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Auteur principal: Lindeberg, Tony
Format: Preprint
Publié: 2019
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Accès en ligne:https://arxiv.org/abs/1905.13555
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author Lindeberg, Tony
author_facet Lindeberg, Tony
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.
format Preprint
id arxiv_https___arxiv_org_abs_1905_13555
institution arXiv
publishDate 2019
record_format arxiv
spellingShingle Provably scale-covariant continuous hierarchical networks based on scale-normalized differential expressions coupled in cascade
Lindeberg, Tony
Computer Vision and Pattern Recognition
Machine Learning
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.
title Provably scale-covariant continuous hierarchical networks based on scale-normalized differential expressions coupled in cascade
topic Computer Vision and Pattern Recognition
Machine Learning
url https://arxiv.org/abs/1905.13555