Provably scale-covariant continuous hierarchical networks based on scale-normalized differential expressions coupled in cascade
This work addresses the challenge of scale covariance in hierarchical networks for computer vision, particularly in texture analysis, but it appears incremental as it builds on existing scale-space and receptive field models.
The paper tackles the problem of constructing hierarchical networks that are provably scale covariant, using scale-normalized differential expressions, and demonstrates promising results on texture analysis datasets with a simplified representation.
This article presents a theory for constructing hierarchical networks in such a way that the networks are guaranteed to be provably scale covariant. We first present a general sufficiency argument for obtaining scale covariance, which holds for a wide class of networks defined from linear and non-linear differential expressions expressed in terms of scale-normalized scale-space derivatives. Then, we present a more detailed development of one example of such a network constructed from 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 we give explicit proofs of how the resulting representation allows for 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.