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.%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.
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