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.

中文翻译：

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运动模糊的几何矩不变量

在本文中，我们专注于通过推导运动模糊不变量来消除运动模糊的干扰。与早期的工作不同，我们不会恢复任何模糊的图像。基于几何矩和运动模糊数学模型，证明模糊图像和原始图像的几何矩线性相关。根据此属性，我们可以分析现有的基于矩的特征是否对运动模糊不变。令人惊讶地，我们发现一些几何矩不变量不仅对空间变换而且对运动模糊都是不变量。同时，我们使用合成和真实模糊图像数据集测试这些不变性的不变性和鲁棒性。结果表明，在图像检索，分类和模板匹配中，这些不变量优于某些广泛使用的模糊矩不变性和非矩图像特征。