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The influence of natural image transformations on receptive field responsesis crucial for modelling visual operations in computer vision and biologicalvision. In this regard, covariance properties with respect to geometric imagetransformations in the earliest layers of the visual hierarchy are essentialfor expressing robust image operations and for formulating invariant visualoperations at higher levels. This paper defines and proves a joint covarianceproperty under compositions of spatial scaling transformations, spatial affinetransformations, Galilean transformations and temporal scaling transformations,which makes it possible to characterize how different types of imagetransformations interact with each other. Specifically, the derived relationsshow how the receptive field parameters need to be transformed, in order tomatch the output from spatio-temporal receptive fields with the underlyingspatio-temporal image transformations.

Joint covariance property under geometric image transformations for  spatio-temporal receptive fields according to the generalized Gaussian  derivative model for visual receptive fields