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

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