Invariance of visual operations at the level of receptive fields

The brain is able to maintain a stable perception although the visual stimuli vary substantially on the retina due to geometric 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 mammalian vision. 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 spacetime, from a requirement that the visual system should be invariant to the natural types of image transformations that occur in its environment. Citation: Lindeberg T (2013) Invariance of visual operations at the level of receptive fields. PLoS ONE 8(7): e66990. doi:10.1371/journal.pone.0066990 Editor: Luis M Martinez, CSIC-Univ Miguel Hernandez, Spain Received October 16, 2012; Accepted May 14, 2013; Published July 19, 2013 Copyright: 2013 Tony Lindeberg. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: Funding was received from The Swedish Research Council contract 2010–4766; The Royal Swedish Academy of Sciences; and The Knut and Alice Wallenberg foundation. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The author has declared that no competing interests exist. * E-mail: tony@csc.kth.se