Department of Biophysics, Faculty of Biology, Moscow State University, Leninskie gory 1/24, 119234 Russia.
Phys Rev E. 2018 Jun;97(6-1):061301. doi: 10.1103/PhysRevE.97.061301.
New spatial entropy and complexity measures for two-dimensional patterns are proposed. The approach is based on the notion of disequilibrium and is built on statistics of directional multiscale coefficients of the fast finite shearlet transform. Shannon entropy and Jensen-Shannon divergence measures are employed. Both local and global spatial complexity and entropy estimates can be obtained, thus allowing for spatial mapping of complexity in inhomogeneous patterns. The algorithm is validated in numerical experiments with a gradually decaying periodic pattern and Ising surfaces near critical state. It is concluded that the proposed algorithm can be instrumental in describing a wide range of two-dimensional imaging data, textures, or surfaces, where an understanding of the level of order or randomness is desired.
提出了用于二维模式的新的空间熵和复杂度度量方法。该方法基于不平衡的概念，并基于快速有限剪切变换的方向多尺度系数的统计构建。采用香农熵和 Jensen-Shannon 散度度量。可以获得局部和全局空间复杂度和熵估计，从而可以对非均匀模式中的复杂度进行空间映射。该算法在具有逐渐衰减的周期性模式和接近临界状态的 Ising 表面的数值实验中得到验证。结论是，所提出的算法可用于描述广泛的二维成像数据、纹理或表面，其中需要了解有序或随机性的水平。
