# Provably scale-covariant networks from oriented quasi quadrature measures in cascade

## TL;DR

This paper introduces a mathematically grounded hierarchical network model based on oriented quasi quadrature measures, achieving provable scale and rotation covariance, with promising results in texture analysis.

## Contribution

It presents a new continuous model of hierarchical networks using oriented quasi quadrature measures that are provably scale and rotation covariant.

## Key findings

- The model demonstrates scale and rotation covariance properties.
- A prototype application to texture analysis shows promising results.
- The simplified representation performs well on multiple datasets.

## Abstract

This article presents a continuous model for hierarchical networks based on a combination of mathematically derived models of receptive fields and biologically inspired computations. Based on a functional model of complex cells in terms of an oriented quasi quadrature combination of first- and second-order directional Gaussian derivatives, we couple such primitive computations in cascade over combinatorial expansions over image orientations. Scale-space properties of the computational primitives are analysed and it is shown that the resulting representation allows for provable scale and rotation covariance. A prototype application to texture analysis is developed and it is demonstrated that a simplified mean-reduced representation of the resulting QuasiQuadNet leads to promising experimental results on three texture datasets.