论文标题
复合细胞的差分模型
A Differential Model of the Complex Cell
论文作者
论文摘要
视觉皮层中简单细胞的接受场可以理解为线性过滤器。这些过滤器可以通过Gabor函数或高斯导数来建模。 Gabor函数也可以与复杂细胞响应的“能量模型”合并。本文提出了基于高斯衍生物的复杂细胞的替代模型。最重要的是说明对图像小移位的复杂响应的不敏感性。新模型在一系列相邻位置处使用了一个位置的前几个导数过滤器的线性组合，以近似第一个衍生滤波器。在所有位置上，最大响应给出了对图像的小移位不敏感的信号。与以前的方法不同，该模型基于视觉处理的比例空间理论。特别是，复杂的单元格是由对图像的\ twod \差异结构响应的过滤器构建的。使用高斯衍生物的可调性，在一个和二维中研究了新模型的计算方面。模型对基本图像（例如边缘和光栅）的响应是正式得出的。还使用移动不敏感的统计测量评估了对自然图像的响应。讨论了新模型与皮质图像表示的相关性。
The receptive fields of simple cells in the visual cortex can be understood as linear filters. These filters can be modelled by Gabor functions, or by Gaussian derivatives. Gabor functions can also be combined in an `energy model' of the complex cell response. This paper proposes an alternative model of the complex cell, based on Gaussian derivatives. It is most important to account for the insensitivity of the complex response to small shifts of the image. The new model uses a linear combination of the first few derivative filters, at a single position, to approximate the first derivative filter, at a series of adjacent positions. The maximum response, over all positions, gives a signal that is insensitive to small shifts of the image. This model, unlike previous approaches, is based on the scale space theory of visual processing. In particular, the complex cell is built from filters that respond to the \twod\ differential structure of the image. The computational aspects of the new model are studied in one and two dimensions, using the steerability of the Gaussian derivatives. The response of the model to basic images, such as edges and gratings, is derived formally. The response to natural images is also evaluated, using statistical measures of shift insensitivity. The relevance of the new model to the cortical image representation is discussed.
