University of Oulu

Jitka Kostková, Jan Flusser, Matěj Lébl, Matteo Pedone, Handling Gaussian blur without deconvolution, Pattern Recognition, Volume 103, 2020, 107264, ISSN 0031-3203,

Handling Gaussian blur without deconvolution

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Author: Kostková, Jitka1; Flusser, Jan1; Lébl, Matěj1;
Organizations: 1Czech Academy of Sciences, Institute of Information Theory and Automation, Pod vodárenskou věží 4, 182 08 Prague 8, Czech Republic
2Center for Machine Vision Research, Department of Computer Science and Engineering, University of Oulu, Oulu FI-90014, Finland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 7.3 MB)
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Language: English
Published: Elsevier, 2020
Publish Date: 2022-02-15


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 blur kernel parameters and does not include any deconvolution. The invariance property could be extended also to linear transformation of the image coordinates and combined affine-blur invariants can be constructed. Experimental comparison to three other blur-invariant methods is given. Potential applications of the new invariants are in blur/position invariant image recognition and in robust template matching.

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Series: Pattern recognition
ISSN: 0031-3203
ISSN-E: 1873-5142
ISSN-L: 0031-3203
Volume: 103
Article number: 107264
DOI: 10.1016/j.patcog.2020.107264
Type of Publication: A1 Journal article – refereed
Field of Science: 113 Computer and information sciences
Funding: This work has been supported by the Czech Science Foundation under the grant no. GA18-07247S, by the grant SGS18/188/OHK4/3T/14 provided by the Ministry of Education, Youth, and Sports of the Czech Republic (MŠMT ČR), and by the Praemium Academiae.
Copyright information: © 2020 Elsevier Ltd. All rights reserved. This manuscript version is made available under the CC-BY-NC-ND 4.0 license