顾及海岸线地理弯曲特征约束的可控分形插值方法
|
摘要
针对海岸线分形插值缺乏地理特征约束和分形过程不可控的局限,提出了一种顾及海岸线地理弯曲特征约束的可控分形插值方法。首先,根据不同海岸地貌类型所呈现的不同弯曲特征和分形特征,对海岸线进行地貌单元划分,将传统的整体分形插值变换为以海岸线地貌弯曲特征为划分单元的分段插值组合;其次,利用一维随机中点移位法对各划分单元分别进行插值,并结合各划分单元的弯曲特征对分形参量分别进行约束控制,以保持海岸线不同地貌单元的弯曲特征;最后,将各插值单元顺次连接起来得到最终插值曲线。实验结果表明,所提方法能够很好地顾及海岸线不同地貌单元的弯曲特征和分形特征,且分形插值过程可控。
To overcome the shortcoming of the existing fractal interpolation methods that don't take into account the constraints of geographical bending characteristics and the fractal interpolation process is uncontrollable for coastline. A controlled fractal interpolation method for coastline is proposed by considering its geographical bending characteristic constraints. Firstly, the coastline is divided into several parts according to the bending characteristics and fractal characteristics of different coastal landform types, which will change the traditional integral fractal interpolation into a combination of several piecewise landform bending interpolation units. Secondly, the one-dimensional random midpoint displacement method is used as a fractal interpolation function for each divided unit of the coastline, and in order to maintain the bending characteristics of different landform units in the coastline, the fractal parameters of the interpolation function are restricted by the constraints of each unit fractal characteristics. Finally, the result curve is got by linking the interpolation units in order. The experiments show that this method can keep well the geographical bending characteristics and fractal characteristics of different landform units of coastline, and the process of fractal interpolation is controllable.
To overcome the shortcoming of the existing fractal interpolation methods that don't take into account the constraints of geographical bending characteristics and the fractal interpolation process is uncontrollable for coastline. A controlled fractal interpolation method for coastline is proposed by considering its geographical bending characteristic constraints. Firstly, the coastline is divided into several parts according to the bending characteristics and fractal characteristics of different coastal landform types, which will change the traditional integral fractal interpolation into a combination of several piecewise landform bending interpolation units. Secondly, the one-dimensional random midpoint displacement method is used as a fractal interpolation function for each divided unit of the coastline, and in order to maintain the bending characteristics of different landform units in the coastline, the fractal parameters of the interpolation function are restricted by the constraints of each unit fractal characteristics. Finally, the result curve is got by linking the interpolation units in order. The experiments show that this method can keep well the geographical bending characteristics and fractal characteristics of different landform units of coastline, and the process of fractal interpolation is controllable.
引文
[1] Mandelbrot B B. How Long is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension[J]. Science, 1967, 156(3 775): 636-638
[2] Jiang B. The Fractal Nature of Maps and Mapping[J]. International Journal of Geographical Information Science, 2015, 29(1): 159-174
[3] Ghanbarian A B, Millán H B, Huang G H. A Review of Fractal, Prefractal and Pore-Solid-Fractal Models for Parameterizing the Soil Water Retention Curve[J]. Canadian Journal of Soil Science, 2011, 91(1): 1-14
[4] Zhu Hua, Ji Cuicui. Fractal Theory and Its Applications [M]. Beijing: China Science Publishing &Media Ltd, 2011(朱华, 姬翠翠.分形理论及其应用[M]. 北京: 科学出版社, 2011)
[5] Peng Dongliang, Deng Min, Zhao Binbin. Multi-Scale Transformation of River Networks Based on Morphing Technology[J]. Journal of Remote Sen-sing, 2012, 16(5): 953-968(彭东亮, 邓敏, 赵彬彬. 河网多尺度Morphing的变换方法研究[J]. 遥感学报, 2012, 16(5): 953-968)
[6] Liu Pengcheng, Ai Tinghua, Bi Xu. Multi-Scale Representation Model for Contour Based on Fourier Series[J]. Geomatics and Information Science of Wuhan University, 2013, 38(2): 221-224(刘鹏程, 艾廷华, 毕旭. 傅里叶级数支持下的等高线多尺度表达模型[J]. 武汉大学学报·信息科学版, 2013, 38(2): 221-224)
[7] Shu X, Pan L, Wu X J. Multi-Scale Contour Flexibility Shape Signature for Fourier Descriptor[J]. Journal of Visual Communication and Image Representation, 2015, 26(1): 161-167
[8] Wang Qiao. Fractal Interpolation of Map Curve[J]. WTUSM Bulletin of Science and Technology, 1995(4): 8-13(王桥. 地图曲线的分形插值[J]. 武测科技, 1995(4): 8-13)
[9] Barnsley M F. Fractal Functions and Interpolation[J]. Constructive Approximation, 1986, 2(1): 303-329
[10] Wang Hongyong,Fan Zhaolei. Analytical Characteristics of Fractal Interpolation Functions with Function Vertical Scaling Factors[J]. Acta Mathe-matica Sinica, 2011, 54(1): 147-158(王宏勇, 樊昭磊. 具有函数纵向尺度因子的分形插值函数的分析特性[J]. 数学学报, 2011, 54(1): 147-158)
[11] Metzler W, Yun C H. Construction of Fractal Interpolation Surfaces on Rectangular Grids[J]. International Journal of Bifurcation and Chaos, 2011, 20(12):4 079-4 086
[12] Wu Hehai. Application of Extended Fractal Dimension in Map Generalization[J]. Science of Surve-ying and Mapping, 2010, 35(4): 10-13 (毋河海. 扩展分维在地图信息综合中的应用[J]. 测绘科学, 2010, 35(4): 10-13)
[13] Zhang Huaguo, Huang Weigen, Zhou Changbao. A New Fractal Interpolation Approach for Geographic Curve[J]. Acta Geodaetica et Cartographica Sinica, 2002, 31(3): 255-261 (张华国, 黄韦艮, 周长宝. 一种新的地理线要素分形插值方法[J]. 测绘学报, 2002, 31(3): 255-261)
[14] Huang Yafeng, Ai Tinghua, Liu Yaolin, et al. Geo-graphic-Feature Oriented Ria Coastline Simplification[J]. Acta Geodaetica et Cartographica Sinica, 2013, 42(4): 595-601 (黄亚锋, 艾廷华, 刘耀林, 等. 顾及地理特征保持的溺谷海岸线化简算法[J]. 测绘学报, 2013, 42(4): 595-601)
[15] Wang Qiao, Wu Jitao. Automated Cartographic Generalization Based on a New Method of Fractal Dimension Estimation[J]. Acta Geodaetica et Cartographica Sinica, 1996, 25(1): 11-16 (王桥, 吴纪桃. 一种新分维估值方法作为工具的自动制图综合[J]. 测绘学报, 1996, 25(1): 11-16)
[16] Wang Qiao, Wu Jitao. The Research on Fractal Method of Determining Reduced Length of Cartographic Lines[J]. WTUSM Bulletin of Science and Technology,1996(3): 5-7 (王桥, 吴纪桃. 地图上曲线长度归算的分形方法研究[J]. 武测科技, 1996(3): 5-7)
[17] Wang Z, Muller J C. Line Generalization Based on Analysis of Shape Characteristics [J]. Cartography and Geographic Information Systems, 1998, 25(1):3-15
[18] Zhu Qiang, Wu Fang, Qian Haizhong, et al. An Identification Method of Line Curves Based on Cognitive Laws[J]. Journal of Liaoning Technical University, 2014, 33(4):521-526(朱强, 武芳, 钱海忠,等. 一种顾及认知规律的曲线弯曲识别方法[J]. 辽宁工程技术大学学报, 2014, 33(4):521-526)
[19] Beckett P. Cartographic Generalisation[J]. Cartographic Journal, 1977, 14(1): 49-55
[2] Jiang B. The Fractal Nature of Maps and Mapping[J]. International Journal of Geographical Information Science, 2015, 29(1): 159-174
[3] Ghanbarian A B, Millán H B, Huang G H. A Review of Fractal, Prefractal and Pore-Solid-Fractal Models for Parameterizing the Soil Water Retention Curve[J]. Canadian Journal of Soil Science, 2011, 91(1): 1-14
[4] Zhu Hua, Ji Cuicui. Fractal Theory and Its Applications [M]. Beijing: China Science Publishing &Media Ltd, 2011(朱华, 姬翠翠.分形理论及其应用[M]. 北京: 科学出版社, 2011)
[5] Peng Dongliang, Deng Min, Zhao Binbin. Multi-Scale Transformation of River Networks Based on Morphing Technology[J]. Journal of Remote Sen-sing, 2012, 16(5): 953-968(彭东亮, 邓敏, 赵彬彬. 河网多尺度Morphing的变换方法研究[J]. 遥感学报, 2012, 16(5): 953-968)
[6] Liu Pengcheng, Ai Tinghua, Bi Xu. Multi-Scale Representation Model for Contour Based on Fourier Series[J]. Geomatics and Information Science of Wuhan University, 2013, 38(2): 221-224(刘鹏程, 艾廷华, 毕旭. 傅里叶级数支持下的等高线多尺度表达模型[J]. 武汉大学学报·信息科学版, 2013, 38(2): 221-224)
[7] Shu X, Pan L, Wu X J. Multi-Scale Contour Flexibility Shape Signature for Fourier Descriptor[J]. Journal of Visual Communication and Image Representation, 2015, 26(1): 161-167
[8] Wang Qiao. Fractal Interpolation of Map Curve[J]. WTUSM Bulletin of Science and Technology, 1995(4): 8-13(王桥. 地图曲线的分形插值[J]. 武测科技, 1995(4): 8-13)
[9] Barnsley M F. Fractal Functions and Interpolation[J]. Constructive Approximation, 1986, 2(1): 303-329
[10] Wang Hongyong,Fan Zhaolei. Analytical Characteristics of Fractal Interpolation Functions with Function Vertical Scaling Factors[J]. Acta Mathe-matica Sinica, 2011, 54(1): 147-158(王宏勇, 樊昭磊. 具有函数纵向尺度因子的分形插值函数的分析特性[J]. 数学学报, 2011, 54(1): 147-158)
[11] Metzler W, Yun C H. Construction of Fractal Interpolation Surfaces on Rectangular Grids[J]. International Journal of Bifurcation and Chaos, 2011, 20(12):4 079-4 086
[12] Wu Hehai. Application of Extended Fractal Dimension in Map Generalization[J]. Science of Surve-ying and Mapping, 2010, 35(4): 10-13 (毋河海. 扩展分维在地图信息综合中的应用[J]. 测绘科学, 2010, 35(4): 10-13)
[13] Zhang Huaguo, Huang Weigen, Zhou Changbao. A New Fractal Interpolation Approach for Geographic Curve[J]. Acta Geodaetica et Cartographica Sinica, 2002, 31(3): 255-261 (张华国, 黄韦艮, 周长宝. 一种新的地理线要素分形插值方法[J]. 测绘学报, 2002, 31(3): 255-261)
[14] Huang Yafeng, Ai Tinghua, Liu Yaolin, et al. Geo-graphic-Feature Oriented Ria Coastline Simplification[J]. Acta Geodaetica et Cartographica Sinica, 2013, 42(4): 595-601 (黄亚锋, 艾廷华, 刘耀林, 等. 顾及地理特征保持的溺谷海岸线化简算法[J]. 测绘学报, 2013, 42(4): 595-601)
[15] Wang Qiao, Wu Jitao. Automated Cartographic Generalization Based on a New Method of Fractal Dimension Estimation[J]. Acta Geodaetica et Cartographica Sinica, 1996, 25(1): 11-16 (王桥, 吴纪桃. 一种新分维估值方法作为工具的自动制图综合[J]. 测绘学报, 1996, 25(1): 11-16)
[16] Wang Qiao, Wu Jitao. The Research on Fractal Method of Determining Reduced Length of Cartographic Lines[J]. WTUSM Bulletin of Science and Technology,1996(3): 5-7 (王桥, 吴纪桃. 地图上曲线长度归算的分形方法研究[J]. 武测科技, 1996(3): 5-7)
[17] Wang Z, Muller J C. Line Generalization Based on Analysis of Shape Characteristics [J]. Cartography and Geographic Information Systems, 1998, 25(1):3-15
[18] Zhu Qiang, Wu Fang, Qian Haizhong, et al. An Identification Method of Line Curves Based on Cognitive Laws[J]. Journal of Liaoning Technical University, 2014, 33(4):521-526(朱强, 武芳, 钱海忠,等. 一种顾及认知规律的曲线弯曲识别方法[J]. 辽宁工程技术大学学报, 2014, 33(4):521-526)
[19] Beckett P. Cartographic Generalisation[J]. Cartographic Journal, 1977, 14(1): 49-55