Geometric Moment Invariants to Motion Blur

TL;DR

This paper introduces geometric moment invariants that are robust to motion blur, enabling improved image retrieval and classification without restoring blurred images, by leveraging linear relationships between blurred and original image moments.

Contribution

It derives motion blur invariants based on geometric moments, revealing some invariants are unaffected by motion blur, unlike previous methods that focused on image restoration.

Findings

Invariants outperform existing blur moment invariants in retrieval tasks

Some geometric moment invariants are invariant to both spatial transformations and motion blur

Experimental results confirm robustness on synthetic and real datasets

Abstract

In this paper, we focus on removing interference of motion blur by the derivation of motion blur invariants.Unlike earlier work, we don't restore any blurred image. Based on geometric moment and mathematical model of motion blur, we prove that geometric moments of blurred image and original image are linearly related. Depending on this property, we can analyse whether an existing moment-based feature is invariant to motion blur. Surprisingly, we find some geometric moment invariants are invariants to not only spatial transform but also motion blur. Meanwhile, we test invariance and robustness of these invariants using synthetic and real blur image datasets. And the results show these invariants outperform some widely used blur moment invariants and non-moment image features in image retrieval, classification and template matching.