Estimates of the information content and dimensionality of natural scenes from proximity distributions
Estimates of the information content and dimensionality of natural scenes from proximity distributions
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DOI：
10.1364/josaa.24.000922
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发表时间：
2007-04-01
影响因子：
1.9
通讯作者：
Field, David J.
中科院分区：
文献类型：
--
作者：
Chandler, Damon M.;Field, David J.
自然场景，就像大多数自然数据集一样，显示出相当大的冗余。虽然已经研究了许多形式的冗余(例如，像素分布、功率谱、轮廓关系等)，但对自然场景的真实熵的估计在很大程度上被认为是难以处理的。我们描述了一种基于我们称为邻近度分布的函数来估计图像块的熵和相对维度的技术(最近邻技术)。与功率谱等简单统计量相比，该函数的优势在于邻近分布依赖于所有形式的冗余。我们证明了该函数可以用来估计3×3块已知熵以及8×8块高斯白噪声、自然场景和与自然场景具有相同功率谱的噪声的熵(冗余度)。这些技术基于关于数据的内在维度的假设，尽管估计依赖于大于3x3的图像的外推模型，但我们认为这种方法提供了对自然场景斑块的熵和可压缩性的最佳当前估计，并且它提供了对旨在减少冗余的任何编码策略的效率的洞察。结果表明，在相同功率谱下，8×8斑块的自然场景样本具有不到8×8白噪声的一半的熵和不到60%的噪声熵。此外，给定从8×8斑块空间随机抽取的有限数量的样本(<；2(20))，8×8自然场景斑块的子空间显示出依赖于采样密度的维度，并且低密度的维度显著低于8×8斑块空间的维度，且具有相同功率谱的白噪声和噪声。(C)2007年美国光学学会。
Natural scenes, like most all natural data sets, show considerable redundancy. Although many forms of redundancy have been investigated (e.g., pixel distributions, power spectra, contour relationships, etc.), estimates of the true entropy of natural scenes have been largely considered intractable. We describe a technique for estimating the entropy and relative dimensionality of image patches based on a function we call the proximity distribution (a nearest-neighbor technique). The advantage of this function over simple statistics such as the power spectrum is that the proximity distribution is dependent on all forms of redundancy. We demonstrate that this function can be used to estimate the entropy (redundancy) of 3 x 3 patches of known entropy as well as 8 x 8 patches of Gaussian white noise, natural scenes, and noise with the same power spectrum as natural scenes. The techniques are based on assumptions regarding the intrinsic dimensionality of the data, and although the estimates depend on an extrapolation model for images larger than 3 x 3, we argue that this approach provides the best current estimates of the entropy and compressibility of natural-scene patches and that it provides insights into the efficiency of any coding strategy that aims to reduce redundancy. We show that the sample of 8 x 8 patches of natural scenes used in this study has less than half the entropy of 8 x 8 white noise and less than 60% of the entropy of noise with the same power spectrum. In addition, given a finite number of samples (< 2(20)) drawn randomly from the space of 8 x 8 patches, the subspace of 8 x 8 natural-scene patches shows a dimensionality that depends on the sampling density and that for low densities is significantly lower dimensional than the space of 8 x 8 patches of white noise and noise with the same power spectrum. (c) 2007 Optical Society of America.