University of Oulu

Kostková J., Flusser J., Lébl M., Pedone M. (2019) Image Invariants to Anisotropic Gaussian Blur. In: Felsberg M., Forssén PE., Sintorn IM., Unger J. (eds) Image Analysis. SCIA 2019. Lecture Notes in Computer Science, vol 11482. Springer, Cham

Image invariants to anisotropic Gaussian blur

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Author: Kostková, Jitka1; Flusser, Jan1; Lébl, Matěj1;
Organizations: 1The Czech Academy of Sciences, Institute of Information Theory and Automation, Prague 8, Czech Republic
2The Center for Machine Vision Research, Department of Computer Science and Engineering, University of Oulu, Oulu, Finland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 2.9 MB)
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Language: English
Published: Springer Nature, 2019
Publish Date: 2020-05-12


The paper presents a new theory of invariants to Gaussian blur. Unlike earlier methods, the blur kernel may be arbitrary oriented, scaled and elongated. Such blurring is a semi-group action in the image space, where the orbits are classes of blur-equivalent images. We propose a non-linear projection operator which extracts blur-insensitive component of the image. The invariants are then formally defined as moments of this component but can be computed directly from the blurred image without an explicit construction of the projections. Image description by the new invariants does not require any prior knowledge of the particular blur kernel shape and does not include any deconvolution. Potential applications are in blur-invariant image recognition and in robust template matching.

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Series: Lecture notes in computer science
ISSN: 0302-9743
ISSN-E: 1611-3349
ISSN-L: 0302-9743
ISBN: 978-3-030-20205-7
ISBN Print: 978-3-030-20204-0
Pages: 140 - 151
DOI: 10.1007/978-3-030-20205-7_12
Host publication: 21st Scandinavian Conference, SCIA 2019, Norrköping, Sweden, June 11–13, 2019, Proceedings
Host publication editor: Felsberg, Michael
Forssén, Per-Erik
Sintorn, Ida-Maria
Unger, Jonas
Conference: Scandinavian Conference on Image Analysis
Type of Publication: A4 Article in conference proceedings
Field of Science: 113 Computer and information sciences
Copyright information: © Springer Nature Switzerland AG 2019. This is a post-peer-review, pre-copyedit version of an article published in Scandinavian Conference on Image Analysis. The final authenticated version is available online at: