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Equi-affine differential invariants for invariant feature point detection

Part of: Classical differential geometry

Published online by Cambridge University Press:  06 March 2019

STANLEY L. TUZNIK ,
PETER J. OLVER Open the ORCID record for PETER J. OLVER [Opens in a new window]  and
ALLEN TANNENBAUM
STANLEY L. TUZNIK
Affiliation:
Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794, USA e-mail: stanley.tuznik@stonybrook.edu
PETER J. OLVER*
Affiliation:
Department of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA e-mail: olver@umn.edu
ALLEN TANNENBAUM
Affiliation:
Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794, USA e-mail: stanley.tuznik@stonybrook.edu Department of Computer Science, Stony Brook University, Stony Brook, NY 11794, USA e-mail: arobertan@gmail.com
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Abstract

Image feature points are detected as pixels which locally maximise a detector function, two commonly used examples of which are the (Euclidean) image gradient and the Harris–Stephens corner detector. A major limitation of these feature detectors is that they are only Euclidean-invariant. In this work, we demonstrate the application of a 2D equi-affine-invariant image feature point detector based on differential invariants as derived through the equivariant method of moving frames. The fundamental equi-affine differential invariants for 3D image volumes are also computed.

Keywords

Differential invariantfeature detectionequi-affine groupmoving fram

MSC classification

Primary: 53A15: Affine differential geometry
Secondary: 53A55: Differential invariants (local theory), geometric objects 68U10: Image processing
Type
Papers
Information
European Journal of Applied Mathematics , Volume 31 , Issue 2 , April 2020 , pp. 277 - 296
Copyright
© Cambridge University Press 2019 

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Footnotes

This work was supported by AFOSR [grant number FA9550-17-1-0435] and the National Institutes of Health [grant number R01-AG048769].

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