In this paper, we propose a new theory of invariants to Gaussian blur. We introduce a notion of a primordial image as a canonical form of all Gaussian blur-equivalent images. The primordial image is defined in spectral domain by means of projection operators. We prove that the moments of the primordial image are invariant to Gaussian blur and we derive recursive formulas for their direct computation without actually constructing the primordial image itself. We show how to extend their invariance also to image rotation. The application of these invariants is in blur-invariant image comparison and recognition. In the experimental part, we perform an exhaustive comparison with two main competitors: 1) the Zhang distance and 2) the local phase quantization.

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The paper presents a new theory of invariants to Gaussian blur. Unlike earlier methods, the blur kernel may be arbitrary oriented, scaled and elongated. Such blurring is a semi-group action in the image space, where the orbits are classes of blur-equivalent images. We propose a non-linear projection operator which extracts blur-insensitive component of the image. The invariants are then formally defined as moments of this component but can be computed directly from the blurred image without an explicit construction of the projections. Image description by the new invariants does not require any prior knowledge of the particular blur kernel shape and does not include any deconvolution. Potential applications are in blur-invariant image recognition and in robust template matching.

In this paper, we propose a new registration method designed particularly for registering differently blurred images. Such a task cannot be successfully resolved by traditional approaches. Our method is inspired by traditional phase correlation, which is now applied to certain blur-invariant descriptors instead of the original images. This method works for unknown blurs assuming the blurring PSF exhibits an N-fold rotational symmetry. It does not require any landmarks. We have experimentally proven its good performance, which is not dependent on the amount of blur. In this paper, we explicitly address only registration with respect to translation, but the method can be readily generalized to rotation and scaling.

Because of their permanent charge, strong polyelectrolytes remain challenging to characterize, in particular, when they are combined with hydrophobic features. For this reason, they are typically prepared through a postmodification of a fully hydrophobic precursor. Unfortunately, these routes often result in an incomplete functionalization or otherwise require harsh reaction conditions, thus limiting their applicability. To overcome these problems, in this work a strategy is presented that facilitates the preparation of well-defined strong polyanions by starting from protected 3-sulfopropyl methacrylate monomers. Depending on the chemistry of the protecting group, the hydrophobic precursor could be quantitatively converted into a strong polyanion under nucleophilic, acidic, or basic conditions. As a proof of concept, orthogonally protected diblock copolymers were synthesized, selectively deprotected, and allowed to self-assemble in aqueous solution. Further conversion into a fully water-soluble polyanion was achieved by deprotecting the second block as well.