# Normative theory of visual receptive fields

arXiv: https://arxiv.org/abs/1701.06333 · HTML: https://mlsanity.com/paper/1701.06333/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2017.

## Built on by (most cited first, 15 of 15)

- [Scale-invariant scale-channel networks: Deep networks that generalise to previously unseen scales](https://mlsanity.com/paper/2106.06418/) (2021)
- [Covariance properties under natural image transformations for the generalized Gaussian derivative model for visual receptive fields](https://mlsanity.com/paper/2303.09803/) (2023)
- [Discrete approximations of Gaussian smoothing and Gaussian derivatives](https://mlsanity.com/paper/2311.11317/) (2023)
- [Unveiling the Unseen: Identifiable Clusters in Trained Depthwise Convolutional Kernels](https://mlsanity.com/paper/2401.14469/) (2024)
- [Unified theory for joint covariance properties under geometric image transformations for spatio-temporal receptive fields according to the generalized Gaussian derivative model for visual receptive fields](https://mlsanity.com/paper/2311.10543/) (2023)
- [Approximation properties relative to continuous scale space for hybrid discretizations of Gaussian derivative operators](https://mlsanity.com/paper/2405.05095/) (2024)
- [Covariant spatio-temporal receptive fields for spiking neural networks](https://mlsanity.com/paper/2405.00318/) (2024)
- [Scale generalisation properties of extended scale-covariant and scale-invariant Gaussian derivative networks on image datasets with spatial scaling variations](https://mlsanity.com/paper/2409.11140/) (2024)
- [Relationships between the degrees of freedom in the affine Gaussian derivative model for visual receptive fields and 2-D affine image transformations, with application to covariance properties of simple cells in the primary visual cortex](https://mlsanity.com/paper/2411.05673/) (2024)
- [Enhancing CNNs robustness to occlusions with bioinspired filters for border completion](https://mlsanity.com/paper/2504.17619/) (2025)
- [The Quest for Universal Master Key Filters in DS-CNNs](https://mlsanity.com/paper/2509.11711/) (2025)
- [Reconstructing group wavelet transform from feature maps with a reproducing kernel iteration](https://mlsanity.com/paper/2110.00600/) (2021)
- [Modelling and analysis of the 8 filters from the "master key filters hypothesis" for depthwise-separable deep networks in relation to idealized receptive fields based on scale-space theory](https://mlsanity.com/paper/2509.12746/) (2025)
- [Hybrid Lie semi-group and cascade structures for the generalized Gaussian derivative model for visual receptive fields](https://mlsanity.com/paper/2509.15748/) (2025)
- [Scale-invariant Gaussian derivative residual networks](https://mlsanity.com/paper/2603.02843/) (2026)

## Abstract (arXiv)

This article gives an overview of a normative computational theory of visual receptive fields, by which idealized functional models of early spatial, spatio-chromatic and spatio-temporal receptive fields can be derived in an axiomatic way based on structural properties of the environment in combination with assumptions about the internal structure of a vision system to guarantee consistent handling of image representations over multiple spatial and temporal scales. Interestingly, this theory leads to predictions about visual receptive field shapes with qualitatively very good similarity to biological receptive fields measured in the retina, the LGN and the primary visual cortex (V1) of mammals.