Image Moment Invariants to Rotational Motion Blur

Rotational motion blur caused by the circular motion of the camera or/and object is common in life. Identifying objects from images affected by rotational motion blur is challenging because this image degradation severely impacts image quality. Therefore, it is meaningful to develop image invariant features under rotational motion blur and then use them in practical tasks, such as object classification and template matching. This paper proposes a novel method to generate image moment invariants under general rotational motion blur and provides some instances. Further, we achieve their invariance to similarity transform. To the best of our knowledge, this is the first time that moment invariants for rotational motion blur have been proposed in the literature. We conduct extensive experiments on various image datasets disturbed by similarity transform and rotational motion blur to test these invariants' numerical stability and robustness to image noise. We also demonstrate their performance in image classification and handwritten digit recognition. Current state-of-the-art blur moment invariants and deep neural networks are chosen for comparison. Our results show that the moment invariants proposed in this paper significantly outperform other features in various tasks.