Blur Invariants and Projection Operators

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


Blurred image, object recognition, N-fold rotation symmetry, projection operator, blur invariants


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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