Handling Gaussian blur without deconvolution

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.

Authors:

Publication type:
A1 Journal article – refereed

Place of publication:

Keywords:
Affine transformation, Blur invariants, Combined invariants, Gaussian blur, Image moments, Projection operator, Semi-group

Published:

Full citation:
Jitka Kostková, Jan Flusser, Matěj Lébl, Matteo Pedone, Handling Gaussian blur without deconvolution, Pattern Recognition, Volume 103, 2020, 107264, ISSN 0031-3203, https://doi.org/10.1016/j.patcog.2020.107264

DOI:
https://doi.org/10.1016/j.patcog.2020.107264

Read the publication here:
http://urn.fi/urn:nbn:fi-fe2020051333278