時像空間的幾何約制條件。像空間到物空間的PMFs，可以用來進行前方交會，直接得到TM影座標。而物空間到像空間的PMFs，則可用來產生正射像片。研究結果顯示經由SPOT全色態立體影像匹配，高程約可達10公尺等級的精度。另外，雖然SPOT影像的成像特性使其無如航測影像般的核線，但藉著PMFs可以得到很好的近似核線，將搜尋匹配降低至1D，增加匹配的成功率。

關鍵字

數值地形模型 ； 多項式投影函數 ； 影像匹配

並列摘要

The geometric relationships between the SPOT stereo images and the ground points can be approximately described by simplified polynomials in place of collinearity equations.Because the SPOT image is obtained by the so-called ”push broom” scanning principle, the position of projecting centers is a time-dependent function. Using rigorous collinearity equations to solve space intersection problems is much more difficult than that of the aerial photography. Kratky proposed the polynomial mapping functions (PMFs) to solve the problem of real-time positioning in analytical plotter. Here, we attempt to apply them to the matching problems of digital SPOT stereo images.The PMFs in this research have three major applications: First, the polynomial functions for the image-to-image relationships are used to define geometric constraints in image space. Second, the image-to-object PMFs are used to perform space intersection to get the ground coordinates. Finally, the object-to-image PMFs are used to project grid points of the DTM up ward to SPOT images for orthoimage generation.The matching of SPOT stereo panchromatic images using PMFs can achieve an accuracy of 10 m in elevation. Moreover, PMFs can be used to derive a very good approximation of the epipolar lines, which can be used to reduce the search space from 2-D to 1-D and also increase the success rate of the image matching.

並列關鍵字

digital terrain model ； polynomial mapping functions ； image matching