Blur Invariants and Projection Operators

Jan Flusser, Tomáš Suk, Jiří Boldyš, and Barbara Zitová

Keywords

Blurred image, object recognition, Nfold rotation symmetry, projection operator, blur invariants

Abstract

In this paper, we introduce a new theory of blur invariants. Blur invariants are image features which preserve their values if the image is convolved with a point-spread function (PSF) of a certain class. We present the invariants to convolution with an arbitrary N-fold symmetric PSF, defined in Fourier domain by means of projection operators. We introduce a notion of a primordial image as a canonical form of all blur-equivalent images. We illustrate by experiments the invariance and recognition power of the new features. Potential applications of this method are wherever one wants to recognize blurred images.

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