Júlio S. Neves

Optimality of embeddings of Bessel-potential-type spaces into generalized Hölder spaces

We establish the sharpness of embedding theorems for Bessel-potential spaces modelled upon Lorentz-Karamata spaces and we prove the non-compactness of such embeddings. Target spaces in our embeddings are generalized Holder spaces. As consequences of our results, we get continuous envelopes of Bessel-potential spaces modelled upon Lorentz-Karamata spaces

Pattern Classes in Retinal Fundus Images Based on Function Norms

Retinal fundus images are widely used for screening, diagnosis and prognosis purposes in ophthalmology. Additionally these can also be used in retinal identification/recognition systems, for identification/authentication of an identity. In this paper the aim is to explain how norms in function spaces can be used to set up, automatically, classes of different retinal fundus images. These classifications rely on crucial and unique retinal features, such as the vascular network, whose location and measurement are appropriately quantified by weighted norms in function spaces. These quantifications can be understood as retinal pattern assessments and used for improving the efficiency and speed of retinal identification/recognition frameworks. The proposed methods are evaluated in a large dataset of retinal fundus images, and, besides being very fast, they achieve a reduction of the search in the dataset (for identification/recognition purposes), by 70% on average.

Automated retina identification based on multiscale elastic registration

In this work we propose a novel method for identifying individuals based on retinal fundus image matching. The method is based on the image registration of retina blood vessels, since it is known that the retina vasculature of an individual is a signature, i.e., a distinctive pattern of the individual. The proposed image registration consists of a multiscale affine registration followed by a multiscale elastic registration. The major advantage of this particular two-step image registration procedure is that it is able to account for both rigid and non-rigid deformations either inherent to the retina tissues or as a result of the imaging process itself. Afterwards a decision identification measure, relying on a suitable normalized function, is defined to decide whether or not the pair of images belongs to the same individual. The method is tested on a data set of 21721 real pairs generated from a total of 946 retinal fundus images of 339 different individuals, consisting of patients followed in the context of different retinal diseases and also healthy patients. The evaluation of its performance reveals that it achieves a very low false rejection rate (FRR) at zero FAR (the false acceptance rate), equal to 0.084, as well as a low equal error rate (EER), equal to 0.053. Moreover, the tests performed by using only the multiscale affine registration, and discarding the multiscale elastic registration, clearly show the advantage of the proposed approach. The outcome of this study also indicates that the proposed method is reliable and competitive with other existing retinal identification methods, and forecasts its future appropriateness and applicability in real-life applications.

Growth Envelopes of Anisotropic Function Spaces

The present paper is devoted to the study of growth envelopes of anisotropic function spaces. An affirmative answer is given t the question of (19, Conjecture 13), whether the growth envelopes are independent of anisotropy. As an application, related anisotropic Hardy inequalities are presented and we also discuss a connection to some anisotropic fractal sets.