The influence of natural image transformations on receptive field responses is crucial for modelling visual operations in computer vision and biological vision. In this regard, covariance properties with respect to geometric image transformations in the earliest layers of the visual hierarchy are essential for expressing robust image operations and for formulating invariant visual operations at higher levels. This paper defines and proves a joint covariance property under compositions of spatial scaling transformations, spatial affine transformations, Galilean transformations and temporal scaling transformations, which makes it possible to characterize how different types of image transformations interact with each other. Specifically, the derived relations show how the receptive field parameters need to be transformed, in order to match the output from spatio-temporal receptive fields with the underlying spatio-temporal image transformations.

翻译：自然图像变换对感受野响应的影响对于计算机视觉和生物视觉中的视觉操作建模至关重要。在这方面，视觉层次最早期层中关于几何图像变换的协方差性质对于表达鲁棒的图像操作以及在更高层次上制定不变的视觉操作至关重要。本文定义并证明了在空间缩放变换、空间仿射变换、伽利略变换和时间缩放变换的组合下的一种联合协方差性质，这使得能够刻画不同类型的图像变换如何相互作用。具体而言，推导出的关系展示了感受野参数需要如何变换，以使时空感受野的输出与底层的时空图像变换相匹配。