Retinal image registration is commonly required in order to combine the complementary information in different retinal modalities. In this paper, a new automatic scheme to register retinal images is presented and is currently tested in a clinical environment. The scheme considers the suitability and efficiency of different image transformation models and function optimization techniques, following an initial preprocessing stage. Three different transformation models-affine, bilinear and projective-as well as three optimization techniques-downhill simplex method, simulated annealing and genetic algorithms-are investigated and compared in terms of accuracy and efficiency. The registration of 26 pairs of fluoroscein angiography and indocyanine green chorioangiography images with the corresponding red-free retinal images, showed the superiority of combining genetic algorithms with the affine and bilinear transformation models. A comparative study of the proposed automatic registration scheme against the manual method, commonly used in clinical practice, is finally presented showing the advantage of the proposed automatic scheme in terms of accuracy and consistency.

In this work we study in detail the connection between the solutions to the Dirac and Weyl equations and the associated electromagnetic four-potentials. First, it is proven that all solutions to the Weyl equation are degenerate, in the sense that they correspond to an infinite number of electromagnetic four-potentials. As far as the solutions to the Dirac equation are concerned, it is shown that they can be classified into two classes. The elements of the first class correspond to one and only one four-potential, and are called non-degenerate Dirac solutions. On the other hand, the elements of the second class correspond to an infinite number of four-potentials, and are called degenerate Dirac solutions. Further, it is proven that at least two of these four-potentials are gauge-inequivalent, corresponding to different electromagnetic fields. In order to illustrate this particularly important result we have studied the degenerate solutions to the force-free Dirac equation and shown that they correspond to massless particles. We have also provided explicit examples regarding solutions to the force-free Weyl equation and the Weyl equation for a constant magnetic field. In all cases we have calculated the infinite number of different electromagnetic fields corresponding to these solutions. Finally, we have discussed potential applications of our results in cosmology, materials science and nanoelectronics.