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.
翻译:视觉皮层中的简单单元格的可接受字段可以被理解为线性过滤器。 这些过滤器可以通过 Gabor 函数或 Gausian 衍生物来模拟。 Gabor 函数也可以结合到复杂单元格响应的“能源模型”中。 本文提议了一个基于 Gaussian 衍生物的复杂单元格的替代模型。 最重要的是, 要说明对图像小移动的复杂反应的不敏感性。 新模型使用最初几个衍生过滤器的线性组合, 在一个位置上, 在一系列相邻的位置上接近第一个衍生过滤器。 对所有位置的最大反应, 发出一个对图像小移动不敏感的信号。 这个模型与以前的方法不同, 以视觉处理的空间理论为基础。 特别是, 复杂的单元格是从对图像小移动的复杂反应的过滤器中构建的。 新模型的计算方面, 使用高斯 衍生物的可控性位置, 模型对基本图像的反应, 如图像的边缘值和色度等, 与图像的精确度变化是正式分析的。