Invariance of visual operations at the level of receptive fields

Tony Lindeberg

PLoS ONE 8(7): e66990, pages 1-33.

Digitally published with DOI:10.1371/journal.pone.0066990 in July 2013.

Poster presented at CNS 2013 in Paris, France, July 13-18, 2013 with abstract published in BMC Neuroscience 14(Suppl 1); P242, 2013.

Preprint deposited at arXiv:1210.0754 in October 2012.


The brain is able to maintain a stable perception although the visual stimuli vary substantially on the retina due togeometric transformations and lighting variations in the environment. This paper presents a theory for achieving basic invariance properties already at the level of receptive fields.

Specifically, the presented framework comprises (i) local scaling transformations caused by objects of different size and at different distances to the observer, (ii) locally linearized image deformations caused by variations in the viewing direction in relation to the object, (iii) locally linearized relative motions between the object and the observer and (iv) local multiplicative intensity transformations caused by illumination variations.

The receptive field model can be derived by necessity from symmetry properties of the environment and leads to predictions about receptive field profiles in good agreement with receptive field profiles measured by cell recordings in mammalia nvision. Indeed, the receptive field profiles in the retina, LGN and V1 are close to ideal to what is motivated by the idealized requirements.

By complementing receptive field measurements with selection mechanisms over the parameters in the receptive field families, it is shown how true invariance of receptive field responses can be obtained under scaling transformations, affine transformations and Galilean transformations. Thereby, the framework provides a mathematically well-founded and biologically plausible model for how basic invariance properties can be achieved already at the level of receptive fields and support invariant recognition of objects and events under variations in viewpoint, retinal size, object motion and illumination.

The theory can explain the different shapes of receptive field profiles found in biological vision, which are tuned to different sizes and orientations in the image domain as well as to different image velocities in space-time, from a requirement that the visual system should be invariant to the natural types of image transformations that occur in its environment.

PDF: (longer journal article in PLoS ONE) (shorter extended abstract of CNS*2013 poster in BMC Neuroscience)

On-line versions: (At the official site of PLoS ONE) (At the official site of BMC Neuroscience) (Preprint at arXiv)

Background and related material: (Underlying computational theory for visual receptive fields) (Underlying mathematical necessity results regarding scale covariant, affine covariant and Galilean covariant receptive fields) (Main paper on mechanism for achieving scale invariance by automatic scale selection) (Mechanism for achieving affine invariance by affine shape adaptation) (Mechanism for achieving Galilean invariance by velocity adaptation)

Responsible for this page: Tony Lindeberg