Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2019
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/1905.13555 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- 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.