On the local behavior of spaces of natural images
On the local behavior of spaces of natural images
复制标题
DOI：
10.1007/s11263-007-0056-x
复制
发表时间：
2008-01-01
影响因子：
19.5
通讯作者：
Zornorodian, Afra
中科院分区：
文献类型：
--
作者：
Carlsson, Gunnar;Ishkhanov, Tigran;Zornorodian, Afra
在这项研究中，我们专注于定性拓扑分析的自然图像空间的局部行为。为此，我们使用3 × 3的高对比度斑块M的空间。我们发展了一个理论模型的高密度2维子流形的M表明，它具有的拓扑结构的克莱因瓶。使用我们的拓扑软件包PLEX，我们实验验证了我们的理论结论。我们使用多项式表示来对M的各个子空间进行坐标化。我们找到了Klein瓶在M的周围空间中的最佳嵌入。我们的研究结果目前正在开发一个压缩算法的基础上克莱因瓶字典。
In this study we concentrate on qualitative topological analysis of the local behavior of the space of natural images. To this end, we use a space of 3 by 3 high-contrast patches M. We develop a theoretical model for the high-density 2-dimensional submanifold of M showing that it has the topology of the Klein bottle. Using our topological software package PLEX we experimentally verify our theoretical conclusions. We use polynomial representation to give coordinatization to various subspaces of M. We find the best-fitting embedding of the Klein bottle into the ambient space of M. Our results are currently being used in developing a compression algorithm based on a Klein bottle dictionary.