[论文解读] Visual Information flow in Wilson-Cowan networks

Alexander Gómez-Villa, Marcelo Bertalmı́o+1 more|PubMed|Jul 30, 2019

Visual perception and processing mechanisms参考文献 67被引用 4

一句话总结

本文通过多元总相关性分析了基于心理物理学调谐的威尔逊-科恩网络在视网膜-V1通路中的通信效率。结果表明，尽管未显式优化统计独立性，该网络仍显著降低了冗余度，尤其通过非线性局部对比度和定向滤波机制，证实其与高效编码假说的一致性，并提示其在图像压缩中的应用潜力。

ABSTRACT

In this paper, we study the communication efficiency of a psychophysically tuned cascade of Wilson-Cowan and divisive normalization layers that simulate the retina-V1 pathway. This is the first analysis of Wilson-Cowan networks in terms of multivariate total correlation. The parameters of the cortical model have been derived through the relation between the steady state of the Wilson-Cowan model and the divisive normalization model. The communication efficiency has been analyzed in two ways: First, we provide an analytical expression for the reduction of the total correlation among the responses of a V1-like population after the application of the Wilson-Cowan interaction. Second, we empirically study the efficiency with visual stimuli and statistical tools that were not available before <i>1</i>) we use a recent, radiometrically calibrated, set of natural scenes, and <i>2</i>) we use a recent technique to estimate the multivariate total correlation in bits from sets of visual responses, which only involves univariate operations, thus giving better estimates of the redundancy. The theoretical and the empirical results show that, although this cascade of layers was not optimized for statistical independence in any way, the redundancy between the responses gets substantially reduced along the neural pathway. Specifically, we show that <i>1</i>) the efficiency of a Wilson-Cowan network is similar to its equivalent divisive normalization model; <i>2</i>) while initial layers (Von Kries adaptation and Weber-like brightness) contribute to univariate equalization, and the bigger contributions to the reduction in total correlation come from the computation of nonlinear local contrast and the application of local oriented filters; and <i>3</i>) psychophysically tuned models are more efficient (reduce more total correlation) in the more populated regions of the luminance-contrast plane. These results are an alternative confirmation of the efficient coding hypothesis for the Wilson-Cowan systems, and, from an applied perspective, they suggest that neural field models could be an option in image coding to perform image compression.<b>NEW & NOTEWORTHY</b> The Wilson-Cowan interaction is analyzed in total correlation terms for the first time. Theoretical and empirical results show that this psychophysically tuned interaction achieves the biggest efficiency in the most frequent region of the image space. This is an original confirmation of the efficient coding hypothesis and suggests that neural field models can be an alternative to divisive normalization in image compression.

研究动机与目标

• 分析威尔逊-科恩网络在多元总相关性方面的通信效率，后者是神经群体响应冗余度的度量。
• 评估基于心理物理学调谐的威尔逊-科恩模型是否如高效编码假说所预测的那样，在视网膜-V1通路中降低冗余度。
• 比较威尔逊-科恩网络与其等效的除法归一化模型在冗余度降低方面的性能。
• 通过精确的统计估计，评估各个处理阶段（如对比度、方向滤波）对总相关性降低的贡献。
• 通过量化其信息论效率，探索神经场模型在图像压缩中的潜力。

提出的方法

• 本研究采用四阶段级联的同构线性+非线性模块，模拟视网膜-V1通路，其中最终非线性部分替换为等效的威尔逊-科恩模型。
• 威尔逊-科恩动力学由一组微分方程定义，其参数通过与除法归一化模型的稳态等价性推导得出，包括自衰减（α）、相互作用矩阵（W）和饱和函数（f(x) = c·x^γ）。
• 使用经过辐射校准的自然场景数据库作为输入刺激，以确保响应分析的视觉输入真实可靠。
• 应用一种近期的多元高斯化技术，仅通过单变量操作从神经响应中估计以比特为单位的总相关性，从而在无需多变量密度估计的情况下实现对冗余度的精确测量。
• 计算变换的雅可比矩阵，以建模局部信号形变，这对冗余度的信息论分析至关重要。
• 理论分析推导出威尔逊-科恩变换后总相关性降低的解析表达式，并通过自然图像刺激的实证数据加以验证。

实验结果

研究问题

• RQ1 威尔逊-科恩网络在视网膜-V1通路的神经群体响应中，能将多元总相关性降低到何种程度？
• RQ2 威尔逊-科恩模型在冗余度降低方面的性能与等效的除法归一化模型相比如何？
• RQ3 哪些处理阶段（如冯-克里思、对比度、方向滤波）对总相关性降低的贡献最大？
• RQ4 在亮度-对比度平面的不同区域中，心理物理学调谐模型是否在冗余度降低方面表现出更高的效率？
• RQ5 基于其信息论效率，像威尔逊-科恩这样的神经场模型是否可在图像压缩中发挥有效作用？

主要发现

• 即使未显式优化统计独立性，威尔逊-科恩网络在神经通路中仍显著降低了总相关性。
• 在冗余度降低方面，威尔逊-科恩模型的通信效率与等效的除法归一化模型相当。
• 非线性局部对比度计算和局部定向滤波对冗余度降低的贡献，显著高于单变量均衡化阶段（如冯-克里思适应）。
• 心理物理学调谐模型在亮度-对比度平面中更密集的区域中降低了更多的总相关性，表明其在自然刺激统计下具有更高的效率。
• 基于多元高斯化的估计方法可实现对总相关性的精确、基于单变量的估计，克服了以往多变量密度估计的局限性。
• 结果为威尔逊-科恩神经场模型在高效编码假说背景下的适用性提供了有力支持，提示其在生物启发式图像压缩中的潜在应用价值。