Lee Sang-Hee, Park Cheol-Min, Choi UJin
Division of Industrial Mathematics, National Institute for Mathematical Sciences, Daejeon 34047, Korea.
Entropy (Basel). 2020 Sep 22;22(9):1061. doi: 10.3390/e22091061.
We propose a new measure () to quantify the degree of self-similarity of a shape using branch length similarity (BLS) entropy which is defined on a simple network consisting of a single node and its branches. To investigate the properties of this measure, we computed the values for 70 object groups (20 shapes in each group) in the MPEG-7 shape database and performed grouping on the values. With relatively high values, identical groups had visually similar shapes. On the other hand, the identical groups with low values had visually different shapes. However, the aspect of topological similarity of the shapes also warrants consideration. The shapes of statistically different groups exhibited significant visual difference from each other. Also, in order to show that the can have a wide variety of applicability when properly used with other variables, we showed that the finger gestures in the (, ) space are successfully classified. Here, the means a correlation coefficient value between entropy profiles for gesture shapes. As shown in the applications, has a strong advantage over conventional geometric measures in that it captures the geometrical and topological properties of a shape together. If we could define the BLS entropy for color, could be used to characterize images expressed in RGB. We briefly discussed the problems to be solved before the applicability of can be expanded to various fields.
我们提出了一种新的度量方法（），使用分支长度相似性（BLS）熵来量化形状的自相似程度，该熵是在一个由单个节点及其分支组成的简单网络上定义的。为了研究这种度量方法的性质，我们计算了MPEG - 7形状数据库中70个对象组（每组20个形状）的 值，并对这些值进行了分组。 值较高时，相同组的形状在视觉上相似。另一方面， 值较低的相同组形状在视觉上不同。然而，形状的拓扑相似性方面也值得考虑。统计上不同组的形状在视觉上彼此有显著差异。此外，为了表明 在与其他变量正确结合使用时可以有广泛的适用性，我们展示了在（，）空间中的手指手势能够成功分类。这里， 表示手势形状的熵轮廓之间的相关系数值。如应用所示， 相对于传统几何度量具有很大优势，因为它能同时捕捉形状的几何和拓扑属性。如果我们能为颜色定义BLS熵， 就可用于表征以RGB表示的图像。我们简要讨论了在 将其适用性扩展到各个领域之前需要解决的问题。
