V1中的自然图像编码：方向选择性有多大用处？
Natural Image Coding in V1: How Much Use is Orientation Selectivity?
摘要：
方向选择性是V1中简单细胞编码的最显著特征，这已被证明是在各种统计图像模型中自然图像中高阶相关性的减少中出现的。在这些模型中最简约的是线性独立分量分析（ICA），而二阶去相关变换，如主分量分析（PCA）不产生定向滤波器。由于这一发现，有人建议，出现的方向选择性可以解释高阶冗余减少。为了评估这一假设的可接受性，这是一个重要的经验问题，与PCA或其他二阶去相关方法相比，ICA可以去除多少冗余。这个问题还没有得到解决，因为在过去的十年里，已经报道了相互矛盾的结果，从不到5%到超过100%的ICA额外增益。在这里，我们的目标是解决这个冲突，提出了一个非常仔细和全面的分析，使用三个评估标准相关的冗余减少：除了多信息和平均对数损失，我们计算，第一次，完整的率失真曲线ICA相比，PCA。毫无例外，我们发现ICA滤波器的优势是令人惊讶的小。此外，我们表明，一个简单的球对称分布，只有两个参数，可以更好地拟合数据比ICA的概率模型。由于球对称模型是不可知的，相对于特定的过滤器的形状，我们推断，方向选择性是不可能发挥关键作用的冗余减少。
英文摘要：
Orientation selectivity is the most striking feature of simple cell coding in V1 which has been shown to emerge from the reduction of higher-order correlations in natural images in a large variety of statistical image models. The most parsimonious one among these models is linear Independent Component Analysis (ICA), whereas second-order decorrelation transformations such as Principal Component Analysis (PCA) do not yield oriented filters. Because of this finding it has been suggested that the emergence of orientation selectivity may be explained by higher-order redundancy reduction. In order to assess the tenability of this hypothesis, it is an important empirical question how much more redundancies can be removed with ICA in comparison to PCA, or other second-order decorrelation methods. This question has not yet been settled, as over the last ten years contradicting results have been reported ranging from less than five to more than hundred percent extra gain for ICA. Here, we aim at resolving this conflict by presenting a very careful and comprehensive analysis using three evaluation criteria related to redundancy reduction: In addition to the multi-information and the average log-loss we compute, for the first time, complete rate-distortion curves for ICA in comparison with PCA. Without exception, we find that the advantage of the ICA filters is surprisingly small. Furthermore, we show that a simple spherically symmetric distribution with only two parameters can fit the data even better than the probabilistic model underlying ICA. Since spherically symmetric models are agnostic with respect to the specific filter shapes, we conlude that orientation selectivity is unlikely to play a critical role for redundancy reduction.
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