Modeling of the rhodopsin bleaching with variational analysis of retinal images

This paper discusses a variational method of processing the scanning laser ophthalmoscope(cSLO) image sequences in the context of extracting the local rhodopsin density and modeling the bleaching kinetics. This work supports the characterization and detection of early pathological changes in clinical retinal data. Our goals include providing automated tools for tracing early pathological changes over time, in particular rhodopsin density variations and local lesion progression. Aside from helping to distinguish between healthy and possibly pathological regions, information about the bleaching parameters allows to separate and classify certain elements in the retinal image and may be utilized to refine the output of the edge-detection based method of the microvessel detection. Our computational approach is a variational technique that approximates measured cSLO image sets optimally within the range of the bleaching model. The characterizing parameters of the approximating curves are computed locally and their spatial changes reflect variations in bleaching kinetics and hence changes in the local rhodopsin density. We prove the consistency of the numerical results by showing that minimization of three different energy functionals measuring the deviation of the approximating curve from the original, leads to almost identical results despite the differences in the variational settings. We also show that the technique is naturally robust to noise. The curve fitting in the temporal direction of the image stack can be also viewed as a denoising/enhancement routine. The advantages of the temporal correction include a better fit of the image intensity function to the model and the avoidance of local averaging that would impair the spatial resolution.