This article introduces a new model for direction relations between multiple spatial objects at multiple scales and a corresponding similarity assessment method.The model is an improvement of direction relation matrix,which quantitatively models direction relations on object scale,and by the idea of decomposition and means of the optimum solution of the transportation problem to solve the minimum conversion cost between multiple direction matrices,namely distance between a pair of matrices,thus quantified the difference between a pair of directions,finally obtain the similarity values between arbitrary pairs of multiple spatial objects and compare the results.Experiments on calculating similarity between objects at different scales show that the presented method is efficient,accurate,and capable of obtaining results consistent with human cognition.%介绍了一种顾及尺度差异的复合空间对象的方向关系表达模型,及基于该模型的方向相似度度量方法.该方向关系模型对方向关系矩阵模型进行改进,根据空间对象的形状定量描述空间对象之间的方向关系.采用分解思想,借鉴平衡传输问题的优化方法计算复合方向矩阵间最小转换代价,即方向矩阵间的距离,从而量化方向对间的差异,最终获得不同尺度下的复合对象的方向相似度并对其进行比较.对不同尺度复合空间对象的方向相似性的试验表明,该方法简单可行且不失精度,结果符合人类认知.
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