Embedding Naka-Rushton's equation in the geometric setting of Möbius transformations

The Naka-Rushton equation that models the transduction from electromagnetic energy carried by a photon to difference of potential of the membrane of a retinal photoreceptor has been used for two decades in tone mapping algorithms to compress the range of high dynamic range (HDR) images. Up to now, only its analytical properties of linear fractional transformation have been considered and exploited. In this paper, we recast the Naka-Rushton equation in the abstract setting of Möbius transformations, pointing out the hidden geometric properties of Naka-Rushton formula and discussing their pertinence to what a tone mapping algorithm is expected to comply.