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

Highlights：

• Suppose the PSF has N-fold rotational symmetry, we prove its geometric moments of the same order are linearly dependent.

• A new method is proposed to determine whether an existing similarity or affine moment invariant also has invariance to N-fold symmetric blur.

• We analyse classical moment invariants, and find that five of Hu moment invariants are naturally invariant to N-fold symmetric blur.

• We first prove the existence of moment invariants to both affine transform and N-fold symmetric blur.

• The experiments on synthetic and real images are conducted. We find Hu moment invariants outperform most of widely used blur moment invariants.

摘要

•Suppose the PSF has N-fold rotational symmetry, we prove its geometric moments of the same order are linearly dependent.•A new method is proposed to determine whether an existing similarity or affine moment invariant also has invariance to N-fold symmetric blur.•We analyse classical moment invariants, and find that five of Hu moment invariants are naturally invariant to N-fold symmetric blur.•We first prove the existence of moment invariants to both affine transform and N-fold symmetric blur.•The experiments on synthetic and real images are conducted. We find Hu moment invariants outperform most of widely used blur moment invariants.

论文评审过程：Received 16 June 2020, Revised 25 January 2021, Accepted 9 February 2021, Available online 13 February 2021, Version of Record 18 February 2021.