controls how far from the winning neuron the input signal can reach. In order to find the global optimum of the objective function, the decrease of the size of the radius of the circular region around the position of the winning neuron should be done gradually. We have found out experimentally that a choice of in the range 150 to 250 and in the range 0.99 to 1.0 gives satisfactory results. Regarding the value of the parameter , experiments have shown that it should be near unity and in particular in the range 0.995 to 1.0. It should be emphasized that the algorithm is not critically influenced by the specific chosen values of the aforementioned parameters. The condition given by (11) is necessary to protect the SOM network from generating a signal that is much more different than the weighting vectors of the neurons in the current iteration. The condition is not too strict in the sense that it is not prohibitive of the production of a winner with a measure of match lower than that in the previous iteration. Consequently, it is achieved the escape from local optima of the objective function, since solutions that do not lead to better values of the objective function are accepted too. This approach is similar to the Metropolis process that takes place in simulated annealing [12]. Another aspect of the proposed registration scheme that should be addressed is the utilization of the gradient difference as a measure of match. The selected measure of match provided accurate results for almost all image pairs that were used in the current study. However, it should be stressed that the gradient difference may fail for images characterized by apparent hyperfluorescence. Hyperfluorescence is caused usually by a breakdown or lack of tight vascular junctions in abnormal blood vessels. Any leakage of fluorescein from a retinal vessel or within the retinal tissues indicates an abnormality. For example, capillary microaneurysms, retinal telangiectasias, arterial macroanuerysm, papilledema, and some vascularized tumors exhibit leakage. Finally, it should be noted that the focus of the paper was to show the feasibility of the SOM theory for registering multimodal retinal images. The proposed implementation of the SOM model could be considered as a method for finding the optimum value of an objective function. Under this framework, the proposed registration scheme provides several “degrees of freedom” regarding its parameters. For example, another measure of match (such as the mutual information) could be used, the bifurcation points could be extracted by means of other methods, another transformation (such as bilinear or elastic) could be adopted after the training of the SOM network. VI. CONCLUSION In this paper, a new registration algorithm for registering multimodal retinal images was presented. Two basic novel implementations were introduced. First, the application of the vessel centerline detection and bifurcations extraction process only on the reference image. This step simplifies the registration methodology since candidate points are identified only on the reference image. Second, the novel implementation of the SOM network to define automatic correspondence of the bifurcation points between the reference and the image to be transformed. The proposed algorithm was tested for 24 pairs of multimodal images providing an accuracy of approximately 40 for all retinal pairs.
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