顾及“保真性”原则的双向滚动球变换DDM多尺度表达算法

doi:10.11947/j.AGCS.2017.20160558

测绘学报 ›› 2017, Vol. 46 ›› Issue (6): 789-801.doi: 10.11947/j.AGCS.2017.20160558

顾及“保真性”原则的双向滚动球变换DDM多尺度表达算法

董箭^1,2, 彭认灿^1,2, 张立华^1,2, 刘国辉³, 朱强⁴

1. 海军大连舰艇学院海洋测绘系, 辽宁大连 116018;
2. 海军大连舰艇学院海洋测绘工程军队重点实验室, 辽宁大连 116018;
3. 海军出版社, 天津 300450;
4. 92403部队, 福建福州 350501

收稿日期:2016-11-04 修回日期:2017-05-03 出版日期:2017-06-20 发布日期:2017-06-28
通讯作者: 彭认灿 E-mail:pengrencan63@163.com
作者简介:董箭(1985—),男,博士,讲师,研究方向为海图制图理论与方法。E-mail:navydj@163.com
基金资助:
国家自然科学基金（41471380；41601498）

Multi-scale Representation of Digital Depth Model Based on Double Direction Rolling Ball Transform according to the Reality Principle

DONG Jian^1,2, PENG Rencan^1,2, ZHANG Lihua^1,2, LIU Guohui³, ZHU Qiang⁴

1. Department of Hydrography and Cartography, Dalian Naval Academy, Dalian 116018, China;
2. Key Laboratory of Hydrographic Surveying and Mapping of PLA, Dalian Naval Academy, Dalian 116018, China;
3. Navy Press, Tianjin 300450, China;
4. 92403 Troop, Fuzhou 350501, China

Received:2016-11-04 Revised:2017-05-03 Online:2017-06-20 Published:2017-06-28
Supported by:
The National Natural Science Foundation of China (Nos. 41471380;41601498)

摘要/Abstract

摘要： 在分析符合“安全性”要求的数字水深模型（DDM）正向滚动球变换应用局限的基础上，根据高保真DDM多尺度表达评价标准中对水深值准确性、严密有序性及地形信息等级嵌套性的要求，从顾及“保真性”原则的DDM多尺度表达需要出发，提出一种基于双向滚动球变换的DDM多尺度表达算法。分析了海底地貌特征点在DDM双向滚动球变换过程中的变化趋势，根据DDM正向滚动球变换的尺度依赖特性，计算出了一定尺度下海底地貌的横向分布范围与纵向分布高度，建立了DDM多尺度表达中细部（骨架）地貌的判定准则。通过保留给定尺度下DDM中的骨架地貌，使海底地形的整体变化趋势得到了保持，满足了DDM多尺度表达对水深值准确性的要求；论证了DDM单值曲面等距离面变换的水深序同构特性，通过对给定尺度下的细部地貌进行DDM双向滚动球变换的等距离面提取，使海底地形的局部起伏形态得到了保持，满足了DDM多尺度表达对水深值严密有序性的要求；从满足DDM多尺度表达对地形信息等级嵌套性的要求出发，分析了DDM双向滚动球变换中尺度因子与地形信息等级单元逻辑包含关系的不相关性，论证了任意尺度因子条件下具有的相应等级地形信息范围的一致性。试验结果表明该算法克服了DDM正向滚动球变换存在的无法保留负向骨架地貌和保持海底局部地形起伏形态等不足，可有效保留DDM中骨架地貌并综合细部地貌，满足顾及“保真性”原则的DDM多尺度表达要求。

关键词: 数字水深模型, 多尺度表达, 双向滚动球变换, 水深值准确性, 水深值严密有序性, 地形信息等级嵌套性

Abstract: After having analyzed the application deficiency of positive direction rolling ball transform according to the safety principle, and concerned essentially with the evaluation principles of depth precision, depth order isomorphism and hierarchical nesting of terrain information for morphologic fidelity of digital depth model (DDM for short) multi-scale representation, a reality principle-compliant algorithm for DDM multi-scale representation had been proposed based on double direction rolling ball transform. Firstly, by the analysis of the variation tendency of sea floor relief feature point throughout the procedure of double direction rolling ball transform, and combined with the scale dependence character of positive direction rolling ball transform, both the traverse distribution range and the vertical distribution height of sea floor reliefs of a certain scale had been calculated. Secondly, based on the statistic characteristics of DDM grid point undulation extent, a rule of identifying detail (skeleton) reliefs had been established. Finally, by preserving the skeleton reliefs of specific scale factor, the overall trend of the changes of marine topography had been kept to meet the requirement of depth precision principle of DDM multi-scale representation. Besides, the paper demonstrated the ordered isomorphism characteristic of equidistant surface transform, and by extracting equidistant surface through double direction rolling ball transform of detail reliefs, the local undulation morphology of marine topography had been maintained to fulfill the depth order isomorphism principle of DDM multi-scale representation. Furthermore, the hierarchical nesting characteristic of terrain information in the process of double direction rolling ball transform had been demonstrated. The experiment results showed that this algorithm overcomed positive direction rolling ball transform's inability to reserve concave skeleton reliefs and preserve undulating marine topography, among its other inherent deficiencies. In addition, the algorithm preserved the hierarchical nesting of terrain information well with low terrain description uncertainty. It suggested that this algorithm could not only realize the automatic multi-scale representation of DDM but also preserve the basic terrain characteristics according to the reality principle.

Key words: digital depth model, multi-scale representation, double direction rolling ball transform, depth precision, depth order isomorphism, hierarchical nesting characteristic of terrain information

中图分类号:

P229

董箭, 彭认灿, 张立华, 刘国辉, 朱强. 顾及“保真性”原则的双向滚动球变换DDM多尺度表达算法[J]. 测绘学报, 2017, 46(6): 789-801.

DONG Jian, PENG Rencan, ZHANG Lihua, LIU Guohui, ZHU Qiang. Multi-scale Representation of Digital Depth Model Based on Double Direction Rolling Ball Transform according to the Reality Principle[J]. Acta Geodaetica et Cartographica Sinica, 2017, 46(6): 789-801.

参考文献

[1] 董箭. 格网水深插值优化及滚动球变换处理方法研究[D]. 大连: 海军大连舰艇学院, 2013. DONG Jian. Research on Grid Depth Interpolation and Rolling Ball Transform Processing[D]. Dalian: Dalian Naval Academy, 2013.
[2] 贾帅东, 张立华, 宋国大, 等. 基于区域平均垂直不确定度的自适应网格水深建模方法[J]. 测绘学报, 2012, 41(3): 454-460. JIA Shuaidong, ZHANG Lihua, SONG Guoda, et al. A Method for Constructing an Adaptive Grid Digital Depth Model Based on Mean Vertical Uncertainty of Area[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(3): 454-460.
[3] 刘鹏程, 艾廷华, 杨敏. 基于傅里叶级数的等高线网络渐进式传输模型[J]. 测绘学报, 2012, 41(2): 284-290. LIU Pengcheng, AI Tinghua, YANG Min. The Internet Progressive Transmission Model for Contour Based on Fourier Series[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(2): 284-290.
[4] 艾廷华, 成建国. 对空间数据多尺度表达有关问题的思考[J]. 武汉大学学报(信息科学版), 2005, 30(5): 377-382. AI Tinghua, CHENG Jianguo. Key Issues of Multi-scale Representation of Spatial Data[J]. Geomatics and Information Science of Wuhan University, 2005, 30(5): 377-382.
[5] 费立凡, 何津, 马晨燕, 等. 3维Douglas-Peucker算法及其在DEM自动综合中的应用研究[J]. 测绘学报, 2006, 35(3): 278-284. FEI Lifan, HE Jin, MA Chenyan, et al. Three Dimensional Douglas-Peucker Algorithm and the Study of Its Application to Automated Generalization of DEM[J]. Acta Geodaetica et Cartographica Sinica, 2006, 35(3): 278-284.
[6] 万刚, 朱长青. 多进制小波及其在DEM数据有损压缩中的应用[J]. 测绘学报, 1999, 28(1): 36-40. DOI: 10.3321/j.issn:1001-1595.1999.01.007. WAN Gang, ZHU Changqing. Application of Multi-band Wavelet on Simplifying DEM with Lose of Feature Information[J]. Acta Geodaetica et Cartographica Sinica, 1999, 28(1): 36-40. DOI: 10.3321/j.issn:1001-1595.1999.01.007.
[7] 贾帅东, 张立华, 彭认灿, 等. 确保水深模型航海安全性的深度保证率控制方法[J]. 交通运输工程学报, 2015, 15(5): 101-109. JIA Shuaidong, ZHANG Lihua, PENG Rencan, et al. Control Method of Probability of Adequate Depth Ensuring Navigation Safety of Depth Model[J]. Journal of Traffic and Transportation Engineering, 2015, 15(5): 101-109.
[8] 张立华, 贾帅东, 元建胜, 等. 一种基于不确定度的水深控浅方法[J]. 测绘学报, 2012, 41(2): 184-190. ZHANG Lihua, JIA Shuaidong, YUAN Jiansheng, et al. A Method for Controlling Shoal-bias Based on Uncertainty[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(2): 184-190.
[9] 张立华, 贾帅东, 王涛, 等. 深度保证率和表达度指标的定义及评估方法[J]. 武汉大学学报(信息科学版), 2015, 40(5): 695-700. ZHANG Lihua, JIA Shuaidong, WANG Tao, et al. Definitions and Estimating Methods of a Probability of an Adequate Depth and Representiveness[J]. Geomatics and Information Science of Wuhan University, 2015, 40(5): 695-700.
[10] 贾帅东. 航海DDM的构建理论与方法[D]. 大连: 海军大连舰艇学院, 2015. JIA Shuaidong. The Theory and Methods for Constructing Digital Depth Model Serving for Navigation[D]. Dalian: Dalian Naval Academy, 2015.
[11] 吴凡, 祝国瑞. 基于小波分析的地貌多尺度表达与自动综合[J]. 武汉大学学报(信息科学版), 2001, 26(2): 170-176. WU Fan, ZHU Guorui. Multi-scale Representation and Automatic Generalization of Relief Based on Wavelet Analysis[J]. Geomatics and Information Science of Wuhan University, 2001, 26(2): 170-176.
[12] 杨族桥, 郭庆胜, 牛冀平, 等. DEM多尺度表达与地形结构线提取研究[J]. 测绘学报, 2005, 34(2): 134-137. DOI: 10.3321/j.issn:1001-1595.2005.02.008. YANG Zuqiao, GUO Qingsheng, NIU Jiping, et al. A Study on Multi-scale DEM Representation and Topographic Feature Line Extraction[J]. Acta Geodaetica et Cartographica Sinica, 2005, 34(2): 134-137. DOI: 10.3321/j.issn:1001-1595.2005.02.008.
[13] 李精忠, 艾廷华, 王洪. 一种基于谷地填充的DEM综合方法[J]. 测绘学报, 2009, 38(3): 272-275. DOI:10.3321/j.issn:1001-1595.2009.03.013. LI Jingzhong, AI Tinghua, WANG Hong. The DEM Generalization Based on the Filing Valley Coverage[J]. Acta Geodaetica et Cartographica Sinica, 2009, 38(3): 272-275. DOI:10.3321/j.issn:1001-1595.2009.03.013.
[14] 李志林. 地理空间数据处理的尺度理论[J]. 地理信息世界, 2005, 3(2): 1-5. LI Zhilin. A Theoretical Discussion on the Scale Issue in Geospatial Data Handling[J]. Geomatics World, 2005, 3(2): 1-5.
[15] 胡鹏, 高俊. 数字高程模型的数字综合原理研究[J]. 武汉大学学报(信息科学版), 2009, 34(8): 940-942. HU Peng, GAO Jun. The Digital Generalization Principle of Digital Elevation Model[J]. Geomatics and Information Science of Wuhan University, 2009, 34(8): 940-942.
[16] CHRISTENSEN A H J. Cartographic Line Generalization with Waterlines and Medial-axes[J]. Cartography and Geographic Information Science, 1999, 26(1): 19-32.
[17] CHRISTENSEN A H J. Two Experiments on Stream Network Generalization[C]//Proceedings of the 21st International Cartographic Conference. Durban: The International Cartographic Associatio, 2003.
[18] International Hydrographic Bureau.A Manual on Technical Aspects of the United Nations Convention on the Law of the Sea-1982[M]. 4th ed. Monaco: International Hydrographic Bureau, 2006.
[19] 董箭, 彭认灿, 陈轶, 等. 一种基于缓冲区边界相向逼近求交模型的曲线间中心线生成算法[J]. 武汉大学学报(信息科学版), 2011, 36(9): 1120-1123. DONG Jian, PENG Rencan, CHEN Yi, et al. An Algorithm for Centre Line Generation Based on Model of Approaching Intersection of Buffering Borderline from Reciprocal Direction[J]. Geomatics and Information Science of Wuhan University, 2011, 36(9): 1120-1123.
[20] 董箭, 彭认灿, 张立华, 等. 利用滚动圆变换的多波束测深数据滤波算法[J]. 武汉大学学报(信息科学版), 2016, 41(1): 86-92. DONG Jian, PENG Rencan, ZHANG Lihua, et al. An Algorithm of Filtering Noises in Multi-beam Data Based on Rolling Circle Transform[J]. Geomatics and Information Science of Wuhan University, 2016, 41(1): 86-92.
[21] SMITH S M. The Navigation Surface: A Multipurpose Bathymetric Database[D]. Durham: University of New Hampshire, 2003.
[22] 高王军. 双向缓冲区模型在海图自动制图综合中的应用研究[D]. 大连: 海军大连舰艇学院, 2009. GAO Wangjun. Research of the Double Direction Buffering Model and Its Application on Chart Generalization[D]. Dalian: Dalian Naval Academy, 2009.
[23] 董箭, 彭认灿, 张立华, 等. 滚动球变换的数字水深模型多尺度表达[J]. 地球信息科学学报, 2012, 14(6): 704-711. DONG Jian, PENG Rencan, ZHANG Lihua, et al. Multi-scale Representation of Digital Depth Model Based on Rolling Ball Transform[J]. Journal of Geo-Information Science, 2012, 14(6): 704-711.
[24] 汤国安, 龚健雅, 陈正江, 等. 数字高程模型地形描述精度量化模拟研究[J]. 测绘学报, 2001, 30(4): 361-365. DOI: 10.3321/j.issn:1001-1595.2001.04.016. TANG Guoan, GONG Jianya, CHEN Zhengjiang, et al. A Simulation on the Accuracy of DEM Terrain Representation[J]. Acta Geodaetica et Cartographica Sinica, 2001, 30(4): 361-365. DOI: 10.3321/j.issn:1001-1595.2001.04.016.
[25] 王光霞, 朱长青, 史文中, 等. 数字高程模型地形描述精度的研究[J]. 测绘学报, 2004, 33(2): 168-173. DOI: 10.3321/j.issn:1001-1595.2004.02.014. WANG Guangxia,ZHU Changqing,SHI Wenzhong, et al. The Further Study on the Accuracy of DEM Terrain Representation[J]. Acta Geodaetica et Cartographica Sinica, 2004, 33(2): 168-173. DOI: 10.3321/j.issn:1001-1595.2004.02.014.
[26] 胡鹏, 杨传勇, 吴艳兰, 等. 新数字高程模型: 理论方法标准和应用[M]. 北京: 测绘出版社, 2007. HU Peng, YANG Chuanyong, WU Yanlan, et al. New DEM Theories Methods Standards and Application[M]. Beijing: Surveying and Mapping Press, 2007.
[27] 王春, 刘学军, 汤国安, 等. 格网DEM地形模拟的形态保真度研究[J]. 武汉大学学报(信息科学版), 2009, 34(2): 146-149. WANG Chun, LIU Xuejun, TANG Guoan, et al. The Morphologic Fidelity of Grid Digital Elevation Model[J]. Geomatics and Information Science of Wuhan University, 2009, 34(2): 146-149.
[28] 胡鹏, 白轶多, 胡海. 数字高程模型生成中的高程序同构[J]. 武汉大学学报(信息科学版), 2009, 34(3): 352-357. HU Peng, BAI Yiduo, HU Hai. Elevation Order Isomorphism Characteristics of DEM[J]. Geomatics and Information Science of Wuhan University, 2009, 34(3): 352-357.
[29] 张锦明, 游雄. DEM保真精度定量化描述模型[J]. 中国图象图形学报, 2013, 18(9): 1206-1214. ZHANG Jinming, YOU Xiong. Quantitative Descriptive Model of DEM Fidelity Accuracy[J]. Journal of Image and Graphics, 2013, 18(9): 1206-1214.
[30] 吴艳兰, 胡海, 胡鹏, 等. 数字高程模型误差及其评价的问题综述[J]. 武汉大学学报(信息科学版), 2011, 36(5): 568-574. WU Yanlan, HU Hai, HU Peng, et al. A Review on the Issues in DEM Error and DEM Quality Assessment[J]. Geomatics and Information Science of Wuhan University, 2011, 36(5): 568-574.
[31] 刘雁春, 肖付民, 暴景阳, 等. 海道测量学概论[M]. 北京: 测绘出版社, 2006. LIU Yanchun, XIAO Fumin, BAO Jingyang, et al. Introduction to Hydrogrophy[M]. Beijing: Surveying and Mapping Press, 2006.
[32] 张立华, 贾帅东, 吴超, 等. 顾及不确定度的数字水深模型内插方法[J]. 测绘学报, 2011, 40(3): 359-365. ZHANG Lihua, JIA Shuaidong, WU Chao, et al. A Method for Interpolating Digital Depth Model Considering Uncertainty[J]. Acta Geodaetica et Cartographica Sinica, 2011, 40(3): 359-365.
[33] 郭仁忠. 空间分析[M]. 2版. 武汉: 武汉测绘科技大学出版社, 2000. GUO Renzhong. Spatial Analysis[M]. 2nd ed. Wuhan: Wuhan Technical University of Surveying and Mapping Press, 2000.
[34] 董箭, 彭认灿, 郑义东, 等. 基于滚动球模型的单值曲面缓冲体边界生成算法[J]. 计算机辅助设计与图形学学报, 2013, 25(7): 996-1004. DONG Jian, PENG Rencan, ZHENG Yidong, et al. An Algorithm of 3D-buffer Boundary Generation for Singular Value Surface Based on Rolling Ball Model[J]. Journal of Computer-aided Design & Computer Graphics, 2013, 25(7): 996-1004.

顾及“保真性”原则的双向滚动球变换DDM多尺度表达算法

Multi-scale Representation of Digital Depth Model Based on Double Direction Rolling Ball Transform according to the Reality Principle

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 9

编辑推荐

Metrics

本文评价

[1]	彭认灿, 董箭, 贾帅东, 唐露露, 王芳. 数字水深模型建模技术研究进展与展望[J]. 测绘学报, 2022, 51(7): 1575-1587.
[2]	艾廷华, 张翔. 地理信息科学中尺度概念的诠释与表达[J]. 测绘学报, 2022, 51(7): 1640-1652.
[3]	刘鹏程, 肖天元, 肖佳, 艾廷华. 曲线多尺度表达的Head-Tail信息量分割法[J]. 测绘学报, 2020, 49(7): 921-933.
[4]	刘洋, 吴自银, 赵荻能, 周洁琼, 尚继宏, 王明伟, 朱超, 鲁号号. MF多源测深数据融合方法及大洋水深模型构建[J]. 测绘学报, 2019, 48(9): 1171-1181.
[5]	俞童, 邓术军, 钱海忠, 杨清丽. 剖分网格下顾及用户兴趣的矢量地图多尺度表达方法[J]. 测绘学报, 2016, 45(S1): 127-134.
[6]	谢天, 李精忠. 面状居民地Morphing变换的转向角函数法[J]. 测绘学报, 2015, 44(7): 797-804.
[7]	贾帅东,张立华,宋国大,丁金挺. 基于区域平均垂直不确定度的自适应格网水深建模方法[J]. 测绘学报, 2012, 41(3): 0-416.
[8]	刘鹏程,艾廷华,杨敏. 基于傅里叶级数的等高线网络渐进式传输模型[J]. 测绘学报, 2012, 41(2): 284-290.
[9]	张立华,贾帅东,吴超,殷晓冬. 顾及不确定度的数字水深模型内插方法[J]. 测绘学报, 2011, 40(3): 359-365.