Abstract
Observing an object under different viewing conditions, in spite of substantial variability in the image structures when changing the distance or the viewing direction relative to the object, we can maintain the identity of the object. How does the vision system cope with this variability, that will substantially influence the receptive field responses? One hypothesis is that the receptive field family should be covariant under geometric image transformations and thereby have variabilities in the shapes of the receptive fields corresponding to the degrees of freedom of the geometric image transformations. Specifically, it has been predicted that the receptive fields should have a variability in the degree of elongation, corresponding to varying the slant angle when observing local surface patches. Such a variability has also been predicted from indirect support in terms of variabilities in the orientation selectivity properties in V1 for monkeys and cats, which by a theoretical model has been linked to variabilities in the elongation of th receptive fields. In this paper, we measure such variabilities in receptive field shapes in a more direct way, by reconstructing receptive fields from calcium imaging experiments for mice previously performed by the Allen Institute. Our findings reveal a variability in the degree of elongation that exceeds what measurement noise produces, spanning about a factor of 5, thereby showing that the predictions that were made for higher mammals with orientation maps, such as primates and cats, also apply to a species without orientation maps, with its primary visual cortex instead based on a salt-and-pepper organization of the receptive fields.