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Provably scale-covariant continuous hierarchical networks based on scale-normalized differential expressions coupled in cascade
KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST). (Computational Brain Science Lab)ORCID iD: 0000-0002-9081-2170
2019 (English)In: Journal of Mathematical Imaging and Vision, ISSN 0924-9907, E-ISSN 1573-7683Article in journal (Refereed) In press
Abstract [en]

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.

Place, publisher, year, edition, pages
Springer, 2019.
Keywords [en]
Handcrafted, Network, Hierarchical, Scale covariance, Differential expression, Quasi quadrature, Complex cell, Feature detection, Texture analysis, Scale space, Deep learning, Computer vision
National Category
Computer Vision and Robotics (Autonomous Systems) Bioinformatics (Computational Biology)
Research subject
Computer Science
Identifiers
URN: urn:nbn:se:kth:diva-252632DOI: 10.1007/s10851-019-00915-xOAI: oai:DiVA.org:kth-252632DiVA, id: diva2:1319579
Projects
Scale-space theory for covariant and invariant visual perception
Funder
Swedish Research Council, 2018-03586
Note

QC 20190611

Available from: 2019-06-03 Created: 2019-06-03 Last updated: 2019-10-28Bibliographically approved

Open Access in DiVA

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Publisher's full textPreprint at arXiv:1905.13555

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