论文标题
双维序列的熵估计
Entropy estimation in bidimensional sequences
论文作者
论文摘要
在二维序列的情况下，我们研究了基于块熵或压缩方法的熵估计方法的性能。我们介绍了由大量不同的自然系统产生的图像制成的验证数据集，其中绝大多数以远程相关性为特征，这些相关性产生了大量的熵。结果表明，基于无损压缩机的框架应用于所考虑的数据集的一维投影，导致估计不佳。这是因为在投影操作中丢失了高维相关性。不引入降低维度的压缩方法的采用可改善这种方法的性能。到目前为止，渐近熵的最佳估计是通过传统的块状方法的更快收敛而产生的。作为我们分析的副产品，我们展示了如何将特定的压缩机方法用作一种潜在有趣的技术，以自动检测纹理和图像中的对称性。
We investigate the performance of entropy estimation methods, based either on block entropies or compression approaches, in the case of bidimensional sequences. We introduce a validation dataset made of images produced by a large number of different natural systems, in the vast majority characterized by long-range correlations, which produce a large spectrum of entropies. Results show that the framework based on lossless compressors applied to the one-dimensional projection of the considered dataset leads to poor estimates. This is because higher-dimensional correlations are lost in the projection operation. The adoption of compression methods which do not introduce dimensionality reduction improves the performance of this approach. By far, the best estimation of the asymptotic entropy is generated by the faster convergence of the traditional block-entropies method. As a by-product of our analysis, we show how a specific compressor method can be used as a potentially interesting technique for automatic detection of symmetries in textures and images.
