Extension of Moment Features' Invariance to Blur

Authors:
Jiří Boldyš;Jan Flusser
Affiliations:
Institute of Information Theory and Automation of the ASCR, Prague 8, Czech Republic 18208;Institute of Information Theory and Automation of the ASCR, Prague 8, Czech Republic 18208
Venue:
Journal of Mathematical Imaging and Vision
Year:
2008

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Abstract

Moment invariants are features calculated on an image, which do not change their values after a transformation of the image. This paper focuses on the so called combined invariants, which obey additional requirement of invariance to image blurring. Our first contribution is a review of achievements most relevant to the derivation of algebraic, moment and combined invariants. The review explains and develops parallels between the moment and the blur invariants. Gradually, it reveals new properties, simplifying construction of the combined invariants, but having more general extent. Resulting substitution rules for easy construction of the combined invariants from other invariants are thus the main results of this paper. All the conclusions can be understood without knowledge of the tensor calculus. This paper addresses construction of the combined invariants in arbitrary dimension.