Evaluation Model for Similarity Based on Curve Generalization
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摘要: 从面状要素形状描述模型中导出线状要素的相似性评价模型:将线状要素以首尾点的连线为对称轴作镜像处理构建其对偶面,以其对偶面的傅立叶形状描述子为其形状向量,以向量的欧氏距离来度量曲线的相似程度。为保证一定的评价精度,通过计算傅立叶第K项X、Y的增量值,来决定K值大小。最后对给定曲线运用不同的化简算法进行多层级的化简,通过本模型对形状的保真度进行分析。该模型具有数学严密性和实用性,能为选择曲线化简算法提供一种参考依据。Abstract: To maintain shape similarity of features is one of evaluation criteria before or after in map generalization.The article derives shape similarity of line-feature from shape descriptor of polygon——rebuilds conjugate polygon of line-feature consisting of mirroring-part of original feature using the axis of symmetry through the first point and the end point of itself,gets a shape vector of the line feature,which is the shape descriptor of its conjugate polygon and further requires the similarity distance among line-features through Euclidean distance between two vectors.To ensure certain evaluation accuracy,the K value is determined by calculating Kth item X,Y value of Fourier series.In the end,the shape fidelity of several simplification methods to given curve is analyzed to provide the reference to select which algorithm will be used.The model is simple,with mathematical rigor,and highly practical.
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Keywords:
- map generalization /
- curve simplification /
- shape similarity
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