# Separable time-causal and time-recursive spatio-temporal receptive fields

arXiv: https://arxiv.org/abs/1504.01502 · HTML: https://mlsanity.com/paper/1504.01502/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Apr 2015.

## Built on by (most cited first, 1 of 1)

- [A deep convolutional neural network that is invariant to time rescaling](https://mlsanity.com/paper/2107.04616/) (2021)

## Abstract (arXiv)

We present an improved model and theory for time-causal and time-recursive spatio-temporal receptive fields, obtained by a combination of Gaussian receptive fields over the spatial domain and first-order integrators or equivalently truncated exponential filters coupled in cascade over the temporal domain. Compared to previous spatio-temporal scale-space formulations in terms of non-enhancement of local extrema or scale invariance, these receptive fields are based on different scale-space axiomatics over time by ensuring non-creation of new local extrema or zero-crossings with increasing temporal scale. Specifically, extensions are presented about parameterizing the intermediate temporal scale levels, analysing the resulting temporal dynamics and transferring the theory to a discrete implementation in terms of recursive filters over time.