提出一种更严密的双介质立体摄影测量物方坐标折射改正算法。该算法用水下目标的空中同名直线光线公垂线段的中点作为摄影测量交会点的理论位置，解决了空中同名直线光线延长线不相交情况下摄影测量交会点不存在导致的点位关系不确定性问题，使摄影测量交会点到真实物点的坐标折射改正公式能够严格推导出来。分析了空中同名直线光线不相交情况对物方大地坐标折射改正的不利影响，研究了摄影测量交会点与水下真实物点的相互位置关系，推导了水下目标点的水深和大地坐标计算公式（即折射改正公式），通过WorldView-2立体影像浅海海底地形测量试验对算法的正确性和测量精度进行验证。研究表明，不论水下目标的空中同名直线光线延长线是否相交，该算法都是适用的，且能显著改善水下目标的高程测量精度。
A more rigorous algorithm is presented for correction of refraction effects in two-media stereo photogrammetry. The mid-point of the shortest line segment joining two aerial corresponding rays of a point on an underwater object is used as a photogrammetric intersection point which doesn't exist when the two rays are non-intersecting. As a result, the uncertainty of the intersection point is removed, the positional relationship between the intersection point and the true object point becomes definite, and the refraction correction formula from the intersection point to the true object point can be strictly derived. The bad effect on the refraction correction is firstly analyzed, which caused by that the two rays are non-intersecting. Then the positional relationship between the intersection point and the true object point is studied. After that, the formulas regarding water depth and geodetic coordinates of points on an underwater object are deduced, that is often known as correction of refraction effects. Finally, the algorithm is tested by two experiments using the data of WorldView-2. The results show that the algorithm is suitable for any case in which whether or not the two aerial corresponding rays of an underwater object point are intersecting, and it can significantly improve the measurement accuracy of underwater object's elevation.
[1] CHONG A K, SCHNEIDER K. Two-medium Photogrammetry for Bottlenose Dolphin Studies[J]. Photogrammetric Engineering and Remote Sensing, 2001, 67(5):621-628.
[2] TELEM G, FILIN S. Photogrammetric Modeling of Underwater Environments[J]. ISPRS Journal of Photogrammetry and Remote Sensing, 2010, 65(5):433-444.
[3] WIMMER M, MANDLBURGER G, RESSL C, et al. Estimation of High Resolution Shallow Water Bathymetry via Two-media-photogrammetry:A Case Study at the Pielach River[C]//Geophysical Research Abstracts vol. 18, EGU General Assembly 2016. Vienna,Austria:EGU, 2016:7197.
[4] WESTAWAY R M, LANE S N, HICKS D M. Remote Survey of Large-scale Braided, Gravel-bed Rivers Using Digital Photogrammetry and Image Analysis[J]. International Journal of Remote Sensing, 2003, 24(4):795-815.
[5] LANE S N, WIDDISON P E, THOMAS R E, et al. Quantification of Braided River Channel Change Using Archival Digital Image Analysis[J]. Earth Surface Processes and Landforms, 2010, 35(8):971-985.
[6] SHAN Jie. Relative Orientation for Two-media Photogrammetry[J]. The Photogrammetric Record, 1994, 14(84):993-999.
[7] TELEM G, FILIN S. Photogrammetric Modeling of the Relative Orientation in Underwater Environments[J]. ISPRS Journal of Photogrammetry and Remote Sensing, 2013(86):150-156.
[8] 王有年, 韩玲, 王云. 水下近景摄影测量试验研究[J]. 测绘学报, 1988, 17(3):217-224. WANG Younian, HAN Ling, WANG Yun. Experimental Research of Underwater Close-range Photogrammetry[J]. Acta Geodaetica et Cartographica Sinica, 1988, 17(3):217-224.
[9] 常本义. 双介质摄影测量基本公式[J]. 测绘学报, 1991, 20(4):288-294. CHANG Benyi. Basic Formulas of Two-media Photogrammetry[J]. Acta Geodaetica et Cartographica Sinica, 1991, 20(4):288-294.
[10] 单杰. 双介质摄影测量的相对定向[J]. 测绘学院学报, 1993, 10(3):38-44. SHAN Jie. Relative Orientation for Two-media Photogrammetry[J]. Journal of the Institute of Surveying and Mapping, 1993, 10(3):38-44.
[11] 周高伟, 李英成, 任延旭, 等. 低空无人机双介质水下礁盘深度测量试验与分析[J]. 测绘学报, 2015, 44(5):548-554. DOI:10.11947/j.AGCS.2015.20140259. ZHOU Gaowei, LI Yingcheng, REN Yanxu, et al. Research of Two-media Underwater Reefs Depth Measurement Experiment Based on Low-altitude UAV[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(5):548-554. DOI:10.11947/j.AGCS.2015.20140259.
[12] 曹彬才, 邱振戈, 朱述龙, 等. 高分辨率卫星立体双介质浅水水深测量方法[J]. 测绘学报, 2016, 45(8):952-963. DOI:10.11947/j.AGCS.2016.20150583. CAO Bincai, QIU Zhenge, ZHU Shulong, et al. Shallow Water Bathymetry through Two-medium Photogrammetry Using High Resolution Satellite Imagery[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(8):952-963. DOI:10.11947/j.AGCS.2016.20150583.
[13] MURASE T, TANAKA M, TANI T, et al. A Photogrammetric Correction Procedure for Light Refraction Effects at a Two-medium Boundary[J]. Photogrammetric Engineering & Remote Sensing, 2008, 74(9):1129-1136.
[14] GEORGOPOULOS A, AGRAFIOTIS P. Documentation of a Submerged Monument Using Improved Two Media Techniques[C]//Proceedings of the 18th International Conference on Virtual Systems and Multimedia. Milan, Italy:IEEE, 2012:173-180.
[15] FRYER J G, KNIEST H T. Errors in Depth Determination Caused by Waves in Through-water Photogrammetry[J]. The Photogrammetric Record, 1985, 11(66):745-753.
[16] WESTAWAY R M, LANE S N, HICKS D M. Remote Sensing of Clear-water, Shallow, Gravel-bed Rivers Using Digital Photogrammetry[J]. Photogrammetric Engineering and Remote Sensing, 2001, 67(11):1271-1282.
[17] BUTLER J, LANE S, CHANDLER J, et al. Through-water Close Range Digital Photogrammetry in Flume and Field Environments[J]. The Photogrammetric Record, 2002, 17(99):419-439.
[18] MAAS H G. A Modular Geometric Model for Underwater Photogrammetry[C]//The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences:Volume XL-5/W5. Dresden, Germany:TSPRS, 2015:139-141.[19] DIETRICH J T. Bathymetric Structure-from-motion:Extracting Shallow Stream Bathymetry from Multi-view Stereo Photogrammetry[J]. Earth Surface Processes and Landforms, 2017, 42(2):355-364.
[20] DigitalGlobe. WorldView-2 Overview[EB/OL].[2017-03-10]. http://content.satimagingcorp.com.s3.amazonaws.com/static/satellite-sensor-specification/WorldView-2-PDF-Download.pdf.
[21] 曹斌, 邱振戈, 曹彬才. 四种遥感浅海水深反演算法的比较[J]. 测绘科学技术学报, 2016, 33(4):388-393. CAO Bin, QIU Zhenge, CAO Bincai. Comparison among Four Inverse Algorithms of Water Depth[J]. Journal of Geomatics Science and Technology, 2016, 33(4):388-393.
[22] 曹斌, 邱振戈, 朱述龙, 等. BP神经网络遥感水深反演算法的改进[J]. 测绘通报, 2017(2):40-44. DOI:10.13474/j.cnki.11-2246.2017.0045. CAO Bin, QIU Zhen'ge, ZHU Shulong, et al. Improvement of BPANN Based Algorithm for Estimating Water Depth from Satellite Imagery[J]. Bulletin of Surveying and Mapping, 2017(2):40-44. DOI:10.13474/j.cnki.11-2246.2017.0045.
[23] HEDLEY J D, HARBORNE A R, MUMBY P J. Technical Note:Simple and Robust Removal of Sun Glint for Mapping Shallow-water Benthos[J]. International Journal of Remote Sensing, 2005, 26(10):2107-2112.
[24] DigitalGlobe. Radiometric Use of WorldView-2 Imagery[EB/OL].[2017-03-10]. http://www.pancroma.com/downloads/Radiometric_Use_of_WorldView-2_Imagery.pdf.
[25] DigitalGlobe. Imagery Support Data (ISD) Documentation[EB/OL].[2017-03-10]. http://www.docin.com/p-345895199.html.
[26] Optech. SHOALS-3000 Product Brochure[EB/OL].[2017-03-10]. http://pdf.directindustry.com/pdf/optech/shoals-3000-product-brochure/25132-53146.html.
