Invariance of visual operations at the level of receptive fields

TL;DR

This paper develops a theoretical model explaining how receptive fields in mammalian vision achieve invariance to scale, orientation, and motion, aligning biological receptive field profiles with environmental invariances.

Contribution

It introduces a mathematical derivation of receptive field profiles from environmental assumptions and explains how invariance properties emerge at the receptive field level.

Findings

Receptive fields can be derived from environmental structural assumptions.

Invariance to scale, orientation, and motion can be achieved through output selection mechanisms.

The shapes of biological receptive fields reflect environmental invariance requirements.

Abstract

Receptive field profiles registered by cell recordings have shown that mammalian vision has developed receptive fields tuned to different sizes and orientations in the image domain as well as to different image velocities in space-time. This article presents a theoretical model by which families of idealized receptive field profiles can be derived mathematically from a small set of basic assumptions that correspond to structural properties of the environment. The article also presents a theory for how basic invariance properties to variations in scale, viewing direction and relative motion can be obtained from the output of such receptive fields, using complementary selection mechanisms that operate over the output of families of receptive fields tuned to different parameters. Thereby, the theory shows how basic invariance properties of a visual system can be obtained already at the level of receptive fields, and we can explain the different shapes of receptive field profiles found in biological vision from a requirement that the visual system should be invariant to the natural types of image transformations that occur in its environment.