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

TL;DR

This paper introduces an improved model for spatio-temporal receptive fields that combines Gaussian spatial filters with cascade-coupled temporal filters, ensuring non-creation of local extrema and enabling efficient discrete implementation.

Contribution

It presents a novel theoretical framework for time-causal and recursive receptive fields with new parameterization, analysis of temporal dynamics, and a discrete recursive filter implementation.

Findings

Receptive fields based on Gaussian and exponential filters maintain scale-space properties.

The model ensures non-creation of new local extrema over increasing temporal scales.

A practical recursive filter implementation is developed for real-time applications.

Abstract

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.