Representing Blurred Image without Deblurring

The effective recognition of patterns from blurred images presents a fundamental difficulty for many practical vision tasks. In the era of deep learning, the main ideas to cope with this difficulty are data augmentation and deblurring. However, both facing issues such as inefficiency, instability, and lack of explainability. In this paper, we explore a simple but effective way to define invariants from blurred images, without data augmentation and deblurring. Here, the invariants are designed from Fractional Moments under Projection operators (FMP), where the blur invariance and rotation invariance are guaranteed by the general theorem of blur invariants and the Fourier-domain rotation equivariance, respectively. In general, the proposed FMP not only bears a simpler explicit definition, but also has useful representation properties including orthogonality, statistical flexibility, as well as the combined invariance of blurring and rotation. Simulation experiments are provided to demonstrate such properties of our FMP, revealing the potential for small-scale robust vision problems.