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 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。为此，视觉层次最早期层次中关于几何图像变换的协方差性质对于表达鲁棒图像操作以及在高层次上构建不变性视觉操作具有基础意义。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复合下的一种联合协方差性质，该性质使得刻画不同类型图像变换之间的相互作用成为可能。具体而言，推导出的关系表明了为匹配时空感受野输出与底层时空图像变换，感受野参数需要进行相应变换的方式。