Geometric moment invariants to spatial transform and N-fold symmetric blur

Abstract

In this paper, we focus on the derivation of blur moment invariants. Blur moment invariants are image moment-based features, which preserve their values when the image is convolved by a point-spread function (PSF). Suppose a PSF has N-fold rotational symmetry, we prove its geometric moments of the same order are linearly dependent. Depending on this property, a new approach is proposed to determine whether an existing similarity or affine moment invariant also has invariance to N-fold symmetric blur. Unlike earlier work, this method is not based on complicated operators and construction formulas. We use it to analyse classical moment-based features, and surprisingly find that five of Hu moment invariants are naturally invariant to N-fold symmetric blur. Meanwhile, we first prove the existence of moment invariants to both affine transform and N-fold symmetric blur. The experiments using synthetic and real blur image datasets are carried out to test these expectations. And the results show that five Hu moment invariants outperform some widely used blur moment invariants and non-moment image features in image retrieval, classification and template matching.