引用本文: 徐丰, 牛继强, 林昊, 陈时雨, 张兵兵, 陈飞燕. 利用等距同构建立多尺度空间实体相似性度量模型[J]. 武汉大学学报 ( 信息科学版), 2019, 44(9): 1399-1406.
XU Feng, NIU Jiqiang, LIN Hao, CHEN Shiyu, ZHANG Bingbing, CHEN Feiyan. Establishment of the Similarity Metric Model of Multi-scale Spatial Object Using Isometry[J]. Geomatics and Information Science of Wuhan University, 2019, 44(9): 1399-1406.
 Citation: XU Feng, NIU Jiqiang, LIN Hao, CHEN Shiyu, ZHANG Bingbing, CHEN Feiyan. Establishment of the Similarity Metric Model of Multi-scale Spatial Object Using Isometry[J]. Geomatics and Information Science of Wuhan University, 2019, 44(9): 1399-1406.

## Establishment of the Similarity Metric Model of Multi-scale Spatial Object Using Isometry

• 摘要: 从度量几何学的观点，建立多尺度空间实体等距同构模型。将多尺度空间实体分别看作刚性图形和弹性图形，利用等距同构不变性的概念，构建多尺度空间实体几何相似性图形距离和拓扑相似性图形距离。通过统一几何和拓扑相似性图形距离，构成一个二元集值距离，作为多尺度空间实体相似性的评价指标。通过对不同复杂性的面状和线状空间实体多尺度表达图形的几何和拓扑相似性度量实验表明，该方法能同时顾及多尺度空间实体几何和拓扑结构的改变，且符合空间实体的多尺度抽象规律。

Abstract: From the perspective of metric geometry, this paper proposes an isomorphic model for multi-scale spatial object representation. Firstly, the multi-scale spatial objects are considered as rigid shapes and non-rigid shapes respectively. Then, the shape distances based on geometry similarity and topology similarity are constructed by the concept of isometry invariance. Finally, the two kinds of similarity shape distances are combined to form a two-element set and are used as an evaluated criterion of multi-scale spatial object similarity. Experiments on different complexity levels of spatial line and polygon objects show that, the two similarity metrics can encode both geometrical and topological changes, and be in accord with the abstract principles of multi-scale spatial object representation.

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