The nonlinear statistics of high-contrast patches in natural images
The nonlinear statistics of high-contrast patches in natural images
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DOI：
10.1023/a:1023705401078
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发表时间：
2003-08-01
影响因子：
19.5
通讯作者：
Mumford, D
中科院分区：
文献类型：
--
作者：
Lee, AB;Pedersen, KS;Mumford, D
最近，人们对自然图像的非高斯结构建模产生了很大的兴趣。然而，尽管在稀疏编码和多分辨率分析方面取得了许多进展，但尚未描述邻域中像素值的完整概率分布。在本研究中，我们探索了表示来自光学和 3D 范围图像的 3 x 3 高对比度色块值的数据点空间。我们发现数据的分布极其“稀疏”，大多数数据点集中在簇和非线性低维流形中。此外，对概率密度的详细研究使我们能够系统地区分不同模态（光学与距离）的图像，否则这些图像会显示相似的边缘分布。我们的工作表明研究自然图像的完整概率分布（而不仅仅是边缘）的重要性，以及了解数据的内在维度和性质的必要性。我们相信，世界上的类物体结构和探测设备的传感器特性会产生集中在状态空间中可预测形状的观测结果。我们对自然图像统计的研究考虑了自然场景中的局部几何形状（例如边缘），但没有对数据强加如此强的假设，如独立分量或通过基数线性变化进行稀疏编码。
Recently, there has been a great deal of interest in modeling the non-Gaussian structures of natural images. However, despite the many advances in the direction of sparse coding and multi-resolution analysis, the full probability distribution of pixels values in a neighborhood has not yet been described. In this study, we explore the space of data points representing the values of 3 x 3 high-contrast patches from optical and 3D range images. We find that the distribution of data is extremely "sparse" with the majority of the data points concentrated in clusters and non-linear low-dimensional manifolds. Furthermore, a detailed study of probability densities allows us to systematically distinguish between images of different modalities (optical versus range), which otherwise display similar marginal distributions. Our work indicates the importance of studying the full probability distribution of natural images, not just marginals, and the need to understand the intrinsic dimensionality and nature of the data. We believe that object-like structures in the world and the sensor properties of the probing device generate observations that are concentrated along predictable shapes in state space. Our study of natural image statistics accounts for local geometries (such as edges) in natural scenes, but does not impose such strong assumptions on the data as independent components or sparse coding by linear change of bases.