Abstract Blur is an image degradation that makes object recognition challenging. Restoration approaches solve this problem via image deblurring, deep learning methods rely on the augmentation of training sets. Invariants with respect to blur offer an alternative way of describing and recognising blurred images without any deblurring and data augmentation. In this paper, we present an original theory of blur invariants. Unlike all previous attempts, the new theory requires no prior knowledge of the blur type. The invariants are constructed in the Fourier domain by means of orthogonal projection operators and moment expansion is used for efficient and stable computation. Applying a general substitution rule, combined invariants to blur and spatial transformations are easy to construct and use. Experimental comparison to Convolutional Neural Networks shows the advantages of the proposed theory.

This article is a comment on the recent TPAMI paper (Gopalan et al., 2012) that introduced a blur-invariant distance measure between two images. We point out two mistakes of the theory presented in (Gopalan et al., 2012) and propose a correction. We also compare the original and corrected methods experimentally.