Covariance properties under natural image transformations for the generalised Gaussian derivative model for visual receptive fields
| Autor: | Lindeberg, Tony |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: |
vision
Bioinformatics (Computational Biology) Image and Video Processing (eess.IV) Neurosciences Neuroscience (miscellaneous) receptive field Galilean covariance Electrical Engineering and Systems Science - Image and Video Processing Cellular and Molecular Neuroscience Datorseende och robotik (autonoma system) FOS: Biological sciences Quantitative Biology - Neurons and Cognition image transformations affine covariance FOS: Electrical engineering electronic engineering information engineering scale covariance Bioinformatik (beräkningsbiologi) theoretical neuroscience Neurons and Cognition (q-bio.NC) primary visual cortex Neurovetenskaper Computer Vision and Robotics (Autonomous Systems) |
| Zdroj: | Frontiers in Computational Neuroscience. 17 |
| ISSN: | 1662-5188 |
| DOI: | 10.3389/fncom.2023.1189949 |
| Popis: | This paper presents a theory for how geometric image transformations can be handled by a first layer of linear receptive fields, in terms of true covariance properties, which, in turn, enable geometric invariance properties at higher levels in the visual hierarchy. Specifically, we develop this theory for a generalized Gaussian derivative model for visual receptive fields, which is derived in an axiomatic manner from first principles, that reflect symmetry properties of the environment, complemented by structural assumptions to guarantee internally consistent treatment of image structures over multiple spatio-temporal scales. It is shown how the studied generalized Gaussian derivative model for visual receptive fields obeys true covariance properties under spatial scaling transformations, spatial affine transformations, Galilean transformations and temporal scaling transformations, implying that a vision system, based on image and video measurements in terms of the receptive fields according to this model, can to first order of approximation handle the image and video deformations between multiple views of objects delimited by smooth surfaces, as well as between multiple views of spatio-temporal events, under varying relative motions between the objects and events in the world and the observer. We conclude by describing implications of the presented theory for biological vision, regarding connections between the variabilities of the shapes of biological visual receptive fields and the variabilities of spatial and spatio-temporal image structures under natural image transformations. 38 pages, 14 figures |
| Databáze: | OpenAIRE |
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